CAUCHY BVP FOR ELASTIC HALF-PLANE POSED IN DISPLACEMENT ORIENTATIONS

Abstract

This study presents a Cauchy-type boundary value problem of plane elasticity in which the boundary conditions are posed in terms of the orientations of the displacement vector and its normal derivative. No magnitudes of the displacements are specified. The problem is reduced to a singular integral equation by using the well-known Muskhelishvili’s theory based on the complex potentials. The solvability of the integral equation is analysed in accordance with the Gakhov’s approach, which reveals that the problem has a finite number of linearly independent solutions depending on the index of the corresponding Riemann BVP. The index is defined through the orientations of the contour displacements. More detailed analysis is performed for the case of elastic half-plane since previously it has been shown that the shape of the domain does not influence the solvability. A numerical approach for solving the problem for the arbitrary domain is outlined.