Shevchuk S. Stress-strain state of layered anisotropic bodies with thin elastic inclusions

The work concerns the investigation of the stress-strain state of layered anisotropic structures with thin elastic inclusions for the complete spectrum of mechanical property change from absolute rigidity to absolute pliability. On the basis of the jump functions method a general procedure for construction of solutions to the 2D problems is developed, using the Fourier integral transform and subsequent reducing the problem to the systems of singular integral equations for the unknown jumps of stresses and displacements on the inclusion median lines. New antiplane and plane problems of elasticity theory are solved for a space, half-space, layer, piecewise-homogeneous medium with thin elastic inclusions under the action of the distributed stress field at infinity and concentrated force and dislocation factors. The influence of the mechanical and geometric characteristics of the medium components on the generalized stress intensity factors near inclusions, stress and displacement fields in the body and the force exerted on the edge dislocation is studied.