In this study, the continuous contact problem for two elastic layers, having different heights and elastic constants, loaded by means of a rigid circular punch and resting on an elastic half infinite plane is considered according to the theory of elasticity. In the first chapter, the historical development of contact problems are mentioned and some studies which are done on contact problems are summarized. In addition, general expressions of stresses and displacements are obtained by using the fundamental equations of theory of elasticity and integral transformation technique. In the second chapter, the problem is described. Stress and displacements expressions are substituted into the boundary conditions of problem and the problem is reduced to a singular integral equation, which the contact stress under the rigid punch is the unknown function. The integral equation is numerically solved for circular punch profile and the contact stress distribution under the punch is obtained. Depending on the contact stresses under the punch, the normal stresses and the shear stress, along the x axis, initial separation loads and initial separation distances of between elastic layers and between lower layer with elastic half infinite plane are determined. In the third chapter, the numerical applications of the problem given in the previous chapter for various dimensionless quantities are done. The contact stresses, the contact lengths, stress components, initial separation loads and initial separation distances are obtained numerically for different parameters of load, material and geometry. Results are shown and discussed in graphics and tables. In the fourth chapter, the conclusions drawn from this study are given.
Key Words : Theory of Elasticity, Contact Stress, Integral Equation, Integral Transform Technique, Initial Separation Load, Initial Separation Distance