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Journal of Applied Mathematics
Volume 2014, Article ID 213478, 12 pages
http://dx.doi.org/10.1155/2014/213478
Research Article

Numerical Solution for an Epicycloid Crack

1Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
2Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia
3Department of Basic Science and Engineering, Faculty of Agriculture and Food Sciences, Universiti Putra Malaysia, Sarawak Campus, 97008 Bintulu, Sarawak, Malaysia

Received 22 March 2014; Accepted 6 June 2014; Published 14 July 2014

Academic Editor: Ray K.L. Su

Copyright © 2014 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

A flat crack, , is lying in a three-dimensional homogenous isotropic elastic solid subjected to shear loading. A mathematical formulation is developed based on the mixed boundary values for such that the problem of finding the resulting force can be written in the form of hypersingular integral equation. Employing conformal mapping, the integral equation is transformed to a similar equation over a circular region, . By making a suitable representation of hypersingular integral equation, the problem is reduced to solve a system of linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions.