Analytical Solution of Continuous Contact Problem in Functionally Graded Layer Resting on Rigid Plane

Abstract

In this study, continuous contact problem for two layers, having different heights and elastic constants, loaded by means of two rigid rectangle stamps and resting on a rigid plane is considered according to theory of elasticity. The problem is solved under the assumptions that all surfaces are frictionless. Using boundary conditions of the problem and integral transform technique, the problem is reduced to a singular integral equation. The integral equation is solved numerically by making use of appropriate Gauss Chebyshev integration formula for rectangular stamp profiles and contact stress distribution under the stamps is obtained. Depending on the contact stress under the stamps, initial separation loads and initial separation distances between the layers and between homogeneous layer and rigid plane are determined.