On structural topology optimization considering material nonlinearity: Plane strain versus plane stress solutions

[1]  L. Armijo.  Minimization of functions having Lipschitz continuous first partial derivatives. , 1966 .

[2]  R. Ogden.  Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solids , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[4]  Ray W. Ogden,et al.  Nonlinear Elastic Deformations , 1985 .

[5]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[6]  R. Haftka,et al.  Simultaneous nonlinear structural analysis and design , 1989 .

[7]  M. Zhou,et al.  Generalized shape optimization without homogenization , 1992 .

[8]  J. E. Taylor,et al.  A global extremum principle for the analysis of solids composed of softening material , 1993 .

[9]  J. E. Taylor,et al.  Analysis and design of trussed structures made of elastic/stiffening materials , 1994 .

[10]  J. Taylor.  A Global Extremum Principle in Mixed Form for Equilibrium Analysis With Elastic/Stiffening Materials (a Generalized Minimum Potential Energy Principle) , 1994 .

[11]  Wolfgang Achtziger.  Truss topology optimization including bar properties different for tension and compression , 1996 .

[12]  W. Achtziger,et al.  Topology Optimization of Discrete Structures , 1997 .

[13]  G. Allaire,et al.  Shape optimization by the homogenization method , 1997 .

[14]  R. D. Wood,et al.  Nonlinear Continuum Mechanics for Finite Element Analysis , 1997 .

[15]  G. Allaire,et al.  Existence of minimizers for non-quasiconvex functionals arising in optimal design , 1998 .

[16]  J. Petersson,et al.  Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima , 1998 .

[17]  P. Podersen,et al.  Some general optimal design results using anisotropic, power law nonlinear elasticity , 1998 .

[18]  M. Bendsøe,et al.  Material interpolation schemes in topology optimization , 1999 .

[19]  Hong Guan,et al.  Evolutionary Structural Optimisation Incorporating Tension and Compression Materials , 1999 .

[20]  O. Sigmund,et al.  Stiffness design of geometrically nonlinear structures using topology optimization , 2000 .

[21]  B. Bourdin.  Filters in topology optimization , 2001 .

[22]  Hirohisa Noguchi,et al.  Homologous topology optimization in large displacement and buckling problems , 2001 .

[23]  A. Chambolle,et al.  Design-dependent loads in topology optimization , 2003 .

[24]  E. Ramm,et al.  Large deformations and stability in topology optimization , 2005 .

[25]  Y. Kim,et al.  Element connectivity parameterization for topology optimization of geometrically nonlinear structures , 2005 .

[26]  Qi-Chang He,et al.  Finite deformations of Ogden's materials under impact loading , 2006 .

[27]  P. Wriggers.  Nonlinear Finite Element Methods , 2008 .

[28]  Atsushi Kawamoto,et al.  Stabilization of geometrically nonlinear topology optimization by the Levenberg–Marquardt method , 2009 .

[29]  M. Dambrine,et al.  ON THE ERSATZ MATERIAL APPROXIMATION IN LEVEL-SET METHODS , 2010 .

[30]  Osvaldo M. Querin,et al.  Topology optimization of truss-like continua with different material properties in tension and compression , 2010 .

[31]  Kun Cai,et al.  A simple approach to find optimal topology of a continuum with tension-only or compression-only material , 2011 .

[32]  Shutian Liu,et al.  Topology optimization of continuum structures with different tensile and compressive properties in bridge layout design , 2011 .

[33]  G. Paulino,et al.  PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab , 2012 .

[34]  A. Klarbring,et al.  A note on the min-max formulation of stiffness optimization including non-zero prescribed displacements , 2012 .

[35]  E. Wachspress,et al.  A Rational Finite Element Basis , 1975 .

[36]  Glaucio H. Paulino,et al.  PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes , 2012 .

[37]  E. A. de Souza Neto,et al.  Topological derivative-based topology optimization of structures subject to Drucker–Prager stress constraints , 2012 .

[38]  A simplified approach to the topology optimization of structures in case of unilateral material/supports , 2013 .

[39]  A. Klarbring,et al.  Topology optimization of hyperelastic bodies including non-zero prescribed displacements , 2013 .

[40]  Fred van Keulen,et al.  Element deformation scaling for robust geometrically nonlinear analyses in topology optimization , 2014 .

[41]  Glaucio H. Paulino,et al.  Convex topology optimization for hyperelastic trusses based on the ground-structure approach , 2015 .

[42]  Jakob S. Jensen,et al.  Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems , 2014 .

[43]  Z. Kang,et al.  Topology optimization of geometrically nonlinear structures based on an additive hyperelasticity technique , 2015 .

[44]  Glaucio H. Paulino,et al.  Polygonal finite elements for finite elasticity , 2015 .

[45]  Jiao Shi,et al.  Optimal layout of multiple bi-modulus materials , 2016 .

[46]  G. Paulino,et al.  A paradigm for higher-order polygonal elements in finite elasticity using a gradient correction scheme , 2016 .

[47]  Adeildo S. Ramos,et al.  Material nonlinear topology optimization using the ground structure method with a discrete filtering scheme , 2017 .

[48]  Glaucio H. Paulino,et al.  Multi-material topology optimization with multiple volume constraints: a general approach applied to ground structures with material nonlinearity , 2017, Structural and Multidisciplinary Optimization.

[49]  Xu Guo,et al.  Structural topology optimization involving bi-modulus materials with asymmetric properties in tension and compression , 2018, Computational Mechanics.

[50]  K. Schittkowski,et al.  NONLINEAR PROGRAMMING , 2022 .