Incorrectly Posed BVPs for Elastic Half- Plane in Terms of Stress and Displacement Orientations

This article presents the general approach to incorrectly posed boundary value problems of the plane theory of elasticity with the boundary conditions formulated through the directions of displacement vectors and principal directions of the stress tensor. The approach is aimed at studying the solvability of problems of this type and allows one to determine the maximum number of arbitrary parameters on which the solution of the problem depends. We report analytical solutions for three particular formulations for the case of elastic half-plane and propose a numerical approach for solving the problems of this type for arbitrary contours.