The receding contact problem of two elastic layers supported by two elastic quarter planes

Abstract

The receding contact problem for two elastic layers whose elastic constants and heights are different supported by two elastic quarter planes is considered. The lower layer is supported by two elastic quarter planes and the upper elastic layer is subjected to symmetrical distributed load whose heights are 2a on its top surface. It is assumed that the contact between all surfaces is frictionless and the effect of gravity force is neglected. The problem is formulated and solved by using Theory of Elasticity and Integral Transform Technique. The problem is reduced to a system of singular integral equations in which contact pressures are the unknown functions by using integral transform technique and boundary conditions of the problem. Stresses and displacements are expressed depending on the contact pressures using Fourier and Mellin formula technique. The singular integral equation is solved numerically by using Gauss-Jacobi integration formulation. Numerical results are obtained for various dimensionless quantities for the contact pressures and the contact areas are presented in graphics and tables.