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Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints

Lianxiong Chen1, Hui Liu1,*, Xihua Chu1,2, Jiao Wang3

1 Department of Engineering Mechanics, School of Civil Engineering, Wuhan University, Wuhan, 430072, China
2 State Key Laboratory for Structural Analysis of Industrial Equipment, Dalian University of Technology, Dalian, 116024, China
3 School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu, 611756, China

* Corresponding Author: Hui Liu. Email:

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

Computer Modeling in Engineering & Sciences 2021, 128(3), 1197-1218.


Functional graded cellular structure (FGCS) usually shows superior mechanical behavior with low density and high stiffness. With the development of additive manufacturing, functional graded cellular structure gains its popularity in industries. In this paper, a novel approach for designing functionally graded cellular structure is proposed based on a subdomain parameterized level set method (PLSM) under local volume constraints (LVC). In this method, a subdomain level set function is defined, parameterized and updated on each subdomain independently making the proposed approach much faster and more cost-effective. Additionally, the microstructures on arbitrary two adjacent subdomains can be connected perfectly without any additional constraint. Furthermore, the local volume constraint for each subdomain is applied by virtue of the augmented Lagrange multiplier method. Finally, several numerical examples are given to verify the correctness and effectiveness of the proposed approach in designing the functionally graded cellular structure. From the optimized results, it is also found that the number of local volume constraints has little influence on the convergence speed of the developed approach.


Cite This Article

Chen, L., Liu, H., Chu, X., Wang, J. (2021). Functionally Graded Cellular Structure Design Using the Subdomain Level Set Method with Local Volume Constraints. CMES-Computer Modeling in Engineering & Sciences, 128(3), 1197–1218.


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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