Analytical and finite element solution of a receding contact problem

Abstract

In this paper, a receding contact problem for an elastic layer resting on two quarter planes is considered. the layer is pressed by a stamp and distributed loads. It is assumed that the contact surfaces are frictionless and only compressive traction can be transmitted through the contact surfaces. in addition the effect of body forces are neglected. Firstly, the problem is solved analytically based on theory of elasticity. in this solution, the problem is reduced into a system of singular integral equations in which contact areas and contact stresses are unknowns using boundary conditions and integral transform techniques. This system is solved numerically using Gauss-Jacobi integral formulation. Secondly, two dimensional finite element analysis of the problem is carried out using ANSYS. the dimensionless quantities for the contact areas and the contact pressures are calculated under various distributed load conditions using both solutions. It is concluded that the position and the magnitude of the distributed load have an important role on the contact area and contact pressure distribution between layer and quarter plane contact surface. the analytic results are verified by comparison with finite element results.