Structural Engineering and Mechanics

  • 제34권5호
  • /
  • Pages.581-595
  • /
  • 2010
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Evolutionary topology optimization of geometrically and materially nonlinear structures under prescribed design load

  • Huang, X. (School of Civil, Environmental and Chemical Engineering, RMIT University) ;
  • Xie, Y.M. (School of Civil, Environmental and Chemical Engineering, RMIT University)
  • 투고 : 2007.10.15
  • 심사 : 2009.11.26
  • 발행 : 2010.03.30
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents topology optimization of geometrically and materially nonlinear structures using a bi-directional evolutionary optimization (BESO) method. To maximum the stiffness of nonlinear structures under prescribed design load, the complementary work is selected as the objective function of the optimization. An optimal design can be obtained by gradually removing inefficient material and adding efficient ones. The proposed method can be applied to a series of geometrically and/or materially nonlinear structures. The results show considerable differences in topologies and stiffness of the optimal designs for linear and nonlinear structures. It is found that the optimal designs for nonlinear structures are much stiffer than those for linear structures when large design loads (which result in significantly nonlinear deformations) are applied.

키워드

참고문헌

  1. Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Comput. Meth. Appl. Mech. Eng., 71, 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
  2. Bendsoe, M.P. and Sigmund, O. (2003), Topology Optimization: Theory, Methods and Applications, Springer- Verlag, Berlin Heidelberg.
  3. Bendsoe, M.P., Guedes, J.M., Plaxton, S. and Taylor, J.E. (1996), "Optimization of structure and material properties for solids composed of softening material", Int. J. Solids Struct., 33(12), 1799-1813. https://doi.org/10.1016/0020-7683(95)00121-2
  4. Buhl, T., Pedersen, C.B.W. and Sigmund, O. (2000), "Stiffness design of geometrically nonlinear structures using topology optimization", Struct. Multidiscip. O., 19, 93-104. https://doi.org/10.1007/s001580050089
  5. Bruns, T.E. and Tortorelli, D.A. (2003), "An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms", Int. J. Numer. Meth. Eng., 57, 1413-1430. https://doi.org/10.1002/nme.783
  6. Chu, D.N., Xie, Y.M., Hira, A. and Steven, G.P. (1996), "Evolutionary structural optimization for problems with stiffness constraints", Finite Elem. Anal. Des., 21, 239-251. https://doi.org/10.1016/0168-874X(95)00043-S
  7. Crisfield, M.A. (1991), Non-linear Finite Element Analysis of Solids and Structures, Wiley, New York.
  8. Huang, X. and Xie, Y.M. (2007), "Numerical stability and parameters study of an improved bi-directional evolutionary structural optimization method", Struct. Eng. Mech., 27(1), 49-61. https://doi.org/10.12989/sem.2007.27.1.049
  9. Li, Q., Steven, G.P. and Xie, Y.M. (2001), "A simple checkerboard suppression algorithm for evolutionary structural optimization", Struct. Multidiscip. O., 22, 230-239. https://doi.org/10.1007/s001580100140
  10. Murio, D.A. (1993), The Mollification Method and the Numerical Solution of Ill-posed Problems, Wiley, New York.
  11. Maute, K., Schwarz, S. and Ramm, E. (1998), "Adaptive topology optimization of elastoplastic structures", Struct. Multidiscip. O., 15, 81-91. https://doi.org/10.1007/BF01278493
  12. Pedersen, C.B.W., Buhl, T.E. and Sigmund, O. (2001), "Topology synthesis of large-displacement compliant mechanisms", Int. J. Numer. Meth. Eng., 50, 2683-2705. https://doi.org/10.1002/nme.148
  13. Pedersen, P. (1998), "Some general optimal design results using anisotropic, power law nonlinear elasticity", Struct. Multidiscip. O., 15, 73-80. https://doi.org/10.1007/BF01278492
  14. Sigmund, O. and Peterson, J. (1998), "Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima", Multidiscip. O., 16, 68-75. https://doi.org/10.1007/BF01214002
  15. Xie, Y.M. and Steven, G.P. (1993), "A simple evolutionary procedure for structural optimization", Comput. Struct., 49, 885-886. https://doi.org/10.1016/0045-7949(93)90035-C
  16. Xie, Y.M. and Steven, G.P. (1997), Evolutionary Structural Optimization, Springer, London.
  17. Yang, X.Y., Xie, Y.M., Steven, G.P. and Querin, O.M. (1999), "Bidirectional evolutionary method for stiffness optimization", AIAA J., 37(11), 1483-1488. https://doi.org/10.2514/2.626
  18. Yuge, K. and Kikuchi, N. (1995), "Optimization of a frame structure subjected to a plastic deformation", Struct. Multidiscip. O., 10, 197-208. https://doi.org/10.1007/BF01742592

피인용 문헌

  1. Application of topology optimization to bridge girder design vol.51, pp.1, 2014, https://doi.org/10.12989/sem.2014.51.1.039
  2. Optimal microstructures of elastoplastic cellular materials under various macroscopic strains vol.118, 2018, https://doi.org/10.1016/j.mechmat.2017.10.002
  3. Topology optimization approaches vol.48, pp.6, 2013, https://doi.org/10.1007/s00158-013-0978-6
  4. Bi-directional evolutionary optimization for photonic band gap structures vol.302, 2015, https://doi.org/10.1016/j.jcp.2015.09.010
  5. The use of topology optimization in the design of truss and frame bridge girders vol.51, pp.1, 2014, https://doi.org/10.12989/sem.2014.51.1.067
  6. Topological material distribution evaluation for steel plate reinforcement by using CCARAT optimizer vol.51, pp.5, 2014, https://doi.org/10.12989/sem.2014.51.5.793
  7. A topological optimization method for flexible multi-body dynamic system using epsilon algorithm vol.37, pp.5, 2010, https://doi.org/10.12989/sem.2011.37.5.475
  8. Biomimetic control for redundant and high degree of freedom limb systems: neurobiological modularity vol.7, pp.3, 2010, https://doi.org/10.12989/sss.2011.7.3.169
  9. Topology optimization of the photovoltaic panel connector in high-rise buildings vol.62, pp.4, 2010, https://doi.org/10.12989/sem.2017.62.4.465
  10. New form of perforated steel plate shear wall in simple frames using topology optimization vol.74, pp.3, 2010, https://doi.org/10.12989/sem.2020.74.3.325