動弾性方程式を対象とした高周波均質化法に基づく弾性体メタマテリアルの最適設計

抄録

This paper presents a topology optimization method for the design of elastic metamaterial based on a high-frequency homogenization method for elastodynamic equation. First, we briefly explain the high-frequency homogenization method for elastodynamic equation to estimate the macroscopic properties and dispersion relation of elastic metamaterial. Next, optimization problem is formulated so that optimized unit cell design of metamaterial exhibits hyperbolic dispersion relation. Two components of second-order tensor in the homogenized equation, which represents approximated dispersion relation of elastic metamaterial, are used in the objective and constraint functions. We use level set-based topology optimization method to solve the optimization problem. We offer a two-dimensional numerical example to show the validity of our method. Optimal configuration obtained by the proposal method consists of steel, and it exhibits hyperbolic dispersion around the point corresponding to the target eigenmode in wavevector space due to a local resonance induced in the unit cell of elastic metamaterial.