On two contact problems for a half-plane with static friction

Abstract

Exact solutions of two contact problems are constructed for a half-plane, when a finite number of absolutely rigid flat punches with friction are pressed into the half-plane under the influence of different concentrated loads, and when a periodic system of absolutely rigid flat punches with friction is pressed into the half-plane. It is assumed that friction in contact zones is associated with normal contact pressure by the generalized law of dry friction, in which the coefficient of friction depends on the coordinates of the contacting points of the contacting bodies and is directly proportional to the difference between the coordinates of these points and the coordinates of the middle points of the contact zones. The governing equations of the posed problems were obtained in the form of singular integral equations with variable coefficients relative to the contact pressure and their closed solutions were constructed.