Contact problem for periodically stratified half-space and rigid foundation possessing geometrical surface defect

A three-dimensional problem of frictionless contact interaction of a periodic two-layered elastic half-space and a rigid foundation with a local sloping surface recess is examined. The analysis is performed within the framework of a homogenized model with microlocal parameters. By constructing appropriate harmonic functions, the resulting boundary-value problem is reduced to some mixed problem of the potential theory. In dealing with its solution, the integro-differential singular equation of Newton's potential type for the function of gap height is obtained. To determine the unknown region of the gap the condition of smooth running of its faces is used. As an example, a certain form of the initial defect is considered and in this case the solution of the equation is found analytically by using an analogue of Dyson's theorem.