Contact problem with wear for a foundation with a surface nonuniform coating

Abstract

The plane contact problem with wear for an elastic foundation with a longitudinally nonuniform (surface nonuniform) coating and a rigid punch with a flat foundation has been solved for the first time. The case of linear wear is considered. The nonuniformity of the coating is described by a rapidly changing function. This strong nonuniformity arises when coatings are deposited using modern additive manufacturing technologies. The problem is reduced to the solution of an integral equation with two different integral operators: a compact self-adjoint positively defined operator with respect to the coordinate and the non-selfadjoint integral Volterra operator with respect to time. The solution is obtained in series using author’s projection method. The efficiency of the proposed approach for constructing a high-accuracy approximate solution to the problem (with only a few expansion terms retained) is demonstrated. A simple engineering formula for estimating the contact stresses under a punch for large values of times is proposed.