Boundary element method for scattering of elastic waves in general anisotropic media

A direct Boundary Element Method (BEM) for scattering of elastic waves in a triclinic medium is investigated. Using the generalized Betti's formula and the full-space fundamental solutions, the boundary integral equations are derived for steady-state motion and scatterers of arbitrary shapes embedded within a full or a half-space. A method for evaluation of the free terms is proposed for any boundary shape and for any type of linearly anisotropic medium. Moreover, the evaluation of the free-field is discussed in detail for a triclinic half-space problems.; The formulation of BEM is given for the full and half-space steady-state elastodynamic problems. The numerical evaluation of the integration constants for a triangular element is discussed in detail. For non-singular elements, both the quadrature over a triangular domain and the standard 2D Gauss quadrature produce similar accuracy. For singular elements, the standard and generalized polar transformations are used to weaken or remove the singularity of the integrands.; The BEM formulation of the half-space problem uses the full-space fundamental solutions and the traction-free conditions on the half-space surface must be imposed. Therefore, a finite portion of the half-space surface arising in the BEM formulation is discretized to simulate the scattering model. Numerical testing is performed for 2D and 3D isotropic cases. These results demonstrate that the size of the half-space discretization surface can be chosen to be about three times that of the scatterer. This ensured the accuracy of the half-space results when the full-space fundamental solutions are used.; Numerical results for scattering of waves by a cavity or a canyon embedded in a triclinic medium include both 2D and 3D problems. The corresponding isotropic cases, for which analytical or numerical results are available, are used as the test cases. These comparisons demonstrate that the proposed BEM formulation can be used to investigate both 2D and 3D scattering problems in triclinic media. In addition, this study shows that the scattered waves in a triclinic medium strongly depend on the nature and frequency of incident waves, shape of the scatterer and the material anisotropy.