Modeling of elastoplastic deformation of flexible shallow shells with spatial reinforcement structures

Abstract

A mathematical model of elastic-plastic deformation is constructed for spatially reinforced flexible flat shells on the basis of the method of time steps. The solution of the corresponding initial-boundary value problem is constructed by an explicit “cross” scheme. The inelastic behavior of the materials of the composition phases is described by the theory of flow with isotropic hardening. The possible weakened resistance of the fibrous shallow shells to transverse shears is taken into account in the framework of a refined kinematic model, from which, as a special case, the Reddy theory is obtained. The geometric nonlinearity of the problem is taken into account in the form of the Karman approximation. The elastic-plastic dynamic bending deformation is investigated for "flat" and spatially reinforced glass-plastic and metal-composite cylindrical panels under the action of explosive loads. It is shown that for both relatively thick and relatively thin flat shells, the replacement of the "flat" cross-reinforcement structure by the spatial one can lead to a decrease in the design flexibility in the transverse direction by several tens of percent. It is demonstrated that the traditional non-classical Reddy theory does not guarantee adequate results of dynamic calculations of non-elastic deformable composite curved panels even with their small relative thickness and weakly expressed anisotropy of the composition (metal-composition). It is found that due to the physical and geometric nonlinearity of the problem under consideration, the maximum deflection modulo in the reinforced shallow shell of small relative thickness can be achieved much later than the removal of short-term dynamic load.