Elastodynamic fundamental solutions for anisotropic solids

Abstract

3-D and 2-D time-domain elastodynamic fundamental solutions (or Green's functions) for linearly elastic anisotropic materials are obtained by the Radon transform. Fundamental solutions in the frequency domain follow directly by a subsequent evaluation of the Fourier transforms of the time-domain solutions. The solutions are in the form of a surface integral over a unit sphere for 3-D cases and in the form of a contour integral over a unit circle for 2-D cases. The integrals have a simple structure that can be interpreted as a superposition of plane waves. The wavefields can be separated into singular and regular parts. The singular parts correspond to the elastostatic fundamental solutions. The regular parts are bounded continuous functions. The integrals have been evaluated numerically for several examples. The results presented in this paper have direct applications to the formulation of boundary-integral equations for bodies of anisotropic materials and for the subsequent solution of these equations by the boundary-element method.