Summary: In this study, the frictionless and receding contact problem for an elastic layer resting on two quarter planes is considered according to the theory of elasticity. The layer is forced with a concentrated load applied over a punch and two uniform load placed symmetrically. In the first chapter, some studies which are done on contact problems are summarized and general expressions of stresses and displacements are obtained for the layer and quarter plane using integral transform techniques. In the second chapter, after the description of the problem, the stress 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 integral equations consisted of two singular integral equations, which the contact stress between the layer and the rigid punch and the contact stress between the layer and the quarter plane are the unknown functions. After that, the system of integral equations is solved numerically by using Gauss-Jacobi integration formulation. In the third chapter, the numerical values for the dimensionless contact lengths, the dimensionless contact stresses between the layer and the rigid punch and between the layer and the quarter plane are calculated for different loading, material and geometric properties using a computer program. These obtained quantities are shown in tables and figures and related assessments are discussed. In the fourth chapter, the conclusions drawn from this study are given. It is concluded that the contact lengths and the contact stress distributions show a related change and the position and the magnitude of the distributed load have an important role on the contact lengths and stress distributions. The sources are given after this chapter.
Key Words: Reciding Contact Problem, Quarter Plane, Singular Integral Equation, Gauss-Jacobi Integration Formulation |