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A method for topology optimization of structures under harmonic excitations

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Abstract

This paper deals with topology optimization of large-scale structures with proportional damping subjected to harmonic excitations. A combined method (CM) of modal superposition with model order reduction (MOR) for harmonic response analysis is introduced. In the method, only the modes corresponding to a frequency range which is a little bigger than that of interest are used for modal superposition, the contribution of unknown higher modes is complemented by a MOR technique. Objective functions are the integral of dynamic compliance of a structure, and that of displacement amplitude of a certain user-defined degree of freedom in the structure, over a range of interested frequencies. The adjoint variable method is applied to analyze sensitivities of objective functions and the accuracy of the sensitivity analyses can also be ensured by CM. Topology optimization procedure is illustrated by three examples. It is shown that the topology optimization based on CM not only remarkably reduce CPU time, but also ensure accuracy of results.

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Acknowledgments

The authors are grateful to Krister Svanberg for providing the Matlab code of GCMMA optimizer. The work was supported by the National Natural Science Foundation of China (Grant No. 11672118).

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Authors and Affiliations

  1. School of Mathematics, Jilin University, Changchun, 130012, People’s Republic of China

    Xuqi Zhao & Zhengguang Li

  2. School of Electro-Mechanical Engineering, Guangdong University of Technology, Guangzhou, 510006, People’s Republic of China

    Baisheng Wu

  3. College of Computer Science and Technology, Jilin University, Changchun, 130012, People’s Republic of China

    Huixiang Zhong

Authors
  1. Xuqi Zhao
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  2. Baisheng Wu
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  3. Zhengguang Li
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  4. Huixiang Zhong
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Correspondence to Baisheng Wu.

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Zhao, X., Wu, B., Li, Z. et al. A method for topology optimization of structures under harmonic excitations. Struct Multidisc Optim 58, 475–487 (2018). https://doi.org/10.1007/s00158-018-1898-2

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  • DOI: https://doi.org/10.1007/s00158-018-1898-2

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