Table of Contents
International Journal of Computational Mathematics
Volume 2014, Article ID 358617, 9 pages
Research Article

Plane Elastostatic Solution in an Infinite Functionally Graded Layer Weakened by a Crack Lying in the Middle of the Layer

1Department of Mathematics, Hooghly Engineering & Technology College, Hooghly, West Bengal 712 103, India
2Department of Mathematics, Gobardanga Hindu College, 24 Parganas (North), West Bengal 743 273, India
3Makhla Debiswari Vidyaniketan, Hooghly, West Bengal 712 245, India
4Department of Applied Mathematics, University of Calcutta, 92 A. P. C. Road, Kolkata 700 009, India

Received 17 June 2014; Revised 6 November 2014; Accepted 14 November 2014; Published 25 November 2014

Academic Editor: Sheung-Hung Poon

Copyright © 2014 R. Patra 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.


This paper is concerned with an internal crack problem in an infinite functionally graded elastic layer. The crack is opened by an internal uniform pressure along its surface. The layer surfaces are supposed to be acted on by symmetrically applied concentrated forces of magnitude with respect to the centre of the crack. The applied concentrated force may be compressive or tensile in nature. Elastic parameters λ and μ are assumed to vary along the normal to the plane of crack. The problem is solved by using integral transform technique. The solution of the problem has been reduced to the solution of a Cauchy-type singular integral equation, which requires numerical treatment. The stress-intensity factors and the crack opening displacements are determined and the effects of graded parameters on them are shown graphically.