Problem solution of the elasticity theory for the half-plane

Abstract

The classical problem of equilibrium of elastic half-plane loaded along boundary contour can be resolved with different methods. In this paper, the solution is received with a new method that is founded on Cauchy-type integral and Plemelj identity. First, we solve with the general half-plane. Then we consider four special half-planes x2 ≤ 0, x2 ≥ 0, x1 ≤ 0, x1 ≥ 0.