Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures

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, multi-material topology optimization can get a better structural design of the TLS. The effects of temperatures, size factor, and mass fraction on optimization results have been presented and discussed in the numerical examples.