On the contact interaction between a strip-shaped punch and a linearly-deformable base through a covering of variable thickness

The contact problem of the frictionless penetration of a punch with strip-shaped section into the surface of a linearly-deformable base protected by a thin elastic layer (covering) of variable thickness, the stiffness of which is comparable to or smaller than that of the supporting elastic body, is investigated. A Fredholm integral equation of the second kind is obtained for the unknown contact pressure with a coefficient in front of the leading term that is a fairly arbitrary function of the longitudinal coordinate. To solve it the Bubnov-Galerkin projection method is used in which the coordinate elements are chosen to be a system of orthogonal polynomials and delta-shaped functions 1, 2] (variational-difference method), together with an algorithm for the required asymptotic expansions 3] when the above-mentioned coefficient is small. In the special case of an elastic half-space protected by a covering of constant thickness, the results obtained are compared with the corresponding characteristics given in 4].