Rectilinear crack in a composite orthotropic plane (Q2753470)

A matrix of fundamental solutions for a composite orthotropic plane is constructed. This is the matrix-function from the space of generalized functions of slow growth, \(S'(R^2)\) elements of which describe stress-strain state of inhomogeneous plane with concentrated jumps of stresses and displacements at arbitrary point. Construction of this matrix is reduced to the matrix Riemann problem in the space \(S'(R^2)\). Solution of the latter problem is constructed on the basis of analytic properties of the generalized Fourier transform. Using the fundamental matrix, the problem on arbitrary thin defects in inhomogeneous orthotropic plane can be reduced to singular integral equations. The technique is illustrated by a problem of rectilinear crack with the tip at the interface of materials.