Boundary element formulation of axisymmetric problems for an elastic halfspace

Axisymmetric problems for an elastic halfspace are commonly analyzed by the boundary element (BE) method by employing the axisymmetric fundamental solution for the fullspace. In such cases, the discretization of the free surface is required, with its truncation at an appropriate location from the axis of symmetry. This paper presents the BE implementation of the axisymmetric fundamental solution for an elastic halfspace, given in terms of integrals of the Lipschitz–Hankel type, that satisfies in advance the boundary condition of zero traction on the free surface and the decay of displacements in the far field. Explicit equations for post-processing the results at internal points are provided, as well as adequate numerical schemes to evaluate the boundary integrals arising in the method. This formulation can be easily implemented in existing BE computational codes for axisymmetric fullspace problems, requiring only a few modifications. Numerical results are provided to validate the proposed formulation.