MODELING OF BENDED BEHAVIOR OF SPACE-REINFORCED PLATES OF NONLINEAR-ELASTIC MATERIALS

Based on the procedure of time steps, a mathematical model of bending behavior is constructed for spatially-reinforced plates with nonlinear elastic deformation of the materials of the composition components. The solution of the formulated initial-boundary value problem is based on an explicit numerical “cross” scheme. The possible weakened resistance of reinforced plates to transverse shear is taken into account on the basis of kinematic hypotheses of the Reddy theory. The geometric nonlinearity of the problem is considered in the Karman approximation. It is shown that in the framework of Reddy theory, an explicit numerical scheme cannot be constructed for all arbitrary structures of spatial reinforcement of plates. The dynamic nonlinear elastic behavior of plane-cross and spatially reinforced rectangular plates under the action of an air blast wave is investigated. It is shown that with a strong anisotropy of the composition for relatively thick plates, the replacement of the plane-cross structure of the reinforcement with the spatial structure allows to reduce the flexibility of the structure in the transverse direction by tens of percent (up to 30% or more), and the intensity of deformations in the binder - at times. The reducing the relative thickness of the plate and the degree of anisotropy of its composition reduces the effect of replacing the plane-cross structure of the reinforcement on the spatial structure. In some cases, this effect may not appear even in relatively thick composite structures of more complex geometric shape, for example, in annular plates with a rigid inner insert.