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Micro‐macro concurrent topology optimization for nonlinear solids with a decoupling multiscale analysis
Author(s) -
Kato Junji,
Yachi Daishun,
Kyoya Takashi,
Terada Kenjiro
Publication year - 2017
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5571
Subject(s) - homogenization (climate) , microscale chemistry , nonlinear system , topology optimization , isotropy , hyperelastic material , decoupling (probability) , boundary value problem , computer science , topology (electrical circuits) , mathematical optimization , finite element method , mathematics , structural engineering , mathematical analysis , engineering , physics , control engineering , biodiversity , ecology , mathematics education , quantum mechanics , combinatorics , biology
Summary The present study proposes a method of micro‐macro concurrent topology optimization for a two‐phase nonlinear solid to minimize the end compliance of its macrostructure undergoing large deformation. To reduce the computational costs to solve a 2‐scale boundary value problem under geometrically nonlinear setting, we use the so‐called method of decoupling multiscale structural analysis , in which the microscopic and macroscopic boundary value problems are decoupled in the homogenization process. An isotropic hyperelasticity model is used for the constitutive model for microstructures, while an orthotropic one is assumed to represent the macroscopic material behavior. Owing to this decoupling framework, the micro‐macro concurrent optimization problem can be split into 2 individual problems at the microscale and macroscale for the sake of algorithmic simplicity. Also, a 2‐scale adjoint sensitivity analysis can be performed within the framework of computational homogenization. It is verified from a series numerical examples that the proposed method is capable of computing the optimal structures at both microscale and macroscale, according to the level of applied load.