Contact problem of elastic strips with initial stresses with periodically placed resilient protective strap

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].