Elastic-Plastic Deformation of Flexible Plates with Spatial Frame Structures
A. P. Yankovskii
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: гибкие пластины, плоское армирование, пространственное армирование, теория Редди, динамический изгиб, упругопластическое деформирование, схема типа 'крест', flexible plates, flat reinforcement, spatial reinforcement, Reddy theory, dynamic bending, elastic-plastic deformation, leap-frog scheme
Abstract
A mathematical model for the elastic-plastic bending deformation of spatially reinforced plates is constructed based on a leap-frog numerical scheme. The elastic-plastic behavior of the component materials of the composition is described by the theory of flow with isotropic hardening. The low resistance of the composite plates to transverse shear is taken into account using Reddy's theory and the geometric nonlinearity of the problem using the von Karman approximation. The dynamic elastic-plastic bending deformation of flat and spatially reinforced metal composite and fiberglass rectangular plates under the action of an air blast wave is investigated. It is shown that for relatively thick plates, replacing a flat leap-frog reinforcement structure by a spatial one leads to a decrease in strain intensity in the binder (a few tens of percent for the metal composite structure and a few hundred percent for the fiberglass structure) and to a decrease in the pliability of the plate in the transverse direction (insignificant for the metal composite structure and a factor of almost 1.5 for fiberglass). It has been found that for relatively thin plates, replacing the flat reinforcement structure by the spatial one leads to a slight decrease in its pliability.
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