Viscoelastic—Plastic Deformation of Plates with Spatial Reinforcement Structures

Abstract

A mathematical model of viscoelastic-plastic bending deformation of spatially reinforced plates is developed based on the time step method. 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 von Karman approximation. The corresponding initial-boundary-value problem is solved using a leapfrog numerical scheme. The dynamic viscoelastic-plastic bending of spatially reinforced fiberglass rectangular plates subjected to air blast wave loading is investigated. It is shown that for relatively thick plates, replacing a flat reinforcement structure by a spatial reinforcement structure leads to a significant decrease in the maximum and residual deflections and strain intensity of the binder material, and 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 far exceeds the residual deflection.