Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 741075, 17 pages
http://dx.doi.org/10.1155/2011/741075
Research Article

Computation of Energy Release Rates for a Nearly Circular Crack

Nik Mohd Asri Nik Long,1,2 Lee Feng Koo,1 and Zainidin K. Eshkuvatov1,2

1Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Malaysia
2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Malaysia

Received 4 August 2010; Revised 6 December 2010; Accepted 14 January 2011

Academic Editor: Jerzy Warminski

Copyright © 2011 Nik Mohd Asri Nik Long et al. 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 paper deals with a nearly circular crack, Ω in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, Ω and it is then transformed into a similar equation over a circular region, 𝐷 , using conformal mapping. Appropriate collocation points are chosen on the region 𝐷 to reduce the hypersingular integral equation into a system of linear equations with ( 2 𝑁 + 1 ) ( 𝑁 + 1 ) unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.