The general elastodynamic problem for a transversely isotropic linearly elastic solid can be formulated in terms of a set of Boundary Integral Equations (BIE's). These equations can be solved numerically by the Boundary Element Method (BEM). This method is particularly well-suited for wave scattering problems in unbounded bodies since the radiation conditions are automatically satisfied and only the internal boundaries of the problem have to be discretized. For a successful implementation of the method, the elastodynamic fundamental solution (Green's functions for an unbounded solid) has to be known in a relatively simple form. In the present work, a 3-D time-harmonic fundamental solution recently presented by Wang and Achenbach is transformed into expressions which can be evaluated in an efficient way. These transformations make possible the implementation of a Boundary Element code for the analysis of wave propagation problems in transversely isotropic solids. Numerical results obtained for scattering by a spherical cavity embedded in a transversely isotropic solid are presented.

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