Browse > Article
http://dx.doi.org/10.12989/scs.2020.35.1.129

Multiphase material topology optimization of Mindlin-Reissner plate with nonlinear variable thickness and Winkler foundation  

Banh, Thanh T. (Department of Architectural Engineering, Sejong University)
Nguyen, Xuan Q. (Department of Architectural Engineering, Sejong University)
Herrmann, Michael (Department of Civil and Environmental Engineering, University of California)
Filippou, Filip C. (Department of Civil and Environmental Engineering, University of California)
Lee, Dongkyu (Department of Architectural Engineering, Sejong University)
Publication Information
Steel and Composite Structures / v.35, no.1, 2020 , pp. 129-145 More about this Journal
Abstract
In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.
Keywords
multiphase material topology optimization; Mindlin-Reissner plate theory; variable thickness; mixed interpolation of tensorial components (MITC4); Winkler foundation;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Bagherinejad, M.H. and Haghollahi, A. (2018), "Topology optimization of steel plate shear walls in the moment frames", Steel Compos. Struct, 29(6), 771-783. https://doi.org/10.12989/scs.2018.29.6.771.   DOI
2 Banh, T.T. and Lee, D. (2019), "Topology optimization of multi-directional variable thickness thin plate with multiple materials", Struct. Multidiscip. O., 59, 1503-1520. https://doi.org/10.1007/s00158-018-2143-8.   DOI
3 Bathe, K.J. and Dvorkin, E. (1985), "A four node plate bending element based on Mindlin-Reissner plate theory and mixed interpolation", Int. J. Numer. Method. Eng., 21, 367-383. https://doi.org/10.1002/nme.1620210213.   DOI
4 Belblidiaa, F., Lee, 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 Softw., 32(2), 159-168. https://doi.org/10.1016/S0045-7949(00)00141-3.   DOI
5 Bendsoe, M.P. and Kikuchi, N. (1988), "Generating optimal topologies in structural design using a homogenization method", Struct. Multidiscip. O., 71, 197-224. http://dx.doi.org/10.1016/0045-7825(88)90086-2.
6 Crusells-Girona, M., Filippou, F.C. and Taylor, R.L. (2017) "A mixed formulation for nonlinear analysis of cable structures", Comput. Struct., 186, 50-61. https://doi.org/10.1016/j.compstruc.2017.03.011.   DOI
7 Doan, Q.H. and Lee, D. (2017), "Optimum topology design of multi-material structures with nonspurious buckling constraints", Adv. Eng. Softw., 114, 110-120. https://doi.org/10.1016/j.advengsoft.2017.06.002.   DOI
8 El-Sabbagh, A., Akl, W. and Baz, A. (2008), "Topology optimization of periodic Mindlin plates", Finite Elem. Anal. Des., 44(8), 439-449. https://doi.org/10.1016/j.finel.2008.01.016.   DOI
9 Ferreira, A.J.M. (2009), The finite element method for solid and structural mechanics, Springer Science Business Media B.V.
10 Herrmann, M. and Sobek, W. (2017), "Functionally graded concrete: Numerical design methods and experimental test of mass-optimized structural components", Struct. Concrete, 18, 54-66. https://doi.org/10.1002/suco.201600011.   DOI
11 Kobayashi, H. and Sonoda, K. (1989), "Rectangular Mindlin plates on elastic foundations", Int. J. Mech.. Sci., 31(9), 679-692. https://doi.org/10.1016/S0020-7403(89)80003-7.   DOI
12 Lee, D. and Shin, S. (2016), "Evaluation of optimized topology design of cross-formed structures with a negative pooisson's ratio", Iran. J. Sci. Technol., Transact. Civil Eng., 40(2), 109-120.   DOI
13 Lieu, X.Q. and Lee, J. (2017), "A multi-resolution approach for multi-material topology optimization based on isogeometric analysis", Comput. Method. Appl. M., 323, 272-302. https://doi.org/10.1016/j.cma.2017.05.009.   DOI
14 Roodsarabi, M., Khatibinia, M. and Sarafrazi, S.R. (2016), "Hybrid of topological derivative-based level set method and isogeometric analysis for structural topology optimization", Steel Compos. Struct., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287.   DOI
15 Luo, Q. and Tong, L. (2017), "A deformation mechanism-based material model for topology optimization of laminated composite plates and shells", Compos. Struct., 159, 246-256. https://doi.org/10.1016/j.compstruct.2016.09.056.   DOI
16 Nguyen, P.A., Banh, T.T., Lee, D., Lee. J., Kang, J. and Shin, S. (2017), "Design of multiphase carbon fiber reinforcement of crack existing concrete structures using topology optimization", Steel Compos. Struct., 29(5), 625-645. https://doi.org/10.12989/scs.2018.29.5.635.
17 Reddy, J.N. (2006), An introduction to the finite element method- Mc GrawHill.
18 Goo, S., Wang, S., Hyun, J. and Jung, J. (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.   DOI
19 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, 1037-1067. https://doi.org/10.1016/S0022-5096(96)00114-7.   DOI
20 Rozvany, G.I.N., Querin, O.M., Gaspar, Z. and Pomezanski, V. (2002), "Extended optimality in topology design", Struct. Multidiscip. O., 24 (24), 257-261. https://doi.org/10.1007/s00158-002-0235-x.   DOI
21 Sun, J., Tian, Q., Hu, H. and Pedersen, N.L. (2019), "Topology optimization or eigenfrequencies of a rotating thin plate via moving morphable components", J. Sound Vib., 448, 83-107. https://doi.org/10.1016/j.jsv.2019.01.054.   DOI