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Uncertain dynamic topology optimization based on the interval reliability evaluation and equivalent static loads (ESLs) algorithm

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Abstract

This study investigates an interval reliability-based topology optimization (IRBTO) scheme for the lightweight design of continuum structures under unknown-but-bounded (UBB) dynamic performances. The dynamic response equation is first discretized, and the optimal design can be further converted into a multi-case time-invariant format using the equivalent static loads (ESLs) approach. In view of the inevitability of multi-source uncertainties during the whole design optimization procedure, the set quantitative model and interval dimension-by-dimension method (IDDM) are proposed for the acquisition of the reasonable characterization of uncertain dynamic responses in each iterative layout configuration. For reasons of structural safety and robustness, a new non-probabilistic reliability index oriented to structural average dynamic compliance is defined via the set-interference principle, and its design sensitivity for each elemental intermediate density is correspondingly analyzed. The method of moving asymptotes (MMA) is employed as the optimization problem solver. The usage and validity of the proposed techniques are demonstrated with several numerical examples, eventually.

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Acknowledgements

The authors would like to thank the National Nature Science Foundation of China (12072007, 12132001, 52192632), the EU Marie Sklodowska-Curie Individual Fellowships (H2020-MSCA-IF-2020:101025743-ROFiDMS), the Ningbo Nature Science Foundation (202003N4018), and the Defense Industrial Technology Development Program (JCKY2019205A006, JCKY2019203A003) for the financial supports. Besides, the authors wish to express their many thanks to the reviewers for their useful and constructive comments.

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Author notes

  1. Yaru Liu and Lei Wang contributed equally to this work.

Authors and Affiliations

  1. Institute of Solid Mechanics, School of Aeronautic Science and Engineering, Beihang University, Beijing, 100083, China

    Yaru Liu, Lei Wang & Dongliang Liu

  2. Aircraft and Propulsion Laboratory, Ningbo Institute of Technology, Beihang University, Ningbo, 315100, China

    Lei Wang

  3. School of Engineering, Cardiff University, Newport Road 30-36, Cardiff, CF24 ODE, UK

    Yaru Liu, Lei Wang & Dongliang Liu

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  1. Yaru Liu
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  2. Lei Wang
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Correspondence to Lei Wang.

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Liu, Y., Wang, L. & Liu, D. Uncertain dynamic topology optimization based on the interval reliability evaluation and equivalent static loads (ESLs) algorithm. Engineering with Computers 38, 5657–5674 (2022). https://doi.org/10.1007/s00366-022-01737-z

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  • DOI: https://doi.org/10.1007/s00366-022-01737-z

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