Receding contact problem for two elastic layers resting on a Winkler foundation

Abstract

In this study, receding contact problem for two elastic layers resting on a Winkler foundation and loaded by means of a rigid circular punch is considered. The elastic layers have different heights and elastic constants. External load is applied to the upper elastic layer by means of a rigid circular punch and the lower elastic layer rests on a Winkler foundation. The problem is solved under the assumptions that the contact between elastic layers, and between the rigid punch and the upper elastic layer are frictionless and the effect of gravity forces is neglected. Since the contact between two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact areas. General equations of stresses and displacements which are required for the solution of the problem are obtained by using the theory of elasticity and the integral transform techniques. Using integral transform technique and boundary conditions of the problem, the problem is reduced to a system of singular integral equations in which the contact stresses and areas are the unknown functions. The system of singular integral equations is solved numerically by making use of appropriate Gauss-Chebyshev integration formulas and an iterative scheme is employed to obtain the correct contact half-areas that satisfies the equilibrium conditions. Numerical results for the contact stresses and the contact areas are given for various dimensionless quantities.