Topology optimization under uncertainty via non-intrusive polynomial chaos expansion

Keshavarzzadeh, Vahid; Fernandez, Felipe; Tortorelli, Daniel A.

doi:10.1016/j.cma.2017.01.019

Title: Topology optimization under uncertainty via non-intrusive polynomial chaos expansion

Journal Article · Thu Jan 26 00:00:00 EST 2017 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2017.01.019· OSTI ID:1632374

Keshavarzzadeh, Vahid ^[1]; Fernandez, Felipe ^[1]; Tortorelli, Daniel A. ^[2]

Univ. of Illinois at Urbana-Champaign, IL (United States)
Univ. of Illinois at Urbana-Champaign, IL (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Design and Optimization

This paper presents a systematic approach for topology optimization under uncertainty that integrates non-intrusive polynomial chaos expansion with design sensitivity analysis for reliability-based and robust topology optimization. Uncertainty is introduced in loading and in geometry to address the manufacturing variability. The manufacturing variability is modeled via a thresholding technique in which the threshold field is represented by a reduced dimensional random field. Response metrics such as compliance and volume are characterized as polynomial chaos expansions of the underlying uncertain parameters thus allowing accurate and efficient estimation of statistical moments, failure probabilities and their sensitivities. The number of simulations is reduced for linear structures under loading uncertainty by means of superposition. Efficiency of the non-intrusive polynomial chaos approach is highlighted by comparison with the Monte Carlo method in terms of the number of simulations. To demonstrate the effect of uncertainty, optimized designs that consider uncertainty are compared to those that do not. Finally, comparisons of polynomial chaos expansion to existing analytical methods on a benchmark numerical example are also provided for reliability-based and worst case designs.

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Research Organization:: Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); George B. Grim Professorship

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1632374

Report Number(s):: LLNL-JRNL-801458; 1004619

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 318, Issue C; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 68 works

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Robust multiphase topology optimization accounting for manufacturing uncertainty via stochastic collocation Keshavarzzadeh, Vahid; James, Kai A. Structural and Multidisciplinary Optimization, Vol. 60, Issue 6 https://doi.org/10.1007/s00158-019-02333-4	journal	July 2019
Current and future trends in topology optimization for additive manufacturing Liu, Jikai; Gaynor, Andrew T.; Chen, Shikui Structural and Multidisciplinary Optimization, Vol. 57, Issue 6 https://doi.org/10.1007/s00158-018-1994-3	journal	May 2018
Robust topology optimization of phononic crystals with random field uncertainty Zhang, Xiaopeng; He, Jingjie; Takezawa, Akihiro International Journal for Numerical Methods in Engineering, Vol. 115, Issue 9 https://doi.org/10.1002/nme.5839	journal	May 2018
Reliability-based topology optimization of continuum structures subject to local stress constraints da Silva, Gustavo Assis; Beck, André Teófilo Structural and Multidisciplinary Optimization, Vol. 57, Issue 6 https://doi.org/10.1007/s00158-017-1865-3	journal	November 2017
A gradient-based uncertainty optimization framework utilizing dimensional adaptive polynomial chaos expansion Fang, Hai; Gong, Chunlin; Su, Hua Structural and Multidisciplinary Optimization, Vol. 59, Issue 4 https://doi.org/10.1007/s00158-018-2123-z	journal	October 2018
Non-intrusive polynomial chaos expansion for topology optimization using polygonal meshes Cuellar, Nilton; Pereira, Anderson; Menezes, Ivan F. M. Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 40, Issue 12 https://doi.org/10.1007/s40430-018-1464-2	journal	November 2018
Robust topology optimization for multiple fiber-reinforced plastic (FRP) composites under loading uncertainties Xu, Yanan; Gao, Yunkai; Wu, Chi Structural and Multidisciplinary Optimization, Vol. 59, Issue 3 https://doi.org/10.1007/s00158-018-2175-0	journal	January 2019
Truss layout design under nonprobabilistic reliability‐based topology optimization framework with interval uncertainties Wang, Lei; Liu, Yisi; Yang, Yaowen International Journal for Numerical Methods in Engineering https://doi.org/10.1002/nme.6092	journal	May 2019
A new uncertainty propagation method considering multimodal probability density functions Zhang, Z.; Wang, J.; Jiang, C. Structural and Multidisciplinary Optimization, Vol. 60, Issue 5 https://doi.org/10.1007/s00158-019-02301-y	journal	June 2019
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An Efficient Strategy for Non-probabilistic Reliability-Based Multi-material Topology Optimization with Evidence Theory Zhao, Qinghai; Zhang, Hongxin; Zhang, Tiezhu Acta Mechanica Solida Sinica, Vol. 32, Issue 6 https://doi.org/10.1007/s10338-019-00121-7	journal	August 2019
Parametric Topology Optimization with Multi-Resolution Finite Element Models Keshavarzzadeh, Vahid; Kirby, Robert M.; Narayan, Akil arXiv https://doi.org/10.48550/arxiv.1808.10367	text	January 2018
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