Stressed state of two-layer strip when interacting with rigid base

Abstract

Relevance. In the calculation of multilayer bases, when the material of one or several layers has a pronounced anisotropy, the nature of the distribution of displacements and stresses depends on the direction of the anisotropy axes in each layer. Therefore, it is necessary to have an evaluation of the influence of this factor in the design and analysis of the operation of multilayer media. The aim of the work - to research the stress state in a strip composed of two anisotropic plane-parallel layers with different physical characteristics, lying without friction on a rigid base. Methods. The integration of the equations of the plane problem of the theory of elasticity of an anisotropic body is carried out by the symbolic method in combination with the method of initial functions. The initial functions on the contact line of the strip and the base are determined from the conditions of tight adhesion between the layers, the conditions of tight contact and the absence of friction between the strip and the base, the nature of the load applied to the upper plane of the strip. After transformations, the functions of displacements and stresses in each layer are written through the normal surface load in the form of improper integrals. Results. Plots of changes in stresses in the strip from the values of the characteristics of anisotropic materials, layer thicknesses are given. The maximum stresses on the interface line of the layers and on the line of contact with the base, depending on the direction of the anisotropy axes in each layer, are presented in the tables and shown in graphs. The effect of the elastic modules of materials on the nature of the stress distribution in a strip composed of two isotropic materials is estimated.

Keywords

• displacement stress
• anisotropy
• elasticity
• band
• layer