Author(s)

Guizhong Xie & Jianming Zhang

Abstract

In this work, exponential transformation is applied for nearly singular boundary element integrals in elasticity problems. Accurate evaluation of nearly singular integrals is an important issue in the implementation of the boundary element method (BEM). In this paper, exponential transformation is firstly developed to evaluate nearly singular boundary integrals in elasticity problems. In our work, firstly, a novel ( , ) coordinate system is introduced. Then an improved exponential transformation is constructed in the new coordinate system. Furthermore, to perform integrations on irregular elements, an adaptive integration scheme considering both the element shape and the nearest point associated with the improved transformation is employed. Compared with conventional methods, we use the nearest point instead of the projection point. So, the drawbacks of how to subdivide the integration element into subtriangles with fine shapes can be overcome. Numerical examples are presented to verify the proposed method. Results demonstrate the accuracy and efficiency of our method. Keywords: nearly singular integrals, boundary element method, boundary face method, exponential transformation.

Keywords

nearly singular integrals, boundary element method, boundary face method, exponential transformation