Elastic–Plastic Deformation of Flexible Plates With Spatial Reinforcement Structures

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 K´arm´an approximation. The dynamic elastic–plastic bending deformation of flat and spatially reinforced metal composite and fiberglass rectangular plates exposed to 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 (of a few tens of percent for metal composite structures and a few hundred percent for fiberglass structures) in strain intensity in the binder and to a decrease (insignificant for metal composite structures and a factor of almost 1.5 for fiberglass) in the compliance of the plate in the transverse direction. It has been found that for relatively thin plates, replacing the flat reinforcement structure by a spatial one leads to a slight decrease in its compliance.