The frictionless contact problem for an elastic layer resting on a half plane

In this study, the frictionless and receding contact problem for an elastic layer resting on a half plane is considered according to the theory of elasticity. The layer is forced with two concentrated load applied over two rigid rectangular stamps placed symmetrically. In the first chapter, some studies on the contact problems investigated until now are mentioned. General equations of stresses and displacements which are required for the solution of the problem are obtained by using theory of elasticity and the integral transform techniques. In the second chapter, after the description of the problem the stresses and the displacements expressions obtained in the first chapter are substituted into the boundary conditions of the problem and the problem is reduced to a system of singular integral equations which the contact stress between the layer and the rigid rectangular stamps , contact stresses between the layer and the half plane are unknown functions. After that, the system of singular integral equations is solved numerically by using Gauss-Jacobi integration formulation. In the third chapter, numerical values for the dimentionless contact lengths, the dimentionless contact stresses between the layer and the half plane are calculated for different material and geometric properties using a computer program. These obtained quantities are shown in tables and figures and related assessment are discussed. Furthermore , and stress components for the layer and the half plane are determined along the y axis. The conclusions obtained from the study are mentioned in the last chapter.