An Application of Topology Optimisation to Defect Identification in Two-Dimensional Elastodynamics with the BEM and H-Matrix Method

This paper presents a numerical method for topology optimisation for two-dimensional elastodynamics based on the level set method and the boundary element method (BEM) accelerated by the H-matrix method and its application to identifications of defects in an infinite elastic medium. Gradient-based topology optimisation methods require design sensitivity, which is obtained by solving some boundary value problems. The BEM is employed for this sensitivity analysis because the BEM can deal with infinite domains rigorously without any approximation. However, the computational cost in the BEM is expensive, and this is a serious drawback since we need to repeat sensitivity analysis even for a single optimisation process. In this study, the H-matrix method is used as an acceleration method of the BEM for the reduction of the computational cost of the sensitivity analysis. Also proposed is a method to improve the efficiency of the H-matrix method by exploiting a property of the kernel function of the elastodynamic fundamental solution. Some numerical examples are demonstrated, and the effectiveness of the proposed method is confirmed.