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<p>This paper proposes a multi-material level set-based topology optimization method for designing phononic crystals with bandgaps. To facilitate bandgap formation and prevent convergence to local optima with zero bandgaps, we introduce a novel optimization formulation that penalizes band intersections using a constraint. The optimization process is conducted using the reaction-diffusion equation-based multi-material level set-based method, which represents multiple material phases without overlap and enables topological changes during the optimization process. Numerical examples confirmed that the proposed method can robustly generate non-zero bandgaps for different initial configurations. Moreover, under the same mass constraint, the maximum relative bandgap width (RBW) obtained in the three-material case exceeds that of the two-material case, suggesting the potential benefits of incorporating an additional material. At the same time, the results indicate that the final RBW remains sensitive to the initial design.</p>

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Multi-material topology optimization of phononic crystals based on bandgap generation and control

  • 期刊论文

  • 发表日期：

    2025年11月13日

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  • Nari Nakayama,
  • Kozo Furuta,
  • Tokiha Yamaguchi,
  • Kazuhiro Izui,
  • Shinji Nishiwaki

摘要

This paper proposes a multi-material level set-based topology optimization method for designing phononic crystals with bandgaps. To facilitate bandgap formation and prevent convergence to local optima with zero bandgaps, we introduce a novel optimization formulation that penalizes band intersections using a constraint. The optimization process is conducted using the reaction-diffusion equation-based multi-material level set-based method, which represents multiple material phases without overlap and enables topological changes during the optimization process. Numerical examples confirmed that the proposed method can robustly generate non-zero bandgaps for different initial configurations. Moreover, under the same mass constraint, the maximum relative bandgap width (RBW) obtained in the three-material case exceeds that of the two-material case, suggesting the potential benefits of incorporating an additional material. At the same time, the results indicate that the final RBW remains sensitive to the initial design.