Closed-form integration of singular terms for constant, linear and quadratic boundary elements. Part 1. SH wave propagation

Abstract

One of the most important aspects in the application of boundary element techniques to wave propagation problems is the accurate representation of the singular terms at the points of application of the virtual loads. It is current practice to carry out this task by means of numerical quadrature. This paper presents an analytical evaluation of the singular integrals for constant, linear and quadratic boundary elements involving SH waves, the results of which are then used to model inclusions in a two-dimensional acoustic medium illuminated by dynamic anti-plane line sources. Finally, the BEM results are compared with the known analytical solutions for cylindrical inclusions.