On the contact of an absolutely rigid stamp with a half-plane taking into account static friction

The plane deformable state of an elastic half-plane into which an absolutely rigid stamp is pressed with friction is considered. It is assumed that the tangential stresses acting in the contact zone are related to normal pressure by the law of dry friction, the coefficient of which is a linear function of the coordinate of the contacting points of the contacting bodies. A determining singular integral equation for the stated problem is obtained, the solution of which is constructed in closed form. Numerical analysis is conducted, and regularities in the variation of contact stresses are determined depending on the ratios of horizontal and normal loads applied to the stamp.