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Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm

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Abstract

By using the finite element method and a “coarse to fine” two-stage genetic algorithm as the forward calculation method and the inverse search scheme, respectively, we perform both the unconstrained and constrained optimal design of the unit cell topology of the two-dimensional square-latticed solid phononic crystals (PnCs), to maximize the relative widths of the gaps between the adjacent energy bands of the PnCs. In the constrained optimizations, the maximization is subjected to the constraint of a predefined average density. In the numerical results, the variation patterns of the optimized structures with the order of the bandgap for both the out-plane shear and the in-plane mixed elastic wave modes are presented, and the effects of both the material contrast and the predefined average density on the obtained optimal structures are discussed.

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Acknowledgments

This research has been supported through the National Natural Science Foundation of China (Grant Nos. 11002018 and 10632020) and the partial support of the Fundamental Research Funds for the Central Universities in China under Grant No. 2013JBM009. The first author also wants to thank his colleague Mr. Sheng-Dong Zhao for his constructive discussion.

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Authors and Affiliations

  1. Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing, 100044, China

    Hao-Wen Dong & Yue-Sheng Wang

  2. School of Electronic and Information Engineering, Beijing Jiaotong University, Beijing, 100044, China

    Xiao-Xing Su

  3. Department of Civil Engineering, University of Siegen, 57068, Siegen, Germany

    Chuanzeng Zhang

Authors
  1. Hao-Wen Dong
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  2. Xiao-Xing Su
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  3. Yue-Sheng Wang
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  4. Chuanzeng Zhang
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Correspondence to Yue-Sheng Wang.

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Dong, HW., Su, XX., Wang, YS. et al. Topological optimization of two-dimensional phononic crystals based on the finite element method and genetic algorithm. Struct Multidisc Optim 50, 593–604 (2014). https://doi.org/10.1007/s00158-014-1070-6

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  • DOI: https://doi.org/10.1007/s00158-014-1070-6

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