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

Jun Yan1,2, Qianqian Sui1, Zhirui Fan1, Zunyi Duan3,*
1 State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology, Dalian, 116024, China
2 Ningbo Research Institute of Dalian University of Technology, Ningbo, 315016, China
3 Institute of Structural Health Monitoring and Control, School of Mechanics, Civil Engineering & Architecture, Northwestern Polytechnical University, Xi'an, 710072, China
* Corresponding Author: Zunyi Duan. Email:
(This article belongs to this Special Issue: New Trends in Structural Optimization)

Computer Modeling in Engineering & Sciences 2022, 130(2), 967-986.

Received 05 June 2021; Accepted 24 August 2021; Issue published 13 December 2021


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.


Multi-material design optimization; thermoelastic lattice structure; multiscale topology optimization; mass constraint; strain energy

Cite This Article

Yan, J., Sui, Q., Fan, Z., Duan, Z. (2022). Multi-Material and Multiscale Topology Design Optimization of Thermoelastic Lattice Structures. CMES-Computer Modeling in Engineering & Sciences, 130(2), 967–986.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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