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An Efficient Method for Topology Optimization of Continuum Structures in the Presence of Uncertainty in Loading Direction

Jie Liu

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China

Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, Australia

E-mail Address: jliu@hnu.edu.cn

E-mail Address: jie.liu@rmit.edu.au

Corresponding author.

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Guilin Wen

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China

E-mail Address: glwen@hnu.edu.cn

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Qixiang Qing

State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha, China

E-mail Address: qixiangen@163.com

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, and

Yi Min Xie

Centre for Innovative Structures and Materials, School of Engineering, RMIT University, Melbourne, Australia

XIE Archi-Structure Design (Shanghai) Co., Ltd., Shanghai 200433, P. R. China

E-mail Address: mike.xie@rmit.edu.au

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https://doi.org/10.1142/S0219876217500542Cited by:21 (Source: Crossref)

Abstract

This paper presents a simple yet efficient method for the topology optimization of continuum structures considering interval uncertainties in loading directions. Interval mathematics is employed to equivalently transform the uncertain topology optimization problem into a deterministic one with multiple load cases. An efficient soft-kill bi-directional evolutionary structural optimization (BESO) method is proposed to solve the problem, which only requires two finite element analyses per iteration for each external load with directional uncertainty regardless of the number of the multiple load cases. The presented algorithm leads to significant computational savings when compared with Monte Carlo-based optimization (MCBO) algorithms. A series of numerical examples including symmetric and nonsymmetric loading variations demonstrate the considerable improvement of computational efficiency of the proposed approach as well as the significance of including uncertainties in topology optimization when to design a structure. Optimums obtained from the proposed algorithm are verified by MCBO method.

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