A Self-regularization Technique in Boundary Element Method for 3-D Stress Analysis

Abstract

The self-regularization technique in the Boundary Element Method (BEM) originally proposed by Cruse and Richardson (1996, 1999) in their work for two-dimensional (2-D) stress analysis is extended to three-dimensional (3-D) elastostatics in this paper. The regularization scheme addresses the issue of accurate numerical evaluation of the integrals due to the singularity of the kernel functions of the integral equations. It is first implemented for the determination of displacements and stresses at interior points of the solution domain, and very accurate results are obtained even when these points are very close to the surface of the domain. A self-regularized traction-BIE is then implemented with two different approaches to deal with the requirement of continuity of the displacement-gradients across element boundaries. The examples presented suggest that when corners are present, this smoothness requirement for the traction-BIE must be met if convergence of the solution is to be assured. Finally, a self-regularized displacement-BIE is developed which can treat thin-body problems by eliminating the near-singularity issues encountered in conventional BEM. This is demonstrated by numerical examples.