A meshless method for multi-material topology optimization based on the alternating active-phase algorithm
Tóm tắt
Từ khóa
Tài liệu tham khảo
Deaton JD, Grandhi RV (2013) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49:1–38
Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Berlin
Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2010) Efficient topology optimization in MATLAB using 88 lines of code. Struct. Multidiscip. Optim 43:1–16
Huang X, Xie YM (2010) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41:671–683
Huang X, Xie YM (2008) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43:393–401
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246
Allaire G, Gournay FD, Jouve F, Toader AM (2005) Structural optimization using topological and shape sensitivity via a level set method. Control Cybernetics 34(1):59–80
Dijk NP, Maute K, Langelaar M, Keulen FV (2013) Level-set methods for structural topology optimization: a review. Struct Multidiscip Optim 48:437–472
Nguyen VP, Rabczuk T, Bordas S, Duflot M (2008) Meshless methods: a review and computer implementation aspects. Math Comput Simul 79:763–813
Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices R Astron Soc 181:375–389
Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Eng 20:1081–1106
Atluri SN, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach in computational mechanics. Comput Mech 22:117–127
Atluri SN, Zhu T (2000) The meshless local Petrov–Galerkin (MLPG) approach for solving problems in elasto-statics. Comput Mech 25:169–179
Zheng J, Long SY, Li GY (2010) The topology optimization design for continuum structures based on the element free Galerkin method. Eng Anal Bound Elem 34:666–672
Luo Z, Zhang N, Gao W, Ma H (2012) Structural shape and topology optimization using a meshless Galerkin level set method. Int J Numer Meth Eng 90:369–389
Luo Z, Zhang N, Wang Y, Gao W (2013) Topology optimization of structures using meshless density variable approximants. Int J Numer Meth Eng 93:443–464
Zhao F (2013) A meshless Pareto-optimal method for topology optimization. Eng Anal Bound Elem 37:1625–1631
Luo Z, Gao W, Song C (2010) Design of multi-phase piezoelectric actuators. J Intell Mater Syst Struct 21:1851–1865
Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654
Hvejsel CF, Lund E (2011) Material interpolation schemes for unified topology and multi-material optimization. Struct Multidiscip Optim 43:811–825
Zhou S, Wang MY (2006) Multimaterial structural topology optimization with a generalized Cahn–Hilliard model of multiphase transition. Struct Multidiscip Optim 33:89–111
Tavakoli R (2014) Multimaterial topology optimization by volume constrained Allen–Cahn system and regularized projected steepest descent method. Comput Methods Appl Mech Eng 276:534–565
Wang MY, Wang X (2004) “Color” level sets: a multi-phase method for structural topology optimization with multiple materials. Comput Methods Appl Mech Eng 193:469–496
Guo X, Zhang W, Zhong W (2014) Stress-related topology optimization of continuum structures involving multi-phase materials. Comput Methods Appl Mech Eng 268:632–655
Wang MY, Wang X (2005) A level-set based variational method for design and optimization of heterogeneous objects. Comput-Aided Des 37:321–337
Allaire G, Dapogny C, Delgado G, Michailidis G (2014) Multi-phase structural optimization via a level set method. ESAIM Control Optim Calc Var 20:576–611
Vermaak N, Michailidis G, Parry G, Estevez R, Allaire G, Bréchet Y (2014) Material interface effects on the topology optimizationof multi-phase structures using a level set method. Struct. Multidiscip. Optim 50:623–644
Wang YQ, Luo Z, Zhang K, Zhang N (2015) A multi-material level set-based topology and shape optimization method. Comput Methods Appl Mech Eng 283:1570–1586
Tavakoli R, Mohseni SM (2014) Alternating active-phase algorithm for multimaterial topology optimization problems: a 115-line MATLAB implementation. Struct Multidiscip Optim 49:621–642
Shepard D (1968) A two-dimensional function for irregularly spaced points. Proceedings of the 23rd ACM National Conference, pp 517–524
Brodlie KW, Asim MR, Unsworth K (2005) Constrained visualization using the Shepard interpolation family. Comput Graph Forum 24(4):809–820