BEM modeling of a 3D homogeneous anisotropic elastic half space under dynamic load

Abstract

In this paper, we consider a problem of a homogeneous anisotropic and linearly elastic half space subjected to dynamic loading. Zero body forces and vanishing initial conditions are assumed. The problem is solved using the Boundary Element Method in the Laplace transformed domain. Integral expressions of the three-dimensional dynamic fundamental solutions for displacements and tractions are utilized. We employ the displacement boundary integral equations which are regularized using the static part of the dynamic anisotropic traction fundamental solution. For the spatial discretization of the boundary integral equations mixed boundary elements are adopted. The geometry of the considered domain is approximated with quadrilateral quadratic eight-noded elements. On the boundary elements displacements and tractions are interpolated using linear and constant shape functions, respectively. Time-domain solutions are obtained using suitable scheme for numerical inverse Laplace transform. The boundary-element solutions for the illustrative problem of an anisotropic elastic half space subjected to a Heaviside-type load are provided.