Application Of Exponential Transformation
Coupled With Adaptive Subdivision Technique
For Nearly Singular Boundary Integrals In
Elasticity Problems
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
Related Book
Other papers in this volume
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