A well connected, locally-oriented and efficient multi-scale topology optimization (EMTO) strategy

Multi-scale Topology Optimization (a.k.a. Micro-structural Topology Optimization, MTO) consists in optimizing macro-scale and micro-scale topology simultaneously. MTO could improve structural performance of products significantly. However a few issues related to connectivity between micro-structures and high computational cost have to be addressed, without resulting in loss of performance. In this paper, a new efficient multi-scale topology optimization framework (EMTO) has been developed for this purpose. Connectivity is addressed through adaptive transmission zones which limit loss of performance. A pre-computed database of micro-structures is used to speed up the computing. Design variables have also been chosen carefully and include the orientation of the micro-structures to enhance performance. The method has been successfully tested on two-dimensional compliance optimization problems. The results show significant improvements compared to mono-scale methods (compliance value lower by up to 20% on a simplistic case or 4% on a more realistic case), and also demonstrate the versatility of this method.

[1]  Shiwei Zhou,et al.  Designing orthotropic materials for negative or zero compressibility , 2014 .

[2]  Krishnan Suresh,et al.  A density-and-strain-based K-clustering approach to microstructural topology optimization , 2020 .

[3]  E. Nadaraya On Estimating Regression , 1964 .

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

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

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

[7]  Zhen Liu,et al.  Data-driven design approach to hierarchical hybrid structures with multiple lattice configurations , 2020, Structural and Multidisciplinary Optimization.

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

[9]  Christian Gout,et al.  Structural topology optimization with smoothly varying fiber orientations , 2020 .

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

[11]  J Oliver,et al.  Two‐scale topology optimization in computational material design: An integrated approach , 2018, International journal for numerical methods in engineering.

[12]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[13]  Martin P. Bendsøe,et al.  An Analytical Model to Predict Optimal Material Properties in the Context of Optimal Structural Design , 1994 .

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

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

[16]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of polycrystals , 1962 .

[17]  Shiwei Zhou,et al.  Design of graded two-phase microstructures for tailored elasticity gradients , 2008, Journal of Materials Science.

[18]  Amir A. Zadpoor,et al.  Compatibility in microstructural optimization for additive manufacturing , 2019, Additive Manufacturing.

[19]  Dawei Li,et al.  Anisotropic design and optimization of conformal gradient lattice structures , 2020, Comput. Aided Des..

[20]  Krishnan Suresh,et al.  Spectral decomposition for graded multi-scale topology optimization , 2021 .

[21]  Y. Xie,et al.  A simple evolutionary procedure for structural optimization , 1993 .

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

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

[24]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[25]  O. Sigmund,et al.  Topology optimization of multi-scale structures: a review , 2021, Structural and Multidisciplinary Optimization.

[26]  Julián A. Norato,et al.  Topology optimization with supershapes , 2018, Structural and Multidisciplinary Optimization.

[27]  Jun Xu,et al.  Multiscale topology optimization for non-uniform microstructures with hybrid cellular automata , 2020 .

[28]  Daniel A. White,et al.  Simple, accurate surrogate models of the elastic response of three-dimensional open truss micro-architectures with applications to multiscale topology design , 2019, Structural and Multidisciplinary Optimization.

[29]  Shutian Liu,et al.  Topology optimization design of quasi-periodic cellular structures based on erode–dilate operators , 2021 .

[30]  Gengdong Cheng,et al.  Two-scale concurrent topology optimization with multiple micro materials based on principal stress orientation , 2018 .

[31]  Damiano Pasini,et al.  Multiscale isogeometric topology optimization for lattice materials , 2017 .

[32]  Y. Xie,et al.  Topological design of microstructures of cellular materials for maximum bulk or shear modulus , 2011 .

[33]  Weihong Zhang,et al.  Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures , 2018, Structural and Multidisciplinary Optimization.

[34]  Xiao-Yi Zhou,et al.  A level set shape metamorphosis with mechanical constraints for geometrically graded microstructures , 2019, Structural and Multidisciplinary Optimization.

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

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

[37]  Michael Yu Wang,et al.  Concurrent design with connectable graded microstructures , 2017 .

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

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

[40]  Shaoying Li,et al.  Concurrent design of hierarchical structures with three-dimensional parameterized lattice microstructures for additive manufacturing , 2020 .

[41]  Joseph Morlier,et al.  Generalized Geometry Projection: A Unified Approach for Geometric Feature Based Topology Optimization , 2019, Archives of Computational Methods in Engineering.

[42]  Jakob Andreas Bærentzen,et al.  Singularity aware de-homogenization for high-resolution topology optimized structures , 2020, Structural and Multidisciplinary Optimization.

[43]  Joaquim R. R. A. Martins,et al.  A Python surrogate modeling framework with derivatives , 2019, Adv. Eng. Softw..

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

[45]  Marco Avellaneda,et al.  Optimal bounds and microgeometries for elastic two-phase composites , 1987 .

[46]  Yi Min Xie,et al.  Concurrent topology optimization of structures and their composite microstructures , 2014 .

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

[48]  Rui Xu,et al.  Clustering-based concurrent topology optimization with macrostructure, components, and materials , 2020, Structural and Multidisciplinary Optimization.

[49]  Shuming Gao,et al.  Cellular structure design based on free material optimization under connectivity control , 2020, Comput. Aided Des..

[50]  Ryan Murphy,et al.  Multiscale structural optimization towards three-dimensional printable structures , 2019, Structural and Multidisciplinary Optimization.

[51]  Helder C. Rodrigues,et al.  A hierarchical model for concurrent material and topology optimisation of three-dimensional structures , 2008 .

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

[53]  Z. Kang,et al.  Two-scale concurrent topology optimization of lattice structures with connectable microstructures , 2020 .

[54]  Daniel A. White,et al.  Multiscale topology optimization using neural network surrogate models , 2019, Computer Methods in Applied Mechanics and Engineering.

[55]  Shutian Liu,et al.  Self-connected multi-domain topology optimization of structures with multiple dissimilar microstructures , 2021, Structural and Multidisciplinary Optimization.

[56]  C. S. Jog,et al.  Topology design with optimized, self‐adaptive materials , 1994 .

[57]  Wojciech Matusik,et al.  Two-Scale Topology Optimization with Microstructures , 2017, TOGS.

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

[59]  Gengdong Cheng,et al.  Multi-objective concurrent topology optimization of thermoelastic structures composed of homogeneous porous material , 2013 .

[60]  Grégoire Allaire,et al.  Topology optimization of modulated and oriented periodic microstructures by the homogenization method , 2019, Comput. Math. Appl..