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Multiscale topology optimization (M-TO) entails generating an optimal global topology, and an optimal set of microstructures at a smaller scale, for a physics-constrained problem.
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M. P. Bendsøe · 1989
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Y. M. Xie and G. P. Steven · 1993
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A review of homogenization and topology optimization I - Homogenization theory for media with periodic structure
B. Hassani and E. Hinton · 1998
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Numerical instabilities in topology optimization: A survey on procedures dealing with checkerboards, mesh-dependencies and local minima
O. Sigmund and J. Petersson · 1998
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Bidirectional evolutionary method for stiffness optimization
X. Y. Yang, Y. M. Xei, G. P. Steven, and O. M. Querin · 1999
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Structural Boundary Design via Level Set and Immersed Interface Methods
J. A. Sethian and Andreas Wiegmann · 2000
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Hierarchical optimization of material and structure
H. C. Rodrigues, J. M. Guedes, and M. P. Bendsøe · 2002
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A level set method for structural topology optimization
M.Y. Wang, X. Wang, and D. Guo · 2003
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Topology optimization
M. P. Bendsøe and O. Sigmund · 2004
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Discrete material optimization of general composite shell structures
J. Stegmann and E. Lund · 2005
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Numerical optimization
Jorge Nocedal and Stephen Wright · 2006
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A 199-line Matlab code for Pareto-optimal tracing in topology optimization
K. Suresh · 2010
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A mass constraint formulation for structural topology optimization with multiphase materials
Tong Gao and Weihong Zhang · 2011
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Understanding the exploding gradient problem
Razvan Pascanu, Tomas Mikolov, and Yoshua Bengio · 2012
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Topology optimization approaches: A comparative review
O. Sigmund and K. Maute · 2013
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How to determine composite material properties using numerical homogenization
Erik Andreassen and Casper Schousboe Andreasen · 2014
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Multi-constrained topology optimization via the topological sensitivity
Shiguang Deng and Krishnan Suresh · 2015
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Adam: A method for stochastic optimization
Diederik P. Kingma and Jimmy Lei Ba · 2015
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A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model
W. Zhang, J. Yuan, J. Zhang, and X. Guo · 2016
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Design of lattice structure for additive manufacturing
Wenjin Tao and Ming C. Leu · 2016
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Simultaneous material and structural optimization by multiscale topology optimization
R. Sivapuram, P. D. Dunning, and H. A. Kim · 2016
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Multiscale isogeometric topology optimization for lattice materials
Y. Wang, H. Xu, and D. Pasini · 2017
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Two-scale concurrent topology optimization with multiple micro materials based on principal stress direction
Liang Xu and Gengdong Cheng · 2017
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Searching for activation functions
Prajit Ramachandran, Barret Zoph, and Quoc V Le · 2017
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Design of graded lattice structure with optimized mesostructures for additive manufacturing
Y. Wang, L. Zhang, S. Daynes, H. Zhang, S. Feih, and M. Y. Wang · 2018
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Functionally graded porous scaffolds in multiple patterns: New design method, physical and mechanical properties
Fei Liu, Zhongfa Mao, Peng Zhang, David Z. Zhang, Junjie Jiang, and Zhibo Ma · 2018
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Data-driven design approach to hierarchical hybrid structures with multiple lattice configurations
Zhen Liu, Liang Xia, Qi Xia, and Tielin Shi · 2020
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An efficient multiscale optimization method for conformal lattice materials
Tongyu Wu and Shu Li · 2021
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Stress-constrained optimization using graded lattice microstructures
Dilaksan Thillaithevan, Paul Bruce, and Matthew Santer · 2021
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Optimal and continuous multilattice embedding
ED Sanders, A Pereira, and GH Paulino · 2021
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Multiscale design of functionally graded cellular structures for additive manufacturing using level-set descriptions
Cong Hong Phong Nguyen and Young Choi · 2021
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Data-driven topology optimization with multiclass microstructures using latent variable gaussian process
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Multiscale concurrent topology optimization for cellular structures with multiple microstructures based on ordered SIMP interpolation
Y. Zhang, M. Xiao, H. Li, L. Gao, and S. Chu · 2018
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Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures
C. Wang, J. H. Zhu, W. H. Zhang, S. Y. Li, and J. Kong · 2018
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Multi-material continuum topology optimization with arbitrary volume and mass constraints
Emily D. Sanders, Miguel A. Aguiló, and Glaucio H. Paulino · 2018
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Multi-material continuum topology optimization with arbitrary volume and mass constraints
Emily D. Sanders, Miguel A. Aguiló, and Glaucio H. Paulino · 2018
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JAX: composable transformations of Python+NumPy programs, 2018
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang · 2018
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On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing
Lin Cheng, Xuan Liang, Jiaxi Bai, Qian Chen, John Lemon, and Albert To · 2019
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Design and Optimization of Graded Cellular Structures with Triply Periodic Level Surface-Based Topological Shapes
Dawei Li, Ning Dai, Yunlong Tang, Guoying Dong, and Yaoyao Fiona Zhao · 2019
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Liwei Wang, Siyu Tao, Ping Zhu, and Wei Chen · 2021
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Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy
Li Zheng, Siddhant Kumar, and Dennis M Kochmann · 2021
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Tounn: topology optimization using neural networks
Aaditya Chandrasekhar and Krishnan Suresh · 2021
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Multi-material topology optimization using neural networks
Aaditya Chandrasekhar and Krishnan Suresh · 2021
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Spectral decomposition for graded multi-scale topology optimization
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Auto: a framework for automatic differentiation in topology optimization
Aaditya Chandrasekhar, Saketh Sridhara, and Krishnan Suresh · 2021
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Multiscale optimisation of resonant frequencies for lattice-based additive manufactured structures
Morgan Nightingale, Robert Hewson, and Matthew Santer · 2021
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An improved ordered simp approach for multiscale concurrent topology optimization with multiple microstructures
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Hierarchical structure optimization with parameterized lattice and multiscale finite element method
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Optimally-tailored spinodal architected materials for multiscale design and manufacturing
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Stress-constrained multiscale topology optimization with connectable graded microstructures using the worst-case analysis
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Data-driven multiscale design of cellular composites with multiclass microstructures for natural frequency maximization
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Improving connectivity and accelerating multiscale topology optimization using deep neural network techniques
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Design of cellular materials for multiscale topology optimization: application to patient-specific orthopedic devices
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