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Multi-material topology optimization of Reissner-Mindlin plates using MITC4

  • Banh, Thien Thanh (Department of Architectural Engineering, Sejong University) ;
  • Lee, Dongkyu (Department of Architectural Engineering, Sejong University)
  • Received : 2017.04.06
  • Accepted : 2018.01.24
  • Published : 2018.04.10

Abstract

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. Alonso, C., Ansola, R. and Querin, O.M. (2014), "Topology synthesis of multi-material compliant mechanisms with a sequential element rejection and admission method", Finite Elem. Anal. Des., 85, 11-19. https://doi.org/10.1016/j.finel.2013.11.006
  2. Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B.S. and Sigmund, O. (2011), "Efficient topology optimization in MATLAB using 88 lines of code", Struct. Multidiscipl. Optimiz., 43(1), 1-16. https://doi.org/10.1007/s00158-010-0594-7
  3. Arnold, D.N., Madureira, A.L. and Zhang, S. (2002), "On the range of applicability of the Reissner-Mindlin and Kirchhoff-Love plate bending models", J. Elast. Phys. Sci. Solids, 67(3), 171-185. https://doi.org/10.1023/A:1024986427134
  4. Banh, T.T. and Lee, D.K. (2018), "Multi-material topology optimization design for continuum structures with crack patterns", Compos. Struct., 186, 193-209. https://doi.org/10.1016/j.compstruct.2017.11.088
  5. Bathe, K.J. and Dvorkin, E.N. (1985), "A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation", Int. J. Numer. Methods Eng., 21(2), 367-383. https://doi.org/10.1002/nme.1620210213
  6. Belblidiaa, F., Leea, J.E.B., Rechakb, S. and Hinton, E. (2001), "Topology optimization of plate structures using a single- or three-layered artificial material model", Adv. Eng. Software, 32(2), 159-168. https://doi.org/10.1016/S0045-7949(00)00141-3
  7. Bendsoe, M. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Computat. Methods Appl. Math., 71(2), 197-224. https://doi.org/10.1016/0045-7825(88)90086-2
  8. Doan, Q.H. and Lee, D.K. (2017), "Optimum topology design of multi-material structures with non-spurious buckling constraints", Adv. Eng. Software, 114, 110-120. https://doi.org/10.1016/j.advengsoft.2017.06.002
  9. Goo, S.Y., Wang, S.Y., Hyun, J.Y. and Jung, J.S. (2016), "Topology optimization of thin plate structures with bending stress constraints", Comput. Struct., 175, 134-143. https://doi.org/10.1016/j.compstruc.2016.07.006
  10. Lee, D.K. (2016), "Additive 2D and 3D performance ratio analysis for steel outrigger alternative design", Steel Compos. Struct., Int. J., 20(5), 1133-1153. https://doi.org/10.12989/scs.2016.20.5.1133
  11. Lee, D.K. and Shin, S.M. (2015a), "Optimizing structural topology patterns using regularization of Heaviside function", Struct. Eng. Mech., Int. J., 55(6), 1157-1176. https://doi.org/10.12989/sem.2015.55.6.1157
  12. Lee, D.K. and Shin, S.M. (2015b), "Automatic position information of web-openings of building using minimized strain energy topology optimization", Adv. Mater. Sci. Eng., 624762.
  13. Lee, D.K., Yang, C.J. and Starossek, U. (2012), "Topology design of optimizing material arrangements of beam-to-column connection frames with maximal stiffness", Scientia Iranica, 19(4), 1025-1032. https://doi.org/10.1016/j.scient.2012.06.004
  14. Lee, D.K., Kim, Y.W., Shin, S.M. and Lee, J.H. (2016), "Real-time response assessment in steel frame remodeling using positionadjustment drift-curve formulations", Automat. Constr., 62, 57-67. https://doi.org/10.1016/j.autcon.2015.11.002
  15. Sigmund, O. and Torquato, S. (1997), "Design of materials with extreme thermal expansion using a three-phase topology optimization method", J. Mech. Phys. Solids, 45(6), 1037-106. https://doi.org/10.1016/S0022-5096(96)00114-7
  16. Tavakoli, R. and Mohseni, S. (2014), "Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line matlab implementation", Struct. Multidiscipl. Optimiz., 49(4), 621-642. https://doi.org/10.1007/s00158-013-0999-1
  17. Xia, L., Da, D. and Yvonnet, J. (2018), "Topology optimization for maximizing the fracture resistance of quasi-brittle composites", Comput. Methods Appl. Mech. Eng., 332, 234-254. https://doi.org/10.1016/j.cma.2017.12.021
  18. Yan, K., Cheng, G. and Wang, B.P. (2016), "Topology optimization of plate structures subject to initial excitations for minimum dynamic performance index", Struct. Multidiscipl. Optimiz., 53(3), 623-633. https://doi.org/10.1007/s00158-015-1350-9
  19. Yun, K.S. and Youn, S.K. (2017), "Multi-material topology optimization of viscoelastically damped structures under timedependent loading", Finite Elem. Anal. Des., 123, 9-18. https://doi.org/10.1016/j.finel.2016.09.006
  20. Zhou, S. and Wang, M. (2006), "Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition", Struct. Multidiscipl. Optimiz., 33(2), 89-111. https://doi.org/10.1007/s00158-006-0035-9
  21. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method: Solid and Fluid Mechanics, (5th Edition), Volume 2.