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

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.