Topology Optimization of Periodic Structures With Substructuring

[1]  Z. Kang,et al.  Topological shape optimization of microstructural metamaterials using a level set method , 2014 .

[2]  Qi Xia,et al.  Bi-directional Evolutionary Structural Optimization on Advanced Structures and Materials: A Comprehensive Review , 2016, Archives of Computational Methods in Engineering.

[3]  J. Petersson,et al.  Large-scale topology optimization in 3D using parallel computing , 2001 .

[4]  Peter D. Dunning,et al.  Introducing the sequential linear programming level-set method for topology optimization , 2015 .

[5]  Xiao Wang,et al.  Topology optimization of multi-material negative Poisson's ratio metamaterials using a reconciled level set method , 2017, Comput. Aided Des..

[6]  O. Sigmund Materials with prescribed constitutive parameters: An inverse homogenization problem , 1994 .

[7]  Weihong Zhang,et al.  Scale‐related topology optimization of cellular materials and structures , 2006 .

[8]  Xiaoming Wang,et al.  A level set method for structural topology optimization , 2003 .

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

[10]  Gengdong Cheng,et al.  Multi-scale concurrent material and structural design under mechanical and thermal loads , 2016 .

[11]  P. Breitkopf,et al.  Design of materials using topology optimization and energy-based homogenization approach in Matlab , 2015 .

[12]  H. Rodrigues,et al.  Hierarchical optimization of material and structure , 2002 .

[13]  Xianmin Zhang,et al.  A level set method with a bounded diffusion for structural topology optimization , 2018 .

[14]  O. Sigmund,et al.  Topology optimization approaches , 2013, Structural and Multidisciplinary Optimization.

[15]  Tielin Shi,et al.  Topology optimization of hierarchical lattice structures with substructuring , 2019, Computer Methods in Applied Mechanics and Engineering.

[16]  Shiwei Zhou,et al.  On design of multi-functional microstructural materials , 2012, Journal of Materials Science.

[17]  M. Wang,et al.  Structure-material integrated design by level sets , 2016 .

[18]  P. Breitkopf,et al.  Multiscale structural topology optimization with an approximate constitutive model for local material microstructure , 2015 .

[19]  Yi Min Xie,et al.  Convergence of topological patterns of optimal periodic structures under multiple scales , 2012 .

[20]  Xiangyang Cui,et al.  Concurrent topological design of composite structures and the underlying multi-phase materials , 2017 .

[21]  Zhen Luo,et al.  Shape and topology optimization for electrothermomechanical microactuators using level set methods , 2009, J. Comput. Phys..

[22]  Chang Liu,et al.  An efficient moving morphable component (MMC)-based approach for multi-resolution topology optimization , 2018, Structural and Multidisciplinary Optimization.

[23]  Xu Guo,et al.  Explicit three dimensional topology optimization via Moving Morphable Void (MMV) approach , 2017, 1704.06060.

[24]  Liping Chen,et al.  A semi-implicit level set method for structural shape and topology optimization , 2008, J. Comput. Phys..

[25]  Zongliang Du,et al.  Connecting Microstructures for Multiscale Topology Optimization With Connectivity Index Constraints , 2018, Journal of Mechanical Design.

[26]  Liang Gao,et al.  Topology optimization for functionally graded cellular composites with metamaterials by level sets , 2018 .

[27]  Peter D. Dunning,et al.  Simultaneous material and structural optimization by multiscale topology optimization , 2016 .

[28]  O. Sigmund,et al.  Higher‐order multi‐resolution topology optimization using the finite cell method , 2017 .

[29]  James K. Guest,et al.  Design of maximum permeability material structures , 2007 .

[30]  Gengdong Cheng,et al.  Optimum structure with homogeneous optimum truss-like material , 2008 .

[31]  Yi Min Xie,et al.  Reinventing the Wheel , 2011 .

[32]  E. Hinton,et al.  A review of homogenization and topology optimization I- homogenization theory for media with periodic structure , 1998 .

[33]  S. Torquato,et al.  Design of materials with extreme thermal expansion using a three-phase topology optimization method , 1997 .

[34]  M. Wang,et al.  Semi-Lagrange method for level-set-based structural topology and shape optimization , 2006 .

[35]  Holger Wendland,et al.  Scattered Data Approximation: Conditionally positive definite functions , 2004 .

[36]  Casper Schousboe Andreasen,et al.  How to determine composite material properties using numerical homogenization , 2014 .

[37]  Jakob S. Jensen,et al.  Topology Optimized Architectures with Programmable Poisson's Ratio over Large Deformations , 2015, Advanced materials.

[38]  Xu Guo,et al.  A novel asymptotic-analysis-based homogenisation approach towards fast design of infill graded microstructures , 2019, Journal of the Mechanics and Physics of Solids.

[39]  G. Allaire,et al.  Structural optimization using sensitivity analysis and a level-set method , 2004 .

[40]  Xu Guo,et al.  Doing Topology Optimization Explicitly and Geometrically—A New Moving Morphable Components Based Framework , 2014 .

[41]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[42]  Shiwei Zhou,et al.  Topology optimization of microstructures of cellular materials and composites for macrostructures , 2013 .

[43]  Anders Clausen,et al.  Efficient topology optimization in MATLAB using 88 lines of code , 2011 .

[44]  Y. Xie,et al.  Comparing optimal material microstructures with optimal periodic structures , 2013 .

[45]  Yi Min Xie,et al.  Optimal design of periodic structures using evolutionary topology optimization , 2008 .

[46]  K. Svanberg The method of moving asymptotes—a new method for structural optimization , 1987 .

[47]  Liang Gao,et al.  Topology optimization for concurrent design of structures with multi-patch microstructures by level sets , 2018 .

[48]  R. Guyan Reduction of stiffness and mass matrices , 1965 .

[49]  Julien Yvonnet,et al.  A consistent nonlocal scheme based on filters for the homogenization of heterogeneous linear materials with non-separated scales , 2014 .

[50]  Boyan S. Lazarov,et al.  Robust topology optimisation of microstructural details without length scale separation - using a spectral coarse basis preconditioner , 2014, ArXiv.

[51]  Yi Min Xie,et al.  Evolutionary Topology Optimization of Continuum Structures: Methods and Applications , 2010 .

[52]  Kurt Maute,et al.  Level-set methods for structural topology optimization: a review , 2013 .

[53]  P. Breitkopf,et al.  Concurrent topology optimization design of material and structure within FE2 nonlinear multiscale analysis framework , 2014 .

[54]  Z. Kang,et al.  A level set method for structural shape and topology optimization using radial basis functions , 2009 .

[55]  Adedeji Aremu,et al.  A voxel-based method of constructing and skinning conformal and functionally graded lattice structures suitable for additive manufacturing , 2017 .

[56]  Ole Sigmund,et al.  Homogenization‐based topology optimization for high‐resolution manufacturable microstructures , 2018 .

[57]  Xu Guo,et al.  Additive manufacturing oriented design of graded lattice structures through explicit topology optimization , 2017 .

[58]  Takayuki Yamada,et al.  A Level Set-Based Topology Optimization Method for Maximizing Thermal Diffusivity in Problems Including Design-Dependent Effects , 2011 .

[59]  Liang Gao,et al.  Design of shell-infill structures by a multiscale level set topology optimization method , 2019, Computers & Structures.

[60]  M. Bendsøe,et al.  Topology Optimization: "Theory, Methods, And Applications" , 2011 .