Singular Integral Equations for the Bending Problems of Multiconnected Anisotropic Finite Plates

Abstract

The bending problem of an anisotropic finite plate with smooth boundary containing defects like nonintersecting through thickness curvilinear cracks and rigid inclusions is considered. The problem is solved by the Lekhnitskii method of complex potentials written in the form of Cauchy-type integrals along the defect contours with unknown integrand density function which has the root type singularity on the defect tips. The boundary-value problem is reduced to a system of singular integral equations subject to the conditions for the displacements to be single-valued upon circulating the closed contours around the cuts and equilibrium conditions for rigid inclusions. To illustrate the efficiency of the method proposed, some specific plate bending problems are solved. The stress distribution in the vicinity of the defect tips are studied for various plate configurations and orientation of defects. For isotropic plates, the solutions are obtained by setting appropriate numerical values of the anisotropic constants.