Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy

An efficient two-dimensional time-domain application of the Boundary Element Method is presented to solve elastodynamic boundary/initial-value problems in solids of general anisotropy. The method is based on the use of integral expressions for the Green's functions derived by Wang and Achenbach (1994) [Elastodynamic fundamental solutions for anisotropic solids. Geophys. J. int. 118, 384-392], and on the partition of these Green's functions into singular static and regular dynamic parts. The singular static parts are the elastostatic Green's functions, which have relatively simple explicit expressions in closed form. The regular dynamic parts are given in terms of line integrals over a unit circle, whose integrands have a simple structure which physically corresponds to a superposition of plane waves. The partition of the Green's functions leads to the decomposition of the singular elastodynamic boundary integral equation into terms corresponding to a singular elastostatic integral equation plus regular dynamic terms. The calculation effort is reduced by analytically evaluating both the integration over each boundary element and the time-convolution over each time-step. As a result only regular line integrals over the unit circle have to be computed numerically. Applications are discussed for scattering of elastic waves by cavities. The method has been checked by comparing numerical results against existing analytical solutions for an isotropic solid. Numerical results for scattering of elastic waves in a transversely isotropic material by a circular cylindrical cavity have also been obtained. Copyright (C) 1996 Elsevier Science Ltd.