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Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties

Xinqing Li1, Qinghai Zhao1,*, Hongxin Zhang1, Tiezhu Zhang2, Jianliang Chen1

1 College of Mechanical and Electrical Engineering, Qingdao University, Qingdao, 266071, China
2 Power Integration and Energy Storage System Engineering Technology Center, Qingdao University, Qingdao, 266071, China

* Corresponding Author: Qinghai Zhao. Email:

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

Computer Modeling in Engineering & Sciences 2021, 127(2), 683-704.


This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties. To characterize the random-field uncertainties with a reduced set of random variables, the Karhunen-Loève (K-L) expansion is adopted. The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization. Under dividing the design domain, the volume fraction of each preset gradient layer is extracted. Based on the ordered solid isotropic microstructure with penalization (Ordered-SIMP), a functionally graded multi-material interpolation model is formulated by individually optimizing each preset gradient layer. The periodic constraint setting of the gradient layer is achieved by redistributing the average element compliance in sub-regions. Then, the method of moving asymptotes (MMA) is introduced to iteratively update the design variables. Several numerical examples are presented to verify the validity and applicability of the proposed method. The results demonstrate that the periodic functionally graded multi-material topology can be obtained under different numbers of sub-regions, and robust design structures are more stable than that indicated by the deterministic results.


Cite This Article

Li, X., Zhao, Q., Zhang, H., Zhang, T., Chen, J. (2021). Robust Topology Optimization of Periodic Multi-Material Functionally Graded Structures under Loading Uncertainties. CMES-Computer Modeling in Engineering & Sciences, 127(2), 683–704.


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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