Stress Analysis of an Anisotropic Plate with Embedded Thin Elastic Inclusions

Abstract

The stress field in an anisotropic plate containing a system of thin elastic inclusions is studied. It is assumed that ideal mechanical contact occurs between the inclusions and the plate. The inclusion is considered as an elastic plate whose width is much smaller than its length. For the inclusions, boundary conditions are formulated under the assumption that the shear and normal stresses and the derivatives of the displacements are discontinuous at the contact line. Special integral representations of the solution of the problem determined from the boundary conditions at the contact line are constructed. The problem is reduced to a system of integral equations, which is solved by a numerical method. The effect of the stiffness and geometry of the elastic inclusions on the distribution and magnitude of the contact stresses is studied. Numerical results are compared with the data obtained by a simplified model in which the elastic inclusion is considered as a thin thread.