Transmitting boundaries for time‐harmonic elastodynamics on infinite domains

Abstract

Abstract A finite element method with transmitting boundary is developed for time‐harmonic elastodynamics on infinite domains. Only a finite inner domain needs to be discretized into conventional finite elements, while the effect of the exterior domain is simulated by introducing the transmitting boundary stiffness matrix on the degrees‐of‐freedom of the transmitting boundary nodes. In order to incorporate the Sommerfeld radiation condition, the reciprocity relation, on the transmitting boundary for the radiating elastodynamic state under consideration and the one which is induced by a finite number of point source is used to calculate the transmitting boundary stiffness matrix. The effectiveness of the transmitting boundary technique has been demonstrated by solving the stress concentration problems of a homogeneous isotropic full space with a circular cylindrical cavity and of the one with a spherical cavity, which are subjected to plane incident waves, and the results are compared with the ones of the conventional FEM and the exact data.