Abstract
The present article considers the formulation and solution of the problem on contact interaction of a pre-stressed band with regularly placed elastic cover plates. The study has been carried out within the framework of the linearized elasticity theory in general form for the theory of large (finite) initial deformations and two variants of the theory of small initial deformations with an arbitrary structure of the elastic potential [1]. The solution of the problem comes down to a singular integro-differential equation for unknown contact stresses with a kernel expressed in the form of a sum of the kernel and some regular kernel under certain boundary conditions. The solution sought is given in the form of a series of Jacobi polynomials. A quasiregular infinite system of linear equations is obtained in order to determine the unknown coefficients of the series [2].
Highlights
Contact interaction of initially stressed bodies is one of topical issues in the field of mechanics of deformable solids
Problems arising with the transfer of stress from the elastic band to regularly placed elastic cover plates – the classical theory of elasticity – are becoming relevant again with the appearance of initial stress in the band
The first is connected with studies of contact interaction of bodies with a concrete form of elastic potential [3]
Summary
Contact interaction of initially stressed bodies is one of topical issues in the field of mechanics of deformable solids The solution to such problems is related to a wide range of questions that arise in engineering, construction and other industries. Strict conditions have been formulated recently: high (guaranteed) durability of structures and machine parts, reliability on the one hand and low material consumption of the latter made with the use of new structural materials. This problem is relevant nowadays and it is of great interest to researchers who solve fundamental and applied problems in the sphere of contact interaction of bodies with initial (residual) stresses. Problems arising with the transfer of stress from the elastic band to regularly placed elastic cover plates – the classical theory of elasticity – are becoming relevant again with the appearance of initial (residual) stress in the band
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