An. Galybin et Sa. Mukhamediev, Plane elastic boundary value problem posed on orientation of principal stresses, J MECH PHYS, 47(11), 1999, pp. 2381-2409
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.