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Multi-Material Topology Optimization of Structures Using an Ordered Ersatz Material Model

Baoshou Liu1,2, Xiaolei Yan1, Yangfan Li3, Shiwei Zhou4, Xiaodong Huang3,*

1 Fujian Key Laboratory of Automotive Electronics and Electric Drive, Fujian University of Technology, Fuzhou, 350118, China
2 Key Laboratory of Advanced Technology for Vehicle Body Design & Manufacture, Hunan University, Changsha, 410082, China
3 Faculty of Science, Engineering and Technology, Swinburne University of Technology, Melbourne, VIC 3122, Australia
4 Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, VIC 3001, Australia

* Corresponding Author: Xiaodong Huang. Email:

(This article belongs to this Special Issue: Novel Methods of Topology Optimization and Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 128(2), 523-540.


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 level-set functions are constructed to tentatively extract the smooth interface between two adjacent materials. Some 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed algorithm and the possible advantage of the multi-material designs over the traditional solid-void designs.


Cite This Article

Liu, B., Yan, X., Li, Y., Zhou, S., Huang, X. (2021). Multi-Material Topology Optimization of Structures Using an Ordered Ersatz Material Model. CMES-Computer Modeling in Engineering & Sciences, 128(2), 523–540.

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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