Abstract
Relevance. Different models of contact between bodies are used in determining the stressed and deformed state in the strip lying on the base. It is necessary to evaluate the qualitative and quantitative nature of the change in stress in the strip depending on the coupling of the strip and base. The aim of the work - to analyze the effect of the coefficient of friction on the value of stresses in an anisotropic band when interacting with a rigid base. Methods. The solution is based on the equations of the plane problem of the theory of elasticity of an anisotropic body under the conditions that the band is closely adjacent to the base and the tangent force on the contact plane is proportional to the normal pressure. Displacements and stresses at any point of the strip are written in the form of the method of initial functions through the functions of displacements and forces on the lower plane, which depend on the nature of the load applied on the upper plane and the conditions of contact between the strip and the base. After the transformations, the calculation formulas for displacements and stresses are expressed using the Fourier integral transform through the normal surface load in the form of improper integrals. Results. Formulas for determining displacements and stresses are obtained for the variant of loading a strip with a concentrated force. These formulas are used to construct influence functions for the problem of equilibrium of an anisotropic strip lying on a rigid base, taking into account friction. Graphs of the effect of the coefficient of friction and the direction of the anisotropy axes of the material on the stress state of the strip are presented. The results of stress calculation are compared using anisotropic and isotropic models.
Highlights
Different models of contact between bodies are used in determining the stressed and deformed state in the strip lying on the base
Article history: Received: January 16, 2020 Revised: February 28, 2020 Accepted: March 12, 2020
Summary
Полоса из анизотропного материала постоянной высоты h и бесконечной длины лежит на жестком основании (рис. 1). Полоса из анизотропного материала постоянной высоты h и бесконечной длины лежит на жестком основании Ось x направим вдоль нижней плоскости полосы, ось y ‒ перпендикулярно основанию. На верхней плоскости действует нормальная симметричная относительно оси y поверхностная нагрузка q(x). Положительные направления нормальных x , y и касательного xy напряжений, перемещений u и совпадают с обозначениями [18]
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