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论文类型：期刊论文

发表时间：2017-04-06

发表刊物：INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING

收录刊物：SCIE、EI、Scopus

卷号：110

期号：1

页面范围：31-56

ISSN号：0029-5981

关键字：geometric uncertainties; level set; polynomial chaos; shape sensitivity; robust shape; topology optimization

摘要：When geometric uncertainties arising from manufacturing errors are comparable with the characteristic length or the product responses are sensitive to such uncertainties, the products of deterministic design cannot perform robustly. This paper presents a new level set-based framework for robust shape and topology optimization against geometric uncertainties. We first propose a stochastic level set perturbation model of uncertain topology/shape to characterize manufacturing errors in conjunction with Karhunen-Loeve (K-L) expansion. We then utilize polynomial chaos expansion to implement the stochastic response analysis. In this context, the mathematical formulation of the considered robust shape and topology optimization problem is developed, and the adjoint-variable shape sensitivity scheme is derived. An advantage of this method is that relatively large shape variations and even topological changes can be accounted for with desired accuracy and efficiency. Numerical examples are given to demonstrate the validity of the present formulation and numerical techniques. In particular, this method is justified by the observations in minimum compliance problems, where slender bars vanish when the manufacturing errors become comparable with the characteristic length of the structures. Copyright (c) 2016 John Wiley & Sons, Ltd.