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.
