Bending of Equally Stressed Reinforced Plates with Account for Their Weakened Resistance to the Transverse Shear
A. P. Yankovskii
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: упругие пластины, равнонапряженное армирование, изгибное деформирование, теория Рейсснера, неединственность решения, elastic plates, equally stressed reinforcement, bending deformation, the Reissner theory, nonuniqueness of solutions
Abstract
The hypotheses of the Reissner theory are used to formulate the problem of equally stressed reinforcement (ESR) of transversely bent elastic plates by fibers with a constant cross section. The corresponding system of governing equations and boundary conditions is performed. The model problem of ESR of rectangular elongated plates subjected to cylindrical bending with various types of loading of one of the longitudinal edges and rigid clamping of the other one. It is shown that there could exist two solutions of the problem of ESR, one of which is regular and the other one singular. The edge effects occurring in the presence of the torque applied to the edge, which significantly affects both the stress-strain state of the binder material and the reinforcement structure.
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