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Reliability‐based topology optimization against geometric imperfections with random threshold model
Author(s) -
Kang Zhan,
Liu Peishuo
Publication year - 2018
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5797
Subject(s) - polynomial chaos , topology optimization , monte carlo method , reliability (semiconductor) , mathematical optimization , random field , mathematics , transformation (genetics) , topology (electrical circuits) , random variable , projection (relational algebra) , gaussian , algorithm , finite element method , engineering , structural engineering , power (physics) , statistics , physics , biochemistry , chemistry , quantum mechanics , combinatorics , gene
Summary This paper develops a new reliability‐based topology optimization framework considering spatially varying geometric uncertainties. Geometric imperfections arising from manufacturing errors are modeled with a random threshold model. The projection threshold is represented by a memoryless transformation of a Gaussian random field, which is then discretized by means of the expansion optimal linear estimation. The structural response and their sensitivities are evaluated with the polynomial chaos expansion, and the accuracy of the proposed method is verified by Monte Carlo simulations. The performance measure approach is adopted to tackle the reliability constraints in the reliability‐based topology optimization problem. The optimized designs obtained with the present method are compared with the deterministic solutions and the reliability‐based design considering random variables. Numerical examples demonstrate the efficiency of the proposed method.