Evaluation of Galerkin Singular Integrals for Anisotropic Elasticity: Displacement Equation

Abstract

Algorithms for the direct evaluation of singular Galerkin boundary integrals for three-dimensional anisotropic elasticity are presented. The integral of the traction kernel is defined as a boundary limit, and (partial) analytic evaluation is employed to compute the limit. The spherical angle components of the Green's function and its derivatives are not known in closed form, and thus the analytic integration requires a splitting of the kernel, into 'singular' and 'non-singular' terms. For the coincident singular integral, a single analytic evaluation suffices to isolate the potentially divergent term, and to show that this term self-cancels. The implementation for a linear element is considered in detail, and the extension to higher order curved interpolation is also discussed. Results from test calculations establish that the algorithms are successful.