Viscoelastic-Plastic Deformation of Plates with Spatial Reinforcement Structures
A. P. Yankovskii
Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia
Keywords: пластины, пространственное армирование, плоское армирование, динамический изгиб, теория Редди, вязкоупругопластическое деформирование, тело Максвелла - Больцмана, схема типа "крест", plates, spatial reinforcement, flat reinforcement, dynamic bending, Reddy theory, viscoelastic-plastic deformation, Maxwell-Boltzmann body, "cross" type scheme
Abstract
A mathematical model of viscoelastic-plastic flexural deformation of spatially reinforced plates was developed based on the method of time steps. The viscoelastic behavior of the components of the composition is described by the Maxwell-Boltzmann equations, and plastic behavior by flow theory with isotropic hardening. The low resistance of composite plates to transverse shear is taken into account within the framework of Reddy's theory, and the geometric nonlinearity of the problem is considered in the Karman approximation. The corresponding initial-boundary-value problem is solved using a numerical scheme of the “cross” type. The dynamic viscoelastic plastic bending of spatially reinforced fiberglass rectangular plates under the influence of an air blast wave was investigated. It is shown that for relatively thick plates, replacing a flat reinforcement structure by spatial leads to a significant decrease in the maximum and residual deflections and strain intensities of the binding material, while for relatively thin plates, this replacement is ineffective. It is found that in the initial stage of deformation, the amplitude of oscillation of the composite plate significantly exceeds the residual deflection.
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