Arbitrary Oriented Defects in Anisotropic Quarter Plane

Abstract

To solve the problems about arbitrary oriented defects in anisotropic quarter plane, a method based on the use of the space of generalized functions with slow growth properties was developed. Two-dimensional integral Fourier transform was used to construct the system of fundamental solutions for anisotropic quarter plane with the concentrated jumps of stresses and displacements in this space. The latter allows the problems about the defects to be reduced to systems of singular integral equations (SIE) with fixed singularities. As an example the problem about the crack exiting to the boundary of the quarter plane has considered, for which the system of SIE with fixed singularities is obtained. To determine the singularities’ indexes of the stresses and displacements at the vertices of the quarter plane and of the crack the transcendental equations are obtained. The asymptotic behavior of the solutions is investigated. The efficient numerical-analytical method for solving systems of SIE with fixed singularities is proposed.