Investigation of Bending of Anisotropic Plates with Inclusions with the Help of Singular Integral Equations

We consider the problem of bending of an anisotropic plate of constant thickness with rigid inclusions. The algorithm of its solution is constructed on the basis of reduction of the problem of bending of a multiply connected anisotropic plate with inclusions to the evaluation of the Lekhnitskii potentials for an auxiliary plane problem of the theory of elasticity with properly chosen elastic constants. To solve this auxiliary problem, we use the method of singular integral equations in the complex form. We consider the problems of bending for plates with inclusions subjected either to the action of moments at infinity (for infinitely large plates) or to transverse loading (for finite plates). We also present some examples of evaluation of stresses acting in the plates containing rigid inclusions of different shapes or systems of inclusions of this kind.