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A new structural uncertainty analysis method based on polynomial expansions

Author

Listed:
  • Zheng, Yongfeng
  • Gu, Yan
  • Gao, Liang
  • Wang, Yanzheng
  • Qu, Jinping
  • Zhang, Chuanzeng

Abstract

This paper proposes a new method based on the polynomial expansions for structural uncertainty analysis. A generalized finite difference method (GFDM) based on the Taylor expansion is adopted to compute the structural responses, which has good adaptabilities to the analysis domains due to its meshless property. With the help of the polynomial chaos expansions (PCE), random variables subjected to any probability distribution are implicitly quantified. The GFDMPCE method combines GFDM and PCE, is verified by the classical Monte Carlo method (MCM) in terms of calculation accuracy and efficiency. This method is non-intrusive, rigorous in mathematical theory, and shows bright prospects for the robust analysis of large-scale and complex structures.

Suggested Citation

  • Zheng, Yongfeng & Gu, Yan & Gao, Liang & Wang, Yanzheng & Qu, Jinping & Zhang, Chuanzeng, 2022. "A new structural uncertainty analysis method based on polynomial expansions," Applied Mathematics and Computation, Elsevier, vol. 427(C).
    • Handle: RePEc:eee:apmaco:v:427:y:2022:i:c:s0096300322002065
    DOI: 10.1016/j.amc.2022.127122
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    References listed on IDEAS

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    1. Sudret, Bruno, 2008. "Global sensitivity analysis using polynomial chaos expansions," Reliability Engineering and System Safety, Elsevier, vol. 93(7), pages 964-979.
    2. Yu, Qian & Wang, Kunyang & Xia, Binhu & Li, Yibao, 2021. "First and second order unconditionally energy stable schemes for topology optimization based on phase field method," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    3. Alazwari, Mashhour A. & Rao, Singiresu S., 2022. "Uncertainty analysis of large structures using universal grey number theory," Applied Mathematics and Computation, Elsevier, vol. 416(C).
    4. Shukla, Vivekanand & Singh, Jeeoot, 2022. "Thermo-mechanical stability analysis of angle-ply plates using meshless method," Applied Mathematics and Computation, Elsevier, vol. 413(C).
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