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An adaptive hybrid expansion method (AHEM) for efficient structural topology optimization under harmonic excitation

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Abstract

One challenge of solving topology optimization problems under harmonic excitation is that usually a large number of displacement and adjoint displacement vectors need to be computed at each iteration step. This work thus proposes an adaptive hybrid expansion method (AHEM) for efficient frequency response analysis even when a large number of excitation frequencies are involved. Assuming Rayleigh damping, a hybrid expansion for the displacement vector is developed, where the contributions of the lower-order modes and higher-order modes are given by the modal superposition and Neumann expansion, respectively. In addition, a simple (yet accurate) expression is derived for the residual error of the approximate displacement vector provided by the truncated hybrid expansion. The key factors affecting the convergence rate of the truncated hybrid expansion series are uncovered. Based on the Strum sequence, the AHEM can adaptively determine the number of lower-order eigenfrequencies and eigenmodes that need to be computed, while the number of terms that need to be preserved in the truncated Neumann expansion can be determined according to the given error tolerance. The performance of the proposed AHEM and its effectiveness for solving topology optimization problems under harmonic excitation are demonstrated by examining several 2D and 3D numerical examples. The non-symmetry of the optimum topologies for frequency response problems is also presented and discussed.

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Acknowledgments

The authors thank Professor Krister Svanberg for providing the matlab code of the MMA optimizer.

Funding

This work was financially supported by the National Research Council of Science and Technology (NST) grant by the Korea government (MSIT) (no. CAP-17-04-KRISS).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China

    Junpeng Zhao

  2. Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, 08826, South Korea

    Heonjun Yoon & Byeng D. Youn

  3. Institute of Advanced Machines and Design, Seoul National University, Seoul, 08826, South Korea

    Byeng D. Youn

  4. OnePredict Inc., Seoul, 08826, South Korea

    Byeng D. Youn

Authors
  1. Junpeng Zhao
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  2. Heonjun Yoon
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Correspondence to Heonjun Yoon or Byeng D. Youn.

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The matlab code of the proposed AHEM is available upon request to the corresponding authors.

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Responsible Editor: Emilio Carlos Nelli Silva

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Zhao, J., Yoon, H. & Youn, B.D. An adaptive hybrid expansion method (AHEM) for efficient structural topology optimization under harmonic excitation. Struct Multidisc Optim 61, 895–921 (2020). https://doi.org/10.1007/s00158-019-02457-7

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