International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 29, Pages 1821-1832
doi:10.1155/S0161171203211480
Contact problem for bonded nonhomogeneous materials under shear loading
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.
Abstract
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.