Multi-material topology optimization based on multiple simp of variable density method

• Published in: Journal of mechanical science and technology Vol. 38; no. 2; pp. 749 - 759
• Main Authors: Wan, Changdong, Jiao, Hongyu, Lv, Liang, Lu, Chunyan
• Format: Journal Article
• Language: English
• Published: Seoul Korean Society of Mechanical Engineers 01.02.2024; Springer Nature B.V; 대한기계학회
• Subjects: Control; Density; Dynamical Systems; Engineering; Industrial and Production Engineering; Interpolation; Isotropic material; Iterative methods; Kuhn-Tucker method; Materials selection; Mechanical Engineering; Modulus of elasticity; Optimization; Original Article; Topology optimization; Vibration; 기계공학; Topology optimization; Multiple SIMP; Variable density method; Multi-material
• ISSN: 1738-494X; 1976-3824
• DOI: 10.1007/s12206-024-0124-y

There are many methods for solving the topology optimization problem of single-material. It is a great challenge how to utilize existing methods or make appropriate improvements to solve multi-material topology optimization problems. In this paper, a multiple solid isotropic material with penalization model (SIMP) of variable density method is proposed to solve the problem of multi-material topology optimization. All candidate materials, including void material, are arranged in descending order of elastic modulus. The material conversion scheme of multiple SIMP is based on the elastic modulus of the candidate material after interpolation. The iterative criterion of multi-material topology optimization is derived from the Kuhn-Tucker condition using the guide-weight method. The innovation of this paper is to transform the multi-material topology optimization problem into multiple SIMP of the variable density method. Three examples show that it is effective and moderate to use the proposed method to solve the problem of multi-material topology optimization.