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Achieving binary topology optimization solutions via automatic projection parameter increase (2404.14111v1)

Published 22 Apr 2024 in math.OC and cs.CE

Abstract: A method is created to automatically increase the threshold projection parameter in three-field density-based topology optimization to achieve a near binary design. The parameter increase each iteration is based on an exponential growth function, where the growth rate is dynamically changed during optimization by linking it to the change in objective function. This results in a method that does not need to be tuned for specific problems, or optimizers, and the same set of hyper-parameters can be used for a wide range of problems. The effectiveness of the method is demonstrated on several 2D benchmark problems, including linear buckling and geometrically nonlinear problems.

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References (20)
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[2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Rozvany, G.I., Zhou, M., Birker, T.: Generalized shape optimization without homogenization. Structural optimization 4, 250–252 (1992) Sigmund and Petersson [1998] Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16, 68–75 (1998) Bruns and Tortorelli [2001] Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16, 68–75 (1998) Bruns and Tortorelli [2001] Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  2. Rozvany, G.I., Zhou, M., Birker, T.: Generalized shape optimization without homogenization. Structural optimization 4, 250–252 (1992) Sigmund and Petersson [1998] Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16, 68–75 (1998) Bruns and Tortorelli [2001] Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16, 68–75 (1998) Bruns and Tortorelli [2001] Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  3. Sigmund, O., Petersson, J.: Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Structural optimization 16, 68–75 (1998) Bruns and Tortorelli [2001] Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  4. Bruns, T.E., Tortorelli, D.A.: Topology optimization of non-linear elastic structures and compliant mechanisms. Computer methods in applied mechanics and engineering 190(26-27), 3443–3459 (2001) Bourdin [2001] Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  5. Bourdin, B.: Filters in topology optimization. International journal for numerical methods in engineering 50(9), 2143–2158 (2001) Wang et al. [2011] Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  6. Wang, F., Lazarov, B.S., Sigmund, O.: On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization 43(6), 767–784 (2011) Guest et al. [2004] Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  7. Guest, J.K., Prévost, J.H., Belytschko, T.: Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International journal for numerical methods in engineering 61(2), 238–254 (2004) Xu et al. [2010] Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  8. Xu, S., Cai, Y., Cheng, G.: Volume preserving nonlinear density filter based on heaviside functions. Structural and Multidisciplinary Optimization 41(4), 495–505 (2010) Ferrari and Sigmund [2020] Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  9. Ferrari, F., Sigmund, O.: A new generation 99 line matlab code for compliance topology optimization and its extension to 3d. Structural and Multidisciplinary Optimization 62, 2211–2228 (2020) Dunning [2023] Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  10. Dunning, P.: Stability constraints for geometrically nonlinear topology optimization. Structural and multidisciplinary optimization (2023) da Silva et al. [2023] Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  11. Silva, A.L.F., Salas, R.A., Silva, E.C.N.: Topology optimization of fiber reinforced structures considering stress constraint and optimized penalization. Composite Structures 316, 117006 (2023) Ha and Carstensen [2024] Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  12. Ha, D., Carstensen, J.: Automatic hyperparameter tuning of topology optimization algorithms using surrogate optimization (2024) https://doi.org/10.21203/rs.3.rs-3944293/v1 Huang and Xie [2007] Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  13. Huang, X., Xie, Y.: Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite elements in analysis and design 43(14), 1039–1049 (2007) Sivapuram and Picelli [2018] Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  14. Sivapuram, R., Picelli, R.: Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design 139, 49–61 (2018) Christensen et al. [2023] Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  15. Christensen, C.F., Wang, F., Sigmund, O.: Topology optimization of multiscale structures considering local and global buckling response. Computer Methods in Applied Mechanics and Engineering 408, 115969 (2023) Hübner et al. [2023] Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  16. Hübner, D., Wein, F., Stingl, M.: Two-scale optimization of graded lattice structures respecting buckling on micro-and macroscale. Structural and Multidisciplinary Optimization 66(7), 163 (2023) Sigmund [2007] Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  17. Sigmund, O.: Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization 33(4-5), 401–424 (2007) Crisfield and Moita [1996] Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  18. Crisfield, M., Moita, G.: A co-rotational formulation for 2-d continua including incompatible modes. International Journal for Numerical Methods in Engineering 39(15), 2619–2633 (1996) Ferrari et al. [2021] Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  19. Ferrari, F., Sigmund, O., Guest, J.K.: Topology optimization with linearized buckling criteria in 250 lines of matlab. Structural and Multidisciplinary Optimization 63(6), 3045–3066 (2021) Svanberg [2002] Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002) Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
  20. Svanberg, K.: A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM journal on optimization 12(2), 555–573 (2002)
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Authors (1)

  1. Peter Donald Dunning