Plane elastic boundary value problem posed on orientation of principal stresses

A non-classical boundary value problem of 2-D elasticity for a simply conne cted domain with a smooth bounding contour is considered. The orientation o f principal stresses and curvature of their trajectories at the boundary ar e used as boundary conditions. Boundary conditions of this type, which have not been investigated before, have direct applications to the problem of c onstruction of the tectonic stress field in lithospheric plates. The method of singular integral equations is applied to analyze the solvability of th e problem. It is shown that for stress fields bounded inside the domain, th e solvability depends upon the number of rotations of the principal stress axes while traversing the contour. The number of rotations determines the n umber of linearly independent solutions of the problem. It is shown how; th e number of solutions can be found in the case of a unit circle. (C) 1999 E lsevier Science Ltd. All rights reserved.