Determination of stress state of anisotropic plates with rigid inclusions based on singular integral equations

In the paper singular integral equations for anisotropic plates with inclusions (the Dirichlet problem) are developed in the simple form on the basis of established dependencies between the Lekhnitskii complex potentials, stress and displacements. The numerical method for solving integral equations is developed on the basis of the quadrature method for the inclusion system. The eigen solutions of the problem were taken into consideration in this method. Simplicity, accuracy of the approach and stability of the obtained systems of algebraic equations are illustrated during: finding stress with controlled accuracy for systems of the large number of rigid inclusions, determining the high stress concentration near inclusions with corner points (the asymptotic method is additionally used).