Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
169 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Simultaneous Analysis of Continuously Embedded Reissner-Mindlin Shells in 3D Bulk Domains (2311.16638v1)

Published 28 Nov 2023 in cs.CE

Abstract: A mechanical model and numerical method for the simultaneous analysis of Reissner-Mindlin shells with geometries implied by a continuous set of level sets (isosurfaces) over some three-dimensional bulk domain is presented. A three-dimensional mesh in the bulk domain is used in a tailored FEM formulation where the elements are by no means conforming to the level sets representing the shape of the individual shells. However, the shell geometries are bounded by the intersection curves of the level sets with the boundary of the bulk domain so that the boundaries are meshed conformingly. This results in a method which was coined Bulk Trace FEM before. The simultaneously considered, continuously embedded shells may be useful in the structural design process or for the continuous reinforcement of bulk domains. Numerical results confirm higher-order convergence rates.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (59)
  1. Vieweg +++ Teubner Verlag, Braunschweig, 1985.
  2. Computers & Structures, 75, 1–30, 2000.
  3. Comp. Methods Appl. Mech. Engrg., 51, 221–258, 1985.
  4. Comp. Methods Appl. Mech. Engrg., 199, 276–289, 2010.
  5. J. Comput. Phys., 174, 759–780, 2001.
  6. (Stein, E.; Borst, R.; Hughes, T.J.; Hughes, T.J., Eds.), Vol. 2, John Wiley & Sons, Chichester, 2017.
  7. Burger, M.: Finite element approximation of elliptic partial differential equations on implicit surfaces. Comput. Vis. Sci., 12, 87–100, 2009.
  8. Burman, E.: A penalty-free nonsymmetric Nitsche-type method for the weak imposition of boundary conditions. SIAM J. Numer. Anal., 50, 1959–1981, 2012.
  9. Applied Numerical Mathematics, 62, 328–341, 2012.
  10. Comp. Methods Appl. Mech. Engrg., 285, 188–207, 2015.
  11. ESAIM: Math. Model. Numer. Anal., 52, 2247–2282, 2018.
  12. Calladine, C. R.: Theory of shell structures. Cambridge University Press, Cambridge, 1983.
  13. Comp. Methods Appl. Mech. Engrg., 310, 98–111, 2016.
  14. Computers & Structures, 66, 19–36, 1998.
  15. Computational Fluid and Solid Mechanics. Springer, Berlin, 2011.
  16. Comp. Methods Appl. Mech. Engrg., 291, 146–172, 2015.
  17. IMA J. Numer. Anal., 30, 351–376, 2010.
  18. SIAM J. Numer. Anal., 52, 2137–2162, 2014.
  19. Journal of Differential Equations, 119, 426–449, 1995.
  20. SIAM, Philadelphia, 2011.
  21. Journal of Differential Equations, 128, 125–167, 1996.
  22. Comp. Methods Appl. Mech. Engrg., 276, 35–66, 2014.
  23. Comp. Methods Appl. Mech. Engrg., 253, 491–504, 2013.
  24. Interface Free Bound, 10, 119–138, 2008.
  25. Comput. Vis. Sci., 13, 17–28, 2010.
  26. Acta Numerica, 22, 289–396, 2013.
  27. Comp. Methods Appl. Mech. Engrg., 254, 170–180, 2013.
  28. Federer, H.: Geometric measure theory. Springer, New York, 1969.
  29. Fries, T.P.: Higher-order surface FEM for incompressible Navier-Stokes flows on manifolds. Internat. J. Numer. Methods Fluids, 88, 55–78, 2018.
  30. Comp. Methods Appl. Mech. Engrg., 415, 116223, 2023.
  31. Comp. Methods Appl. Mech. Engrg., 313, 759–784, 2017.
  32. Comp. Methods Appl. Mech. Engrg., 326, 270–297, 2017.
  33. Comp. Methods Appl. Mech. Engrg., 365, 113031, 2020.
  34. Internat. J. Numer. Methods Engrg., 114, 1163–1178, 2018.
  35. SIAM J. Numer. Anal., 54, 388–414, 2016.
  36. Greer, J.B.: An improvement of a recent Eulerian method for solving PDEs on general geometries. J. Sci. Comput., 29, 321–352, 2006.
  37. J. Comput. Phys., 216, 216–246, 2006.
  38. Comp. Methods Appl. Mech. Engrg., 270, 1–14, 2014.
  39. Comput. Mech., 53, 611–623, 2014.
  40. Interface Free Bound, 20, 353–377, 2018.
  41. Proceedings in Applied Mathematics and Mechanics, Vol. 22, John Wiley & Sons, Chichester, 2023.
  42. Comp. Methods Appl. Mech. Engrg., 198, 3902–3914, 2009.
  43. Comp. Methods Appl. Mech. Engrg., 325, 645–665, 2017.
  44. Love, A.E.H.: XVI. The small free vibrations and deformation of a thin elastic shell. Proceedings of the Royal Society of London, 43, 491–546, 1888.
  45. Morgan, F.: Geometric measure theory: a beginner’s guide. Academic press, San Diego, 1988.
  46. Comp. Methods Appl. Mech. Engrg., 284, 265–291, 2015.
  47. SIAM J. Sci. Comput., 40, A2492–A2518, 2018.
  48. (Bordas, S.P.A.; Burman, E.; Larson, M.G.; Olshanskii, M.A.; Olshanskii, M.A., Eds.), Vol. 121, Lecture notes in computational science and engineering, Springer Nature, Cham, 211–258, 2017.
  49. IMA J. Numer. Anal., 34, 732–758, 2014.
  50. Springer, New York, 2006.
  51. Reissner, E.: The effect of transverse shear deformation on the bending of elastic plates. Journal of Applied Mechanics, 12, A69–A77, 1945.
  52. Comp. Methods Appl. Mech. Engrg., 309, 625–652, 2016.
  53. Comput. Mech., 64, 113–131, 2019.
  54. Comp. Methods Appl. Mech. Engrg., 352, 172–188, 2019.
  55. Internat. J. Numer. Methods Engrg., 122, 1217–1238, 2021.
  56. Butterworth-Heinemann, Oxford, 2013.
  57. Butterworth-Heinemann, Oxford, 2014.
  58. Zingoni, A.: Shell structures in civil and mechanical engineering: theory and analysis. ICE Publishing, London, 2018.
  59. Comp. Methods Appl. Mech. Engrg., 370, 113283, 2020.
Citations (3)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now