期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 370, 期 -, 页码 -出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2020.112976
关键词
Multi-material topology optimization; Hyperelastic materials; Large deformations; ZPR update scheme; Virtual Element Method (VEM); Adaptive refinement and coarsening
资金
- University of Illinois at UrbanaChampaign, United States
- Raymond Allen Jones Chair at the Georgia Institute of Technology, United States
We introduce a general multi-material topology optimization framework for large deformation problems that effectively handles an arbitrary number of candidate hyperelastic materials and addresses three major associated challenges: material interpolation, excessive distortion of low-density elements, and computational efficiency. To account for many nonlinear elastic materials, we propose a material interpolation scheme that, instead of interpolating multiple material parameters (such as Young's modulus), interpolates multiple nonlinear stored-energy functions. To circumvent convergence difficulties caused by excessive distortions of low-density elements under large deformations, an energy interpolation scheme is revisited to account for multiple candidate hyperelastic materials. Computational efficiency is addressed from both structural analysis and optimization perspectives. To solve the nonlinear state equations efficiently, we employ the lower-order Virtual Element Method in conjunction with tailored adaptive mesh refinement and coarsening strategies. To efficiently update the design variables of the multi-material system, we exploit the separable nature and improve the ZPR (Zhang-Paulino-Ramos) update scheme to account for positive sensitivities and update the design variables associated with each volume constraint in parallel. Four design examples with three types of nonlinear material models demonstrate the efficiency and effectiveness of the proposed framework. (C) 2020 Elsevier B.V. All rights reserved.
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