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, 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.
Highlights
Analysis and design of thermoelastic structures are an important part of structural design in many mechanical and aerospace engineering applications
Comparing the actual total mass fraction with the constrained total mass fraction, we found that the total mass constraint is not active when the constrained mass fraction is larger than 0.50 in this example
A multiscale and multi-material topology design optimization model of thermoelastic lattice structures (TLSs) subjected to mechanical and thermal loading based on the Extended Multiscale Finite Element Method (EMsFEM) is established in this research
Summary
Analysis and design of thermoelastic structures are an important part of structural design in many mechanical and aerospace engineering applications. Deng et al [7] investigated a multi-objective topology design optimization of the thermoelastic structure. Sigmund et al [16] studied the topology design optimization of three-phase material structures using the SIMP interpolation scheme. The concurrent multiscale optimization of theTLS subjected to thermal and mechanical loads by using the EMsFEM was provided by Yan et al [34,35]. Multiscale topology design optimization of TLSs based on clustering method was proposed by Yan et al [36]. There are few studies on multi-material TLSs. By using the same analysis method, the multiscale design optimization of the multi-material TLSs is achieved in the paper.
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