Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach (1704.06060v1)

Abstract: Three dimensional (3D) topology optimization problems always involve huge numbers of Degrees of Freedom (DOFs) in finite element analysis (FEA) and design variables in numerical optimization, respectively. This will inevitably lead to large computational efforts in the solution process. In the present paper, an efficient and explicit topology optimization approach which can reduce not only the number of design variables but also the number of degrees of freedom in FEA is proposed based on the Moving Morphable Voids (MMVs) solution framework. This is achieved by introducing a set of geometry parameters (e.g., control points of B-spline surfaces) to describe the boundary of a structure explicitly and removing the unnecessary DOFs from the FE model at every step of numerical optimization. Numerical examples demonstrate that the proposed approach does can overcome the bottleneck problems associated with a 3D topology optimization problem in a straightforward way and enhance the solution efficiency significantly.

• The paper presents a novel MMV approach that explicitly models void boundaries to reduce degrees of freedom and design variables in 3D topology optimization.
• It employs moving morphable voids with B-spline surface control for a clear geometric representation, improving integration with CAD/CAE systems.
• Numerical examples, including cantilever beam analyses, demonstrate significant efficiency gains, such as halved CPU times and drastically fewer design variables.

Exploring 3D Topology Optimization with the Moving Morphable Void (MMV) Approach

The paper "Explicit three-dimensional topology optimization via Moving Morphable Void (MMV) approach" by Weisheng Zhang et al. introduces a novel methodology for optimizing three-dimensional structural topology. The MMV approach is developed to address the computational challenges inherent to 3D topology optimization, especially the substantial numbers of degrees of freedom (DOFs) and design variables involved in finite element analysis (FEA) and numerical optimization.

Overview of the MMV Approach

Traditional methods used in three-dimensional topology optimization, such as variable density and level set approaches, struggle with computational efficiency due to the high number of DOFs and design variables (often reaching millions). In response, the MMV approach offers a means to significantly reduce these numbers by representing the structure's boundaries explicitly with geometric parameters, such as the control points of B-spline surfaces.

The core of this methodology lies in using moving morphable voids rather than components, which enables clearer geometrical representation and manipulation of void boundaries in the structure. Unlike implicit methods which rely on higher-dimensional level set functions, the MMV approach maintains a purely parametric boundary description, advancing the efficiency of structural evolution during optimization.

Numerical Findings and Implications

Numerical examples underscore the MMV approach's efficacy in enhancing solution efficiency over traditional methods. Through various case studies, including the short cantilever beam, L-shaped chair, and torsion beam examples, the MMV framework showed consistent reductions in the computational time required for FEA by eliminating unnecessary DOFs. For instance, in the short cantilever beam scenario, the CPU time for FEA was reduced approximately to half of that initially required by effectively removing redundant elements as the solid material volume decreased.

The explicit boundary description in the MMV approach minimizes the number of optimization variables without sacrificing the structural resolution. For the cantilever beam problem, the 1394 design variables used under Hermite interpolation were orders of magnitude fewer than the 8000 variables typically associated with full-scale traditional resolution, thus allowing faster convergence during the optimization process.

Theoretical and Practical Implications

The MMV approach offers several advantages beyond computational efficiency. Firstly, the explicit geometric description facilitates direct integration with CAD/CAE systems, allowing for seamless translation of optimized solutions into manufacturable designs. Furthermore, this method's approach to topology evolution exhibits clearer geometrical interpretations, enhancing the practical understanding and application of structural optimization results.

The implications of introducing the MMV framework extend into various engineering fields where real-time computational efficiency and precision in structural design are crucial. Industries such as aerospace, automotive, and civil engineering could leverage the MMV approach to not only improve design processes but also enhance the structural performance and sustainability of materials.

Future Directions

While the MMV approach represents a significant stride in topology optimization, future work might focus on resolving complex boundary smoothness issues in three-dimensional cases, perhaps through advancements in geometry parameterization techniques. Furthermore, integrating this method with parallel computing environments could offer substantial improvements in solution times, making the optimization process even more viable for large-scale industrial applications.

Finally, exploring the potential of combining MMV with boundary element methods (BEM) may unlock additional efficiencies in structural response analyses, leading to better optimized and more resource-efficient structural designs.

Overall, this paper presents a significant contribution to three-dimensional topology optimization, providing a foundation upon which more efficient and practical structural design methodologies can be developed.