ANALYSIS OF THE EDGE EFFECT OF SHEAR STRESSES IN THE SHIFT OF A TWO-LAYER BEAM

The paper presents a system of resolving equations describing the stress-strain state of multilayer beams and allowing solving a wide range of problems, such as shear, bending, and normal separation for any number of layers. For each of the layers, hypotheses similar to the Kirchhoff - Love hypotheses are introduced. In the proposed model, the layers interact with a contact layer. The contact layer is an anisotropic medium, which can be considered as a “brush” of elastic short rods. For simplicity, it is assumed that the rods are oriented normally to the contact surface. The use of a contact layer allows such problems as infinite tangential stresses at the interface between the layers near the end of the beam and also to solve the problem of determining the concentration of the shearing stresses occurring at the boundaries between the layers and in the corner points, their variation, for example, in the creep process. The main feature of the proposed model is strict satisfaction of the boundary conditions. In view of the complexity of the resolving system of equations, we consider, as an example, the problem of shearing the layers of a double-layer beam. An analytical solution is obtained that allows qualitative analysis of the influence of mechanical and geometric characteristics on the stress-strain state of the design model, calculate the true adhesive strength, and determine the physical characteristics of the contact layer on the basis of experimental data. A numerical example is given for calculating a beam in two variants of model loading, on the basis of which a relationship was established between the true and average adhesive strength, depending on various parameters.