Construction of Integral Relations of the Theory of Elasticity and Their Application to the Problems of Linear Fracture Mechanics.

We propose new representations of displacements, relative changes in the volume, and angles of rotation of points of a linearly elastic body via the displacements and stresses specified on its surface and deduce integral representations of the boundary conditions for a half space and plane mathematical cuts of any shape. Integral equations for displacements of the surfaces of these cuts are constructed and the results of their solution aimed at finding the stress intensity factors for three-dimensional cracks are analyzed. The proposed relations are compared with the well-known analytic and numerical solutions of the problems of fracture mechanics. [ABSTRACT FROM AUTHOR]