Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review
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Allaire G, Jouve F, Toader AM (2002) A level-set method for shape optimization. CR Math 334(12):1125–1130
Andreassen E, Jensen J (2014) Topology optimization of periodic microstructures for enhanced dynamic properties of viscoelastic composite materials. Struct Multidiscip Optim 49(5):695–705
Andreassen E, Clausen A, Schevenels M, Lazarov BS, Sigmund O (2011) Efficient topology optimization in matlab using 88 lines of code. Struct Multidiscip Optim 43(1):1–16
Ansola R, Canales J, Tárrago JA (2006) An efficient sensitivity computation strategy for the evolutionary structural optimization (ESO) of continuum structures subjected to self-weight loads. Finite Elem Anal Des 42(14):1220–1230
Bendsøe M, Sigmund O (1999a) Material interpolation schemes in topology optimization. Arch Appl Mech 69(9–10):635–654
Bendsøe MP (1989) Optimal shape design as a material distribution problem. Struct Optim 1(4):193–202
Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71(2):197–224
Bendsøe MP, Sigmund O (1999b) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654
Bendsøe MP, Sigmund O (2003) Topology optimization: theory, methods and applications. Springer, Berlin
Bourdin B, Chambolle A (2003) Design-dependent loads in topology optimization. ESAIM Control Optim Calc Var 9:19–48
Bruns T, Tortorelli D (2003) An element removal and reintroduction strategy for the topology optimization of structures and compliant mechanisms. Int J Numer Methods Eng 57(10):1413–1430
Cadman J, Zhou S, Chen Y, Li Q (2013) On design of multi-functional microstructural materials. J Mater Sci 48(1):51–66
Challis VJ, Roberts AP, Wilkins AH (2008) Design of three dimensional isotropic microstructures for maximized stiffness and conductivity. Int J Solids Struct 45(14–15):4130–4146
Challis VJ, Guest JK, Grotowski JF, Roberts AP (2012) Computationally generated cross-property bounds for stiffness and fluid permeability using topology optimization. Int J Solids Struct 49(23–24):3397–3408
Chen W, Liu S (2014) Topology optimization of microstructures of viscoelastic damping materials for a prescribed shear modulus. Struct Multidiscip Optim 50(2):287–296
Cheng K, Olhoff N (1981) An investigation concerning optimal design of solid elastic plates. Int J Solids Struct 17(3):305–323
Chiandussi G (2006) On the solution of a minimum compliance topology optimisation problem by optimality criteria without a priori volume constraint specification. Comput Mech 38(1):77–S99
Cho S, Jung HS (2003) Design sensitivity analysis and topology optimization of displacement-loaded non-linear structures. Comput Methods Appl Mech Eng 192(22–23):2539–2553
Chu DN, Xie YM, Hira A, Steven GP (1996) Evolutionary structural optimization for problems with stiffness constraints. Finite Elem Anal Des 21(4):239–251
Coenen EWC, Kouznetsova VG, Geers MGD (2012) Multi-scale continuous–discontinuous framework for computational-homogenization-localization. J Mech Phys Solids 60(8):1486–1507
Da D, Cui X, Long K, Li G (2016) Concurrent topological design of composite structures and the underlying multi-phase materials. Comput Struct. doi: 10.1016/j.compstruc.2016.10.006
Deaton JD, Grandhi RV (2014) A survey of structural and multidisciplinary continuum topology optimization: post 2000. Struct Multidiscip Optim 49(1):1–38
Du J, Olhoff N (2007) Topological design of freely vibrating continuum structures for maximum values of simple and multiple eigenfrequencies and frequency gaps. Struct Multidiscip Optim 34(2):91–110
Duysinx P, Bendsøe MP (1998) Topology optimization of continuum structures with local stress constraints. Int J Numer Methods Eng 43(8):1453–1478
Edwards C, Kim H, Budd C (2007) An evaluative study on ESO and SIMP for optimising a cantilever tie-beam. Struct Multidiscip Optim 34(5):403–414
Eschenauer H, Kobelev V, Schumacher A (1994) Bubble method for topology and shape optimization of structures. Struct Optim 8(1):42–51
Feyel F, Chaboche J (2000) $$\text{ FE }^{2}$$ multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials. Comput Methods Appl Mech Eng 183(3–4):309–330
Fleming J, Lin S, El-Kady I, Biswas R, Ho K (2002) All-metallic three-dimensional photonic crystals with a large infrared bandgap. Nature 417(6884):52–55
Fritzen F, Hodapp M (2016) The finite element square reduced (fe2R) method with gpu acceleration: towards three-dimensional two-scale simulations. Int J Numer Methods Eng. doi: 10.1002/nme.5188
Fritzen F, Leuschner M (2013) Reduced basis hybrid computational homogenization based on a mixed incremental formulation. Comput Methods Appl Mech Eng 260:143–154
Fritzen F, Hodapp M, Leuschner M (2014) Gpu accelerated computational homogenization based on a variational approach in a reduced basis framework. Comput Methods Appl Mech Eng 278:186–217
Fritzen F, Xia L, Leuschner M, Breitkopf P (2016) Topology optimization of multiscale elastoviscoplastic structures. Int J Numer Methods Eng. doi: 10.1002/nme.5122
Fujii D, Chen BC, Kikuchi N (2001) Composite material design of two-dimensional structures using the homogenization design method. Int J Numer Methods Eng 50(9):2031–2051
Fullwood DT, Niezgoda SR, Adams BL, Kalidindi SR (2010) Microstructure sensitive design for performance optimization. Prog Mater Sci 55(6):477–562
Geers MGD, Kouznetsova VG, Brekelmans WAM (2010) Multi-scale computational homogenization: trends and challenges. J Comput Appl Math 234(7):2175–2182
Ghabraie K (2015) An improved soft-kill BESO algorithm for optimal distribution of single or multiple material phases. Struct Multidiscipl Optim 52(4):773–790
Ghabraie K, Xie YM, Huang X, Ren G (2010) Shape and reinforcement optimization of underground tunnels. J Comput Sci Technol 4(1):51–63
Gibiansky L, Sigmund O (2000) Multiphase composites with extremal bulk modulus. J Mech Phys Solids 48(3):461–498
Guedes J, Kikuchi N (1990) Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Methods Appl Mech Eng 83(2):143–198
Guest JK, Prévost JH (2006) Optimizing multifunctional materials: Design of microstructures for maximized stiffness and fluid permeability. Int J Solids Struct 43(22–23):7028–7047
Guest JK, Prévost JH (2007) Design of maximum permeability material structures. Comput Methods Appl Mech Eng 196(4–6):1006–1017
Hashin Z, Shtrikman S (1962) A variational approach to the theory of the effective magnetic permeability of multiphase materials. J Appl Phys 33(10):3125–3131
Hassani B, Hinton E (1998b) A review of homogenization and topology opimization II: analytical and numerical solution of homogenization equations. Comput Struct 69(6):719–738
Hinton E, Sienz J (1995) Fully stressed topological design of structures using an evolutionary procedure. Eng Comput 12(3):229–244
Huang X, Xie YM (2007a) Bidirectional evolutionary topology optimization for structures with geometrical and material nonlinearities. AIAA J 45(1):308–313
Huang X, Xie YM (2007b) Convergent and mesh-independent solutions for the bi-directional evolutionary structural optimization method. Finite Elem Anal Des 43(14):1039–1049
Huang X, Xie YM (2008a) A new look at ESO and BESO optimization methods. Struct Multidiscip Optim 35(1):89–92
Huang X, Xie YM (2008b) Optimal design of periodic structures using evolutionary topology optimization. Struct Multidiscip Optim 36(6):597–606
Huang X, Xie YM (2008c) Optimal design of periodic structures using evolutionary topology optimization. Struct Multidiscip Optim 36(6):597–606
Huang X, Xie YM (2008d) Topology optimization of nonlinear structures under displacement loading. Eng Struct 30(7):2057–2068
Huang X, Xie YM (2009) Bi-directional evolutionary topology optimization of continuum structures with one or multiple materials. Comput Mech 43(3):393–401
Huang X, Xie YM (2010a) Evolutionary topology optimization of continuum structures with an additional displacement constraint. Struct Multidiscip Optim 40(1–6):409–416
Huang X, Xie YM (2010b) A further review of ESO type methods for topology optimization. Struct Multidiscip Optim 41(5):671–683
Huang X, Xie YM (2010c) Topology optimization of continuum structures: methods and applications. Wiley, Chichester
Huang X, Xie YM (2011) Evolutionary topology optimization of continuum structures including design-dependent self-weight loads. Finite Elem Anal Des 47(8):942–948
Huang X, Xie YM, Lu G (2007) Topology optimization of energy-absorbing structures. Int J Crashworthiness 12(6):663–675
Huang X, Zuo Z, Xie YM (2010) Evolutionary topological optimization of vibrating continuum structures for natural frequencies. Comput Struct 88(5):357–364
Huang X, Radman A, Xie YM (2011) Topological design of microstructures of cellular materials for maximum bulk or shear modulus. Comput Mater Sci 50(6):1861–1870
Huang X, Xie YM, Jia B, Li Q, Zhou SW (2012) Evolutionary topology optimization of periodic composites for extremal magnetic permeability and electrical permittivity. Struct Multidiscip Optim 46(3):385–398
Huang X, Zhou SW, Xie YM, Li Q (2013) Topology optimization of microstructures of cellular materials and composites for macrostructures. Comput Mater Sci 67:397–407
Huang X, Li Y, Zhou S, Xie YM (2014) Topology optimization of compliant mechanisms with desired structural stiffness. Eng Struct 79:13–21
Huang X, Zhou S, Sun G, Li G, Xie YM (2015) Topology optimization for microstructures of viscoelastic composite materials. Comput Methods Appl Mech Eng 283:503–516
Joannopoulos J, Johnson S, Winn J, Meade R (2011) Photonic crystals: molding the flow of light. Princeton University Press, Princeton
Kato J, Yachi D, Terada K, Kyoya T (2014) Topology optimization of micro-structure for composites applying a decoupling multi-scale analysis. Struct Multidiscip Optim 49(4):595–608
Kim H, Garcia M, Querin O, Steven GP, Xie YM (2000a) Introduction of fixed grid in evolutionary structural optimisation. Eng Comput 17(4):427–439
Kim H, Querin O, Steven GP, Xie YM (2000b) A method for varying the number of cavities in an optimized topology using evolutionary structural optimization. Struct Multidiscip Optim 19(2):140–147
Kim H, Querin O, Steven GP, Xie YM (2002a) Improving efficiency of evolutionary structural optimization by implementing fixed grid mesh. Struct Multidiscip Optim 24(6):441–448
Kim H, Querin OM, Steven GP, Xie YM (2002b) Determination of an optimal topology with a predefined number of cavities. AIAA J 40(4):739–744
Kohn R, Strang G (1986a) Optimal design and relaxation of variational problems (part I). Commun Pure Appl Math 39(1):113–137
Kohn R, Strang G (1986b) Optimal design and relaxation of variational problems (part I). Commun Pure Appl Math 39(2):139–182
Kohn R, Strang G (1986c) Optimal design and relaxation of variational problems (part I). Commun Pure Appl Math 39(3):353–377
Le B, Yvonnet J, He QC (2015) Computational homogenization of nonlinear elastic materials using neural networks. Int J Numer Methods Eng 104(12):1061–1084
Le C, Norato J, Bruns T, Ha C, Tortorelli D (2010) Stress-based topology optimization for continua. Struct Multidiscip Optim 41(4):605–620
Li Q, Steven GP, Xie YM (1999) On equivalence between stress criterion and stiffness criterion in evolutionary structural optimization. Struct Optim 18(1):67–73
Li Q, Steven G, Xie YM (2001) A simple checkerboard suppression algorithm for evolutionary structural optimization. Struct Multidiscip Optim 22(3):230–239
Li Q, Steven GP, Xie YM, Querin OM (2004) Evolutionary topology optimization for temperature reduction of heat conducting fields. Int J Heat Mass Transf 47(23):5071–5083
Li Y, Huang X, Meng F, Zhou S (2016a) Evolutionary topological design for phononic band gap crystals. Struct Multidiscip Optim 54(3):595–617
Li Y, Huang X, Zhou S (2016b) Topological design of cellular phononic band gap crystals. Materials 9(3):186–208
Liu Q, Chan R, Huang X (2016) Concurrent topology optimization of macrostructures and material microstructures for natural frequency. Mater Des 106:380–390
Liu Y, Jin F, Li Q, Zhou S (2008) A fixed-grid bidirectional evolutionary structural optimization method and its applications in tunnelling engineering. Int J Numer Methods Eng 73(12):1788–1810
Luo Z, Wang M, Wang S, Wei P (2008) A level set-based parameterization method for structural shape and topology optimization. Int J Numer Methods Eng 76(1):1–26
Manickarajah D, Xie YM, Steven GP (1998) An evolutionary method for optimization of plate buckling resistance. Finite Elem Anal Des 29(3):205–230
Maute K, Schwarz S, Ramm E (1998) Adaptive topology optimization of elastoplastic structures. Struct Optim 15(2):81–91
McKeown JJ (1997) A note on the equivalence between maximum stiffness and maximum strength trusses. Eng Optim 29(1–4):443–456
Meng F, Huang X, Jia B (2015) Bi-directional evolutionary optimization for photonic band gap structures. J Comput Phys 302:393–404
Meng F, Li S, Lin H, Jia B, Huang X (2016) Topology optimization of photonic structures for all-angle negative refraction. Finite Elem Anal Des 117:46–56
Michel JC, Moulinec H, Suquet P (1999) Effective properties of composite materials with periodic microstructure: a computational approach. Comput Methods Appl Mech Eng 172(1–4):109–143
Michell AGM (1904) Lviii. the limits of economy of material in frame-structures. Lond Edinb Dublin Philos Mag J Sci 8(47):589–597
Munk D, Vio G, Steven GP (2016) A simple alternative formulation for structural optimisation with dynamic and buckling objectives. Struct Multidiscip Optim. doi: 10.1007/s00158-016-1544-9
Neves MM, Rodrigues H, Guedes JM (2000) Optimal design of periodic linear elastic microstructures. Comput Struct 76(1):421–429
Neves MM, Sigmund O, Bendsøe MP (2002) Topology optimization of periodic microstructures with a penalization of highly localized buckling modes. Int J Numer Methods Eng 54(6):809–834
Nguyen T, Ghabraie K, Tran-Cong T (2014) Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour. Comput Geotech 55:57–66
Niu B, Yan J, Cheng G (2009) Optimum structure with homogeneous optimum cellular material for maximum fundamental frequency. Struct Multidiscip Optim 39(2):115–132
Norato JA, Bendsøe MP, Haber RB, Tortorelli DA (2007) A topological derivative method for topology optimization. Struct Multidiscip Optim 33(4–5):375–386
Pedersen N (2000) Maximization of eigenvalues using topology optimization. Struct Multidiscip Optim 20(1):2–11
Pennec Y, Vasseur J, Djafari-Rouhani B, Dobrzyński L, Deymier P (2010) Two-dimensional phononic crystals: examples and applications. Surf Sci Rep 65(8):229–291
Picelli R, Vicente W, Pavanello R (2015a) Bi-directional evolutionary structural optimization for design-dependent fluid pressure loading problems. Eng Optim 47(10):1324–1342
Picelli R, Vicente W, Pavanello R, Xie YM (2015b) Evolutionary topology optimization for natural frequency maximization problems considering acoustic–structure interaction. Finite Elem Anal Des 106:56–64
Picelli R, van Dijk R, Vicente W, Pavanello R, Langelaar M, van Keulen F (2016) Topology optimization for submerged buoyant structures. Eng Optim. doi: 10.1080/0305215X.2016.1164147
Proos K, Steven GP, Querin O, Xie YM (2001) Stiffness and inertia multicriteria evolutionary structural optimisation. Eng Comput 18(7):1031–1054
Querin O, Steven GP, Xie YM (2000a) Evolutionary structural optimisation using an additive algorithm. Finite Elem Anal Des 34(3):291–308
Querin OM (1997) Evolutionary structural optimisation: stress based formulation and implementation. Ph.D. thesis, Department of Aeronautical Engineering, University of Sydney, Australia
Querin OM, Steven GP, Xie YM (1998) Evolutionary structural optimisation (ESO) using a bidirectional algorithm. Eng Comput 15(8):1031–1048
Querin OM, Young V, Steven GP, Xie YM (2000b) Computational efficiency and validation of bi-directional evolutionary structural optimization. Comput Methods Appl Mech Eng 189(2):559–573
Radman A, Huang X, Xie YM (2013a) Topological optimization for the design of microstructures of isotropic cellular materials. Eng Optim 45(11):1331–1348
Radman A, Huang X, Xie YM (2013b) Topology optimization of functionally graded cellular materials. J Mater Sci 48(4):1503–1510
Radman A, Huang X, Xie YM (2014a) Maximizing stiffness of functionally graded materials with prescribed variation of thermal conductivity. Comput Mater Sci 82:457–463
Radman A, Huang X, Xie YM (2014b) Topological design of microstructures of multi-phase materials for maximum stiffness or thermal conductivity. Comput Mater Sci 91:266–273
Ren G, Smith J, Tang J, Xie YM (2005) Underground excavation shape optimization using an evolutionary procedure. Comput Geotech 32(2):122–132
Ren G, Zuo Z, Xie YM, Smith J (2014) Underground excavation shape optimization considering material nonlinearities. Comput Geotech 58:81–87
Rietz A (2001) Sufficiency of a finite exponent in simp (power law) methods. Struct Multidiscip Optim 21(2):159–163
Rozvany G (1972a) Grillages of maximum strength and maximum stiffness. Int J Mech Sci 14(10):651–666
Rozvany G, Zhou M, Sigmund O (1994) Optimization of topology. In: Adeli H (ed) Advances in design optimization. Chapman & Hall, London, pp 340–399
Rozvany GI, Querin OM (2002) Combining ESO with rigorous optimality criteria. Int J Veh Des 28(4):294–299
Rozvany GIN (2009) A critical review of established methods of structural topology optimization. Struct Multidiscip Optim 37(3):217–237
Schwarz S, Maute K, Ramm E (2001) Topology and shape optimization for elastoplastic structural response. Comput Methods Appl Mech Eng 190(15–17):2135–2155
Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163(2):489–528
Sigmund O (1994) Materials with prescribed constitutive parameters: an inverse homogenization problem. Int J Solids Struct 31(17):2313–2329
Sigmund O (1997) On the design of compliant mechanisms using topology optimization. J Struct Mech 25(4):493–524
Sigmund O (2001) A 99 line topology optimization code written in matlab. Struct Multidiscip Optim 21(2):120–127
Sigmund O, Maute K (2013) Topology optimization approaches: a comparative review. Struct Multidiscip Optim 48(6):1031–1055
Sigmund O, Petersson J (1998) Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh-dependencies and local minima. Struct Optim 16(1):68–75
Sigmund O, Torquato S (1997) Design of materials with extreme thermal expansion using a three-phase topology optimization method. J Mech Phys Solids 45(6):1037–1067
Sokolowski J, Zochowski A (1999) On the topological derivative in shape optimization. SIAM J Control Optim 37(4):1251–1272
Steven GP, Li Q, Xie YM (2000) Evolutionary topology and shape design for general physical field problems. Comput Mech 26(2):129–139
Stolpe M, Svanberg K (2001a) An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscip Optim 22(2):116–124
Stolpe M, Svanberg K (2001b) On the trajectories of penalization methods for topology optimization. Struct Multidiscip Optim 21(2):128–139
Su W, Liu S (2010) Size-dependent optimal microstructure design based on couple-stress theory. Struct Multidiscip Optim 42(2):243–254
Tanskanen P (2002) The evolutionary structural optimization method: theoretical aspects. Comput Methods Appl Mech Eng 191(47–48):5485–5498
Theocaris PS, Stavroulaki GE (1999) Optimal material design in composites: an iterative approach based on homogenized cells. Comput Methods Appl Mech Eng 169(1–2):31–42
Van Dijk N, Maute K, Langelaar M, Van Keulen F (2013) Level-set methods for structural topology optimization: a review. Struct Multidiscip Optim 48(3):437–472
Vicente W, Picelli R, Pavanello R, Xie YM (2015) Topology optimization of frequency responses of fluid-structure interaction systems. Finite Elem Anal Des 98:1–13
Vicente W, Zuo Z, Pavanello R, Calixto T, Picelli R, Xie YM (2016) Concurrent topology optimization for minimizing frequency responses of two-level hierarchical structures. Comput Methods Appl Mech Eng 301:116–136
Wadley H, Fleck N, Evans A (2003) Fabrication and structural performance of periodic cellular metal sandwich structures. Compos Sci Technol 63(16):2331–2343
Wang F, Sigmund O, Jensen J (2014a) Design of materials with prescribed nonlinear properties. J Mech Phys Solids 69(1):156–174
Wang MY, Wang X, Guo D (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192(1–2):227–246
Wang Y, Luo Z, Zhang N, Kang Z (2014b) Topological shape optimization of microstructural metamaterials using a level set method. Comput Mater Sci 87:178–186
Xia L (2016) Multiscale structural topology optimization. Elsevier-ISTE, London
Xia L, Breitkopf P (2014a) Concurrent topology optimization design of material and structure within fe$$^{2}$$ nonlinear multiscale analysis framework. Comput Methods Appl Mech Eng 278:524–542
Xia L, Breitkopf P (2014b) A reduced multiscale model for nonlinear structural topology optimization. Comput Methods Appl Mech Eng 280:117–134
Xia L, Breitkopf P (2015a) Design of of materials using topology optimization and energy-based homogenization approach in matlab. Struct Multidiscip Optim 52(6):1229–1241
Xia L, Breitkopf P (2015b) Multiscale structural topology optimization with an approximate constitutive model for local material microstructure. Comput Methods Appl Mech Eng 286:147–167
Xia L, Breitkopf P (2016) Recent advances on topology optimization of multiscale nonlinear structures. Arch Comput Methods Eng. doi: 10.1007/s11831-016-9170-7
Xia L, Raghavan B, Breitkopf P, Zhang W (2013) Numerical material representation using proper orthogonal decomposition and diffuse approximation. Appl Math Comput 224:450–462
Xia L, Fritzen F, Breitkopf P (2016) Evolutionary topology optimization of elastoplastic structures. Struct Multidiscip Optim. doi: 10.1007/s00158-016-1523-1
Xia L, Raghavan B, Breitkopf P (2017) Towards surrogate modeling of material microstructures through the processing variables. Appl Math Comput 294:157–168
Xia Q, Shi T (2016a) Optimization of structures with thin-layer functional device on its surface through a level set based multiple-type boundary method. Comput Methods Appl Mech Eng 311:56–70
Xia Q, Shi T (2016b) Topology optimization of compliant mechanism and its support through a level set method. Comput Methods Appl Mech Eng 305:359–375
Xia Q, Wang M, Wang S, Chen S (2006a) Semi-lagrange method for level-set-based structural topology and shape optimization. Struct Multidiscip Optim 31(6):419–429
Xia Q, Shi T, Wang M (2011) A level set based shape and topology optimization method for maximizing the simple or repeated first eigenvalue of structure vibration. Struct Multidiscip Optim 43(4):473–485
Xia Q, Shi T, Liu S, Wang M (2012) A level set solution to the stress-based structural shape and topology optimization. Comput Struct 90–91:55–64
Xia Q, Wang M, Shi T (2014) A level set method for shape and topology optimization of both structure and support of continuum structures. Comput Methods Appl Mech Eng 272:340–353
Xia Z, Zhang Y, Ellyin F (2003) A unified periodical boundary conditions for representative volume elements of composites and applications. Int J Solids Struct 40(8):1907–1921
Xia Z, Zhou C, Yong Q, Wang X (2006b) On selection of repeated unit cell model and application of unified periodic boundary conditions in micro-mechanical analysis of composites. Int J Solids Struct 43(2):266–278
Xie YM, Steven GP (1992) Shape and layout optimization via an evolutionary procedure. In: Proceedings of the international conference on computational engineering science
Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49(5):885–896
Xie YM, Steven GP (1996) Evolutionary structural optimization for dynamic problems. Comput Struct 58(6):1067–1073
Xie YM, Zuo ZH, Huang X, Rong JH (2012) Convergence of topological patterns of optimal periodic structures under multiple scales. Struct Multidiscip Optim 46(1):41–50
Xie YM, Yang X, Shen J, Yan X, Ghaedizadeh A, Rong J, Huang X, Zhou S (2014) Designing orthotropic materials for negative or zero compressibility. Int J Solids Struct 51(23):4038–4051
Xu B, Xie YM (2015) Concurrent design of composite macrostructure and cellular microstructure under random excitations. Compos Struct 123:65–77
Xu B, Jiang J, Xie YM (2015b) Concurrent design of composite macrostructure and multi-phase material microstructure for minimum dynamic compliance. Compos Struct 128:221–233
Xu B, Huang X, Xie YM (2016a) Two-scale dynamic optimal design of composite structures in the time domain using equivalent static loads. Compos Struct 142:335–345
Xu B, Huang X, Zhou S, Xie YM (2016b) Concurrent topological design of composite thermoelastic macrostructure and microstructure with multi-phase material for maximum stiffness. Compos Struct 150:84–102
Yan X, Huang X, Zha Y, Xie YM (2014) Concurrent topology optimization of structures and their composite microstructures. Comput Struct 133:103–110
Yan X, Huang X, Sun G, Xie YM (2015) Two-scale optimal design of structures with thermal insulation materials. Compos Struct 120:358–365
Yang X, Huang X, Rong J, Xie YM (2013) Design of 3D orthotropic materials with prescribed ratios for effective youngâĂŹs moduli. Comput Mater Sci 67:229–237
Yang XY, Xie YM, Steven GP, Querin OM (1999a) Bidirectional evolutionary method for stiffness optimization. AIAA J 37(11):1483–1488
Yang XY, Xie YM, Steven GP, Querin OM (1999b) Topology optimization for frequencies using an evolutionary method. J Struct Eng 125(12):1432–1438
Yang XY, Xie YM, Liu JS, Parks GT, Clarkson PJ (2002) Perimeter control in the bidirectional evolutionary optimization method. Struct Multidiscip Optim 24(6):430–S440
Yang XY, Xie YM, Steven GP (2005) Evolutionary methods for topology optimisation of continuous structures with design dependent loads. Comput Struct 83(12):956–963
Yi YM, Park SH, Youn SK (2000) Design of microstructures of viscoelastic composites for optimal damping characteristics. Int J Solids Struct 37(35):4791–4810
Yoon G, Kim Y (2007) Topology optimization of material-nonlinear continuum structures by the element connectivity parameterization. Int J Numer Methods Eng 69(10):2196–2218
Young V, Querin OM, Steven GP, Xie YM (1999) 3D and multiple load case bi-directional evolutionary structural optimization (BESO). Struct Optim 18(2–3):183–192
Yvonnet J, Gonzalez D, He QC (2009) Numerically explicit potentials for the homogenization of nonlinear elastic heterogeneous materials. Comput Methods Appl Mech Eng 198(33–36):2723–2737
Yvonnet J, Monteiro E, He QC (2013) Computational homogenization method and reduced database model for hyperelastic heterogeneous structures. Int J Multiscale Comput Eng 11(3):201–225
Zhou M, Rozvany G (2001) On the validity of ESO type methods in topology optimization. Struct Multidiscip Optim 21(1):80–83
Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng 89(1–3):309–336
Zhou S, Cadman J, Chen Y, Li W, Xie YM, Huang X, Appleyard R, Sun G, Li Q (2012) Design and fabrication of biphasic cellular materials with transport properties-a modified bidirectional evolutionary structural optimization procedure and matlab program. Int J Heat Mass Transf 55(25):8149–8162
Zhu J, Zhang W, Qiu K (2007) Bi-directional evolutionary topology optimization using element replaceable method. Comput Mech 40(1):97–109
Zhu J, Zhang W, Xia L (2015) Topology optimization in aircraft and aerospace structures design. Arch Comput Methods Eng. doi: 10.1007/s11831-015-9151-2
Zuo Z, Huang X, Rong J, Xie YM (2013a) Multi-scale design of composite materials and structures for maximum natural frequencies. Mater Des 51:1023–1034
Zuo ZH, Xie YM (2014) Evolutionary topology optimization of continuum structures with a global displacement control. Comput Aided Des 56:58–67
Zuo ZH, Xie YM, Huang X (2010) An improved bi-directional evolutionary topology optimization method for frequencies. Int J Struct Stab Dyn 10(01):55–75