抄録
This paper presents a topology optimisation for designing periodic composite materials which control elastic wave scattering. First, we explain the model of the periodic composite material. Next, we employ the boundary element method to analyse the elastic wave scattering rigorously. We focus on objective functionals expressed in the form of a boundary integral and derive its topological derivative with the help of the adjoint variable method because a lot of important features including far-field characteristics, dissipation energy, and reflectance (or transmission) ratio can be written in this form. Then, we describe the algorithm of our topology optimisation. Our topology optimisation is based on the level set method in which a level set function is spanned by B-spline basis functions to control the complexity of optimal configurations. Finally, we design a periodic composite structure which converts an incident P-wave into S-waves by using the proposed topology optimisation method and demonstrate its effectiveness.
