On the contact problem of layered elastic bodies

Abstract

The contact problem of elastic bodies, each consisting of a finite layer of uniform thickness rigidly adhering to a half-plane, is investigated on the basis of the two-dimensional theory of elasticity. The materials of the layer and the half-plane in the contact body are isotropic and homogeneous, yet each of them may have distinct elastic properties. The mixed boundary value problem is reduced to a single Fredholm integral equation of the second kind where the unknown variable is a fictitious surface deformation, through which the contact pressure can easily be obtained.