Jun Yan^1,2, Qianqian Sui¹, Zhirui Fan¹, Zunyi Duan^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 967-986, 2022, DOI:10.32604/cmes.2022.017708

Abstract This study establishes a multiscale and multi-material topology optimization model for thermoelastic lattice structures (TLSs) considering mechanical and thermal loading based on the Extended Multiscale Finite Element Method (EMsFEM). The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint, respectively. The Solid Isotropic Material with Penalization (SIMP) interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure. The modified volume preserving Heaviside function (VPHF) is utilized to obtain a clear 0/1 material of truss microstructure. Compared with the classic topology optimization of single-material TLSs,… More >

Baoshou Liu^1,2, Xiaolei Yan¹, Yangfan Li³, Shiwei Zhou⁴, Xiaodong Huang^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 523-540, 2021, DOI:10.32604/cmes.2021.017211

Abstract This paper proposes a new element-based multi-material topology optimization algorithm using a single variable for minimizing compliance subject to a mass constraint. A single variable based on the normalized elemental density is used to overcome the occurrence of meaningless design variables and save computational cost. Different from the traditional material penalization scheme, the algorithm is established on the ordered ersatz material model, which linearly interpolates Young's modulus for relaxed design variables. To achieve a multi-material design, the multiple floating projection constraints are adopted to gradually push elemental design variables to multiple discrete values. For the convergent element-based solution, the multiple… More >