Double receding contact problem for a rigid stamp and two elastic layers

The plane symmetric double receding contact problem for a rigid stamp and two elastic layers having different elastic constants and heights is considered. The external load is applied to the upper elastic layer by means of a rigid stamp and the lower elastic layer is bonded to a rigid support. The problem is solved under the assumptions that the contact between two elastic layers, and between the rigid stamp and the upper elastic layer are frictionless, the effect of gravity force is neglected and only compressive normal tractions can be transmitted through the interfaces. The problem is reduced to a system of singular integral equations in which the contact pressures are the unknown functions by using integral transform technique and boundary conditions of the problem. The system of singular integral equations is solved numerically by making use of appropriate Gauss-Chebyshev integration formulas for two stamp geometries. Numerical results for the contact pressures, the contact areas, the normal stresses σx, σy, and the shear stress τxy are given for various dimensionless quantities.