International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 29, Pages 1821-1832

Contact problem for bonded nonhomogeneous materials under shear loading

B. M. Singh,1 J. Rokne,2 R. S. Dhaliwal,1 and J. Vrbik3

1Department of Mathematics and Statistics, University of Calgary, Calgary T2N 1N4, Alberta, Canada
2Department of Computer Science, University of Calgary, Calgary T2N 1N4, Alberta, Canada
3Department of Mathematics and Science, Brock University, St. Catherines, Ontario L2S 3A1, Canada

Received 24 November 2002

Copyright © 2003 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.


The present paper examines the contact problem related to shear punch through a rigid strip bonded to a nonhomogeneous medium. The nonhomogeneous medium is bonded to another nonhomogeneous medium. The strip is perpendicular to the y-axis and parallel to the x-axis. It is assumed that there is perfect bonding at the common plane surface of two nonhomogeneous media. Using Fourier cosine transforms, the solution of the problem is reduced to dual integral equations involving trigonometric cosine functions. Later on, the solution of the dual integral equations is transformed into the solution of a system of two simultaneous Fredholm integral equations of the second kind. Solving numerically the Fredholm integral equations of the second kind, the numerical results of resultant contact shear are obtained and graphically displayed to demonstrate the effect of nonhomogeneity of the elastic material.