Non-axisymmetric contact problem in the case of a normal load applied outside the area of contact

A FORMULA describing the effect of a load acting outside a circular stamp in a plane is known [1]. Below we propose a novel approach to the study of the pressure under a non-axisymmetric plane stamp when normal forces are applied to the free surface of an elastic half-space. The approach includes the method, proposed by Mossakovskii, of reducing the three-dimensional problem of potential theory to a plane problem. The main merit of this method, as compared with that in [2] based on the Sommerfeld method, is the possibility of constructing effective numerical algorithms, since any subsequent approximation can be constructed independently of the preceding one, by adding some supplementary terms. The problem in question is reduced, in the final analysis, to a system of plane problems of potential theory whose boundary conditions contain trigonometric polynomials with unknown coefficients, which can be determined from the condition that the solution is regular within the area of contact.