Steel and Composite Structures

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Topology optimization of Reissner-Mindlin plates using multi-material discrete shear gap method

  • Minh-Ngoc Nguyen (Department of Architectural Engineering, Sejong University) ;
  • Wonsik Jung (Department of Architectural Engineering, Sejong University) ;
  • Soomi Shin (Research Institute of Industrial Technology, Pusan National University) ;
  • Joowon Kang (School of Architecture, Yeungnam University) ;
  • Dongkyu Lee (Research Institute of Industrial Technology, Pusan National University)
  • Received : 2021.11.29
  • Accepted : 2023.03.06
  • Published : 2023.05.10
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Abstract

This paper presents a new scheme for constructing locking-free finite elements in thick and thin plates, called Discrete Shear Gap element (DSG), using multiphase material topology optimization for triangular elements of Reissner-Mindlin plates. Besides, common methods are also presented in this article, such as quadrilateral element (Q4) and reduced integration method. Moreover, when the plate gets too thin, the transverse shear-locking problem arises. To avoid that phenomenon, the stabilized discrete shear gap technique is utilized in the DSG3 system stiffness matrix formulation. The accuracy and efficiency of DSG are demonstrated by the numerical examples, and many superior properties are presented, such as being a strong competitor to the common kind of Q4 elements in the static topology optimization and its computed results are confirmed against those derived from the three-node triangular element, and other existing solutions.

Keywords

Acknowledgement

This research was supported by and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2022R1A2C1003776) and 2021R1I1A1A01054901.

References

  1. 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.
  2. Banh, T.T. and Lee, D.K. (2019), "Topology optimization of multidirectional variable thickness thin plate with multiple materials", Struct Multidisc Optim, 59, 1503-1520. https://doi.org/10.1007/s00158-018-2143-8.
  3. Banh, T.T., Luu, G.N. and Lee D.K. (2021), "A non-homogeneous multi-material topology optimization approach for functionally graded structures with cracks", Compos. Struct., 273(24), 114-230. https://doi.org/10.1016/j.compstruct.2021.114230.
  4. Banh, T.T., Nguyen, Q.X. and Lee, D.K. (2020), "Multiphase material topology optimization of Mindlin-Reissner plate with nonlinear variable thickness and Winkler foundation", Steel Compos. Struct., 35(1), 129-145. https://doi.org/10.12989/scs.2020.35.1.129.
  5. Bathe, K.J., Dvorkin, E.N, (1985), "A four-node plate bending element based on Mindlin-Reissner plate theory and a mixed interpolation", Int. J. Num. Methods Eng, 21, 367-383. https://doi.org/10.1002/nme.1620210213.
  6. Bendsoe, M.P and Sigmund, O. (2013), Topology Optimization: Theory, Methods, and Applications, Springer Science Business Media.
  7. Bletzinger, K.U., Bischoff, M. and Ramm, E. (2003), "A unified approach for shearlocking-free triangular and rectangular shell finite elements", Compos. Struct., 75(3), 321-334. https://doi.org/10.1016/S0045-7949(99)00140-6.
  8. Chau, K.N., Chau, K.N., Ngo, T., Hackl, K. and Xuan, H.N. (2018), ''A polytree-based adaptive polygonal finite element method for multi-material topology optimization'', Comput. Meth. Appl. Mech. Eng., 332, 712-739. https://doi.org/10.1016/j.cma.2017.07.035.
  9. Doan, Q.H and Lee, D.K. (2017), "Optimum topology design of multi-material structures with non-spurious buckling constraints", Adv. Eng. Softw., 114, 110-120. https://doi.org/10.1016/j.advengsoft.2017.06.002.
  10. Hoang, V.N. and Xuan, H.N. (2020), ''Extruded-geometric-component-based 3D topology optimization", Comput. Meth. Appl. Mech. Eng., 371, 113293. https://doi.org/10.1016/j.cma.2020.113293.
  11. Hoang, V.N., Pham, T., Ho, D. and Xuan, H.N. (2022), ''Robust multiscale design of incompressible multi-materials under loading uncertainties'', Eng. Comput., 38, 875-890. https://doi.org/10.1007/s00366-021-01372-0.
  12. Hoang, V.N., Pham, T., Tangaramvong, S., Bordas, S.P.A and Xuan, H.N. (2021), ''Robust adaptive topology optimization of porous infills under loading uncertainties'', Struct. Multidiscipl. Optim., 63, 2253-2266. https://doi.org/10.1007/s00158-020-02800-3.
  13. Hughes, T.J.R., Cohen, M. and Haroun, M. (1978), "Reduced and selective integration techniques in the finite element analysis of plates", Nuclear Eng. Des., 46, 203-222. https://doi.org/10.1016/0029-5493(78)90184-X.
  14. Lieu, Q.X. and Lee, J. (2017), ''A multi-resolution approach for multi-material topology optimization based on isogeometric analysis", Comput. Meth. Appl. Mech. Eng., 323, 272-302. https://doi.org/10.1016/j.cma.2017.05.009.
  15. Lieu, Q.X. and Lee, J. (2018), ''Multiresolution topology optimization using isogeometric analysis'', Int. J. Numer. Meth. Eng., 1-23. https://doi.org/10.1002/nme.5593.
  16. Liu, G.R. (2010), Meshfree Methods - Moving Beyond the Finite Element Method. CRC Press.
  17. Liu, P., Luo, Y. and Kang, Z. (2016), "Multi-material topology optimization considering interface behavior via XFEM and level set method", Comput. Meth. Appl. Mech. Engrg., 308, 113-133. https://doi.org/10.1016/j.cma.2016.05.016.
  18. Manickarajah, D., Xie, Y.M. and Steven, G.P. (1998), "An evolutionary method for optimization of plate buckling resistance", Finite Elem. Anal. Des., 29, 205-230. https://doi.org/10.1016/s0168-874x(98)00012-2.
  19. Onate, E., Zarate, F. and Flores, F. (1994), "A simple triangular element for thick and thin plate and shell analysis", Int. J. Num. Meth. Eng., 37, 2569-2582. https://doi.org/10.1002/nme.1620371505.
  20. Onate, E., Zienkiewicz, O.C., Suarez, B. and Taylor, R.L. (1992), "A general methodology for deriving shear constrained Reissner-Mindlin plate elements", Int. J. Num. Meth. Eng., 33, 345-367. https://doi.org/10.1002/NME.1620330208.
  21. Tavakoli, R. and Mohseni, M. (2014), "Alternating active-phase algorithm for multi-material topology optimization problems: a 115-line MATLAB implementation", Struct. Multidiscipl. Optim., 49, 621-642. https://doi.org/10.1007/s00158-013-0999-1.
  22. Thoi, T.N., Van, P.P., Hoang, C.T. and Xuan, H.N. (2013), "A cell-based smoothed vdiscrete shear gap method (CS-DSG3) using triangular elements for static and free vibration analyses of shell structures", Int. J. Mech. Sci., 74, 35-42. https://doi.org/10.1016/j.ijmecsci.2013.04.005.
  23. Veiga, L.B.D., Hughes, T.J.R., Kiendl, J., Lovadina, C., Niiranen, J., Reali, A. and Speleers, H. (2015), "A locking-free model for Reissner-Mindlin plates: Analysis and isogeometric implementation via NURBS and triangular NURPS", Mathem. Models Meth. Appl. Sci., 25, 1519-1551. https://doi.org/10.1142/S0218202515500402.
  24. Videla, J., Natarajan, S. and Bordas, S.P.A. (2019), "A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields", Compos. Struct., 220, 32-42. https://doi.org/10.1016/j.compstruct.2017.07.092.
  25. Wana, D., Hu, D., Natarajan, S., Bordas, S.P.A. and Long, T. (2017), "A linear smoothed quadratic finite element for the analysis of laminated composite Reissner-Mindlin plates" Compos. Struct., 180, 395-411. https://doi.org/10.1016/j.compstruct.2017.07.092.
  26. Wang, M.Y, Wang, X. and Guo, D. (2003), "A level set method for structural topology optimization", Comput. Meth. Appl. Mech. Engrg., 192, 227-246. https://doi.org/10.1016/S0045-7825(02)00559-5.
  27. Wu, C., Fang, J. and Li, Q. (2019), "Multi-material topology optimization for thermal buckling criteria", Comput. Meth. Appl. Mech. Engrg., 346, 1136-1155. https://doi.org/10.1016/j.cma.2018.08.015.
  28. Xuan, H.N., Liu, G.R., Bordas, S., Natarajan, S. and Rabczuk, T. (2013), ''An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order'', Comput. Meth. Appl. Mech. Eng., 253, 252-273. https://doi.org/10.1016/j.cma.2012.07.017.
  29. Xuan, H.N., Rabczuk, T., Thanh, N.N., Thoi, T.N. and Bordas, S.P.A. (2010), "A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner-Mindlin plates", Comput. Mech., 46, 679-701. https://doi.org/10.1016/j.compstruc.2019.04.009.
  30. Yoon, G.H, Choi, H. and Hur, S. (2018), "Multiphysics topology optimization for piezoelectric acoustic focuser", Comput. Meth. Appl. Mech. Engrg., 332, 600-623. https://doi.org/10.1016/j.cma.2017.12.002.
  31. Zhou, M. (2004), "Topology optimization for shell structures with linear buckling responses", In WCCM VI. Beijing, China.
  32. Zienkiewicz, O.C., Taylor, R.L. and Too, J.M. (1971), "Reduced integration techniques in general of plates and shells", Int. J. Num. Meth. Eng., 3, 275-290. https://doi.org/10.1002/nme.1620030211.