Contact Analysis of Elastic Layer Supported by a Wedge

Abstract

In this paper the contact analysis of elastic layer supported by a wedge is considered in plane. The problem is formulated with closed formed integral equations. The length of the contact region, the pressure between the wedge and the layers, and the pressure between the layer and the punch are unknowns. Both the material and layer are elastic in this problem. This problem can be defined as a layer supported over two wedges with perpendicular angle. The upper surface of the layer is assumed as circle with a large radius. The thickness of the layer is finite. Singular integral equations are used in the formulation of the problem. The benefits of this formulation are the following: the problem can easily be generalized for the case of forces acting through many rigid punches. The solution gives the contact stress directly and the solution of the singular integral equations is an appropriate way in terms of numerical solution technique. The application of this problem is the train wheel that is contacted to the connection part of the rails. It is shown that the divergent terms at the kernels cancel each other by considering the equilibrium conditions. As a numerical example, the contact problem between the wheel and rails is investigated.