The contact problem for a prestressed elastic strip reinforced with equally spaced elastic plates is considered. The Fourier integral transform is used to construct an influence function of a unit concentrated force acting on the infinite elastic strip with one edge constrained. The transmission of forces from the thin elastic plates to the prestressed strip is analyzed. On the assumption that the beam bending model and the uniaxial stress model are valid for an elastic plate subjected to both vertical and horizontal forces, the problem is mathematically formulated as a system of integro-differential equations for unknown contact stresses. This system is reduced to an infinite system of algebraic equations solved by the reduction method. The effect of the initial stresses on the distribution of contact forces in the strip under tension and compression is studied.
The plane contact problem of the transfer of a horizontal concentrated load from an infinite stringer to two identical prestressed strips clamped at one edge is solved using the linearized theory of elasticity. The solution is found in general form for the theory of large initial deformations and different theories of small initial deformations for an arbitrary elastic potential. The problem for the normal and tangential contact stresses is reduced to a system of integro-differential equations derived using the Fourier transform. The contact stresses are represented by Fourier integrals. It is shown that the initial stresses in the strips affect strongly the distribution of contact stresses: the contact stresses substantially decrease under compression and increase under tension, whereas the displacements increase under compression and decrease under tension. The effect of the initial stresses is stronger in highly elastic materials than in stiff material
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].
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