## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2014 (2014), Article ID 213478, 12 pages.

### Numerical Solution for an Epicycloid Crack

Nik Mohd Asri Nik Long, Koo Lee Feng, Wong Tze Jin, and Z. K. Eshkuvatov

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#### Abstract

A flat crack, $\Omega $, 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 $\Omega $ 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, $D$. 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.

#### Article information

**Source**

J. Appl. Math., Volume 2014 (2014), Article ID 213478, 12 pages.

**Dates**

First available in Project Euclid: 2 March 2015

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1425305900

**Digital Object Identifier**

doi:10.1155/2014/213478

#### Citation

Asri Nik Long, Nik Mohd; Feng, Koo Lee; Jin, Wong Tze; Eshkuvatov, Z. K. Numerical Solution for an Epicycloid Crack. J. Appl. Math. 2014 (2014), Article ID 213478, 12 pages. doi:10.1155/2014/213478. https://projecteuclid.org/euclid.jam/1425305900

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