Problem of the pressure of a rigid stamp on the boundary of a non-linearly elastic half-plane under finite deformations

The plane contact problem of non-linear elasticity theory is considered for a half-plane of non-linearly elastic material of harmonic type under finite deformations. It is assumed that there is no friction in the area of stamp contact with the elastic half-plane. The problem is reduced to a non-linear integral equation by using the scheme the author proposed earlier. Unlike where this equation was solved just for a flat stamp with a rectilinear horizontal base, an exact solution is obtained for an inclined stamp with a flat base as well as for a stamp whose base profile is the arc of a circle or wedge. It is shown that the contact pressure is bounded at the stamp edges and at the corner point.