Boundary Value Problems of Plane Elasticity Involving Orientations of Displacements and Tractions

Abstract

This paper presents unconventional formulations of boundary problems of plane elasticity formulated in terms of orientations of tractions and displacements on a closed contour separating internal and external domains as the boundary conditions. These are combined with the conditions of continuity of tractions or displacements across the boundary. Therefore the magnitudes of neither tractions nor displacements are assumed on the contour. Four boundary value problems for both external and internal domains are investigated by analyzing the solvability of the corresponding singular integral equations. It is shown that all considered problems can have non-unique solutions expressed as linear combinations of particular solutions and, hence, contain free arbitrary parameters, the number of which is finite and determined by the contour orientations of tractions and/or displacements