ASYMPTOTIC SOLUTION OF CONTACT PROBLEM FOR A THIN ELASTIC LAYER

The contact problem of impressing a stamp in an elastic layer of finite thickness h lying without friction or adhering rigidly to an underformable foundation is considered. The frictional forces between the stamp and the surface layer are assumed absent, and the surface layer outside the stamp is not loaded. The contact domain ω between the stamp and the layer is assumed simply connected (*) and fixed. An asymptotic solution of the above-mentioned problem has been obtained in [1-3] under the assumption that the relative thickness of the layer is sufficiently large, i.e. the dimensionless parameter λ = h/a, a = 1 2 max RPQ for any P and Q ε{lunate} ω, is large. A scheme for constructing the asymptotic solution of the mentioned problem under the assumption that the relative thickness of the layer is small has been expounded in [4]. © 1969.