Open Access

ARTICLE

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

Xinqing Li¹, Qinghai Zhao^1,*, 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 the Special Issue: Novel Methods of Topology Optimization and Engineering Applications)

Computer Modeling in Engineering & Sciences 2021, 127(2), 683-704. https://doi.org/10.32604/cmes.2021.015685

Received 04 January 2021; Accepted 24 February 2021; Issue published 19 April 2021

Abstract

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.

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Citations