Contact Problem for Layered Medium Supported by a Wedge

In this paper the plane contact problem for a layered medium supported by an elastic wedge is considered. A compressive load is applied to the top of the layered medium through a frictionless rigid punch. It is assumed that all contact areas are frictionless and only compressive normal tractions can be transmitted through the interfaces. Hence, the length of the contact region along the layers and layer-wedge interface is finite and are also unknown. The problem is formulated in terms of a system of singular integral equations in which the unknown functions are the pressure between layers in layered medium and between layered medium and the wedge. The analytical formulation of layered medium supported by wedge is given. As a numerical example, contact length and stress intensity factor at the tip of rails are calculated and the result are given by diagrams.