Table of Contents
ISRN Applied Mathematics
Volume 2011 (2011), Article ID 726402, 25 pages
http://dx.doi.org/10.5402/2011/726402
Research Article

Divergent Integrals in Elastostatics: General Considerations

Materials Department, Centro de Investigacion Cientifica de Yucatan A.C., Calle 43, No. 130, Colonia Chuburná de Hidalgo, 97200 Mérida, YUC, Mexico

Received 4 April 2011; Accepted 31 May 2011

Academic Editors: S.-W. Chyuan and E. A. Navarro

Copyright © 2011 V. V. Zozulya. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This article considers weakly singular, singular, and hypersingular integrals, which arise when the boundary integral equation methods are used to solve problems in elastostatics. The main equations related to formulation of the boundary integral equation and the boundary element methods in 2D and 3D elastostatics are discussed in details. For their regularization, an approach based on the theory of distribution and the application of the Green theorem has been used. The expressions, which allow an easy calculation of the weakly singular, singular, and hypersingular integrals, have been constructed.