1. Introduction

The boundary integral equation method (BIEM) is widely used to study the stress-strain state (SSS) of anisotropic plates with holes [1–3] and cracks [4–9]. The integral equations for anisotropic plates are usually determined based on the Somigliana identity. Such equations for plates with given stresses at the boundaries of the plate are hypersingular. At the same time, the same problem for isotropic plates is reduced to singular integral equations [10, 11], for which simple numerical algorithms for solving with given precision are obtained.

In [12, 13], the simple dependencies between the Lekhnitskii complex potentials and stress and strain are obtained. In a simple form based on them and the Cauchy theorem, the integral equations are written for anisotropic plates with holes [12, 13] and cracks [14–16]. We will use the established dependencies for the construction and regularization of integral equations for anisotropic plates with holes and cracks.

For conducting experimental studies of crack fracture resistance on experimental samples in relation to isotropic materials, theoretical estimates for stresses at cracks are performed.

For such materials, the stresses in samples of different shapes with cracks under the action of stretching or compressing concentrated forces are studied in detail [10]. The experimental samples for the experimental determination of the

characteristics of crack fracture resistance of various types of materials are made based on performed studies. We perform similar studies for composite samples.
