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Mathematical Problems in Engineering
Volume 2006, Article ID 91846, 16 pages

Closed-form solution for piezoelectric layer with two collinear cracks parallel to the boundaries

1Department of Computer Science, The University of Calgary, Calgary, Alberta, Canada T2N-1N4
2Department of Mathematics and Statistics, The University of Calgary, Calgary, Alberta, Canada T2N-1N4

Received 6 February 2005; Revised 16 November 2005; Accepted 26 March 2006

Copyright © 2006 B. M. Singh 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.


We consider the problem of determining the stress distribution in an infinitely long piezoelectric layer of finite width, with two collinear cracks of equal length and parallel to the layer boundaries. Within the framework of reigning piezoelectric theory under mode III, the cracked piezoelectric layer subjected to combined electromechanical loading is analyzed. The faces of the layers are subjected to electromechanical loading. The collinear cracks are located at the middle plane of the layer parallel to its face. By the use of Fourier transforms we reduce the problem to solving a set of triple integral equations with cosine kernel and a weight function. The triple integral equations are solved exactly. Closed form analytical expressions for stress intensity factors, electric displacement intensity factors, and shape of crack and energy release rate are derived. As the limiting case, the solution of the problem with one crack in the layer is derived. Some numerical results for the physical quantities are obtained and displayed graphically.