BEM analysis of wave scattering in transversely isotropic solids

A boundary element approach for wave propagation problems in transversely isotropic solids is developed in this paper. The procedure is based on the well-known formulation for time-harmonic elasticity and a new version of a recently obtained fundamental solution for transversely isotropic media. The fundamental solution is transformed to obtain new expressions which can be efficiently evaluated at any point. This fact allows for a drastic reduction of the computation time and makes possible the implementation of a general purpose three-dimensional quadratic element code. To show the simplicity and accuracy of the approach, the diffraction of waves by a spherical cavity and the interaction between two cavities in a boundless domain are studied. The computed results show a very good agreement with the analytical solution in the simple case where such solution exists. Other geometries can be studied without difficulty.