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Mathematical Problems in Engineering
Volume 2015, Article ID 580980, 14 pages
Research Article

Robust Topology Optimization Based on Stochastic Collocation Methods under Loading Uncertainties

1Collaborative Innovation Center of Electric Vehicles in Beijing, School of Mechanical Engineering, Beijing Institute of Technology, Beijing 100081, China
2Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48105, USA

Received 14 May 2015; Revised 9 July 2015; Accepted 9 July 2015

Academic Editor: Domenico Mundo

Copyright © 2015 Qinghai Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A robust topology optimization (RTO) approach with consideration of loading uncertainties is developed in this paper. The stochastic collocation method combined with full tensor product grid and Smolyak sparse grid transforms the robust formulation into a weighted multiple loading deterministic problem at the collocation points. The proposed approach is amenable to implementation in existing commercial topology optimization software package and thus feasible to practical engineering problems. Numerical examples of two- and three-dimensional topology optimization problems are provided to demonstrate the proposed RTO approach and its applications. The optimal topologies obtained from deterministic and robust topology optimization designs under tensor product grid and sparse grid with different levels are compared with one another to investigate the pros and cons of optimization algorithm on final topologies, and an extensive Monte Carlo simulation is also performed to verify the proposed approach.