Modeling the Dynamic Bending of Rigid-Plastic Hybrid Composite Curvilinear Plates with a Rigid Inclusion

Abstract

A general method has been developed for calculating the dynamic behavior of rigid-plastic composite layered fibrous plates with a rigid inclusion and with the hinged or clamped arbitrary smooth non-concave curvilinear contour subject to a uniformly distributed short dynamic explosive loading of high-intensity. The distribution of layers is symmetric with respect to the middle surface, and in each layer there is a family of reinforcement curvilinear fibers in the directions parallel and normal to the plate contour. The structural model of the reinforcement layer with a one-dimensional stress state in the fibers is used. Depending on the loading amplitude, different types of plate deformation are possible. Based on the principle of virtual power in combination with the d’Alembert principle, the equations of dynamic deformation are derived and their implementation conditions analyzed. The analytical expressions for assessing the limiting loads, deformation time, and residual deflections of the plates are obtained. It is shown that the variation in the reinforcement parameters significantly affects both the loading capacity of such plates and the residual deflections. Examples of numerical solutions are provided.