Frictionless contact problem between an elastic layer bonned to a rigid support and a rigid stamp

SUMMARY FRICTIONLESS CONTACT PROBLEM BETWEEN AN ELASTIC LAYER BONDED TO A RIGID SUPPORT AND A RIGID STAMP A great deal of research on the contact problem for an elastic layer has been carried out because of its possible application to a variety of structures of practical interest. Foundations, higways, railways, airfield pavements, rolling mills, ball and roller bearings are some of the application areas of the contact mechanics. In this study, a fiictionless contact problem between a rigid stamp and an infinite layer of a constant thickness, which is perfectly bonded to a rigid support on its top surface, is considered according to the theory of elasticity. The layer is subjected to a concentrated load by means of a rigid stamp. The effect of gravity is neglected. In the first chapter, studies on contact problems are briefly introduced. Then, general equations of stresses and displacements are obtained by using governing equations of elasticity and integral transform techniques. The problem is described in the second chapter. A set of linear algebraic equation is obtained by applying the expressions of stresses and displacements to boundary conditions of the problem. When this set of algebraic equation is solved, the unknown constant coefficients are expressed by depending on the contact pressure which is unknown. Using the condition that derivative of vertical diplacements under the rigid stamp is equal to derivative of the function F(x) which defines the profile of the rigid stamp, the problem is formulated in terms of a singular integral equation for the contact pressure. In order to obtain the contact pressure, the singular integral equation is evaluated numerically by using appropriate Gauss-Chebyshev integration formula. In the third chapter, numerical results for various dimensionless quantities are presented in graphical forms and discussed. The conclusions drawn from the study are presented in the fourth chapter. Key Words : Elastic Layer, Contact Mechanics, Theory of Elasticity, Integral Transform Technique, Singular Integral Equation, Gauss-Chebyshev Integration Formula, Rigid Stamp, Contact Pressure. VI