Modeling of dynamic behavior of reinforced cylindrical shells under elastic-plastic deformation of materials of composition components

The initial boundary value problem of elastic-plastic deformation of flexible fibrous cylindrical circular shells is formulated. The crossed reinforcement is located on equidistant surfaces. The mechanical behavior of the materials of the composition components is described by the equations of the theory of flow with isotropic hardening. The geometric nonlinearity is taken into account in the Karman approximation. The weakened resistance of the fibrous shells by the transverse shear is taken into account. The system of governing equations and the corresponding boundary and initial conditions, which allow determining the stress-strain state in the components of the composition of flexible cylindrical shells with varying degrees of accuracy, are obtained. The relations of the traditional non-classical Freddy theory follow from the obtained equations, boundary and initial conditions in the first approximation. The solution of the formulated initial-boundary problem is based on an explicit numerical "cross" scheme. The features of inelastic dynamic and quasi-static deformation are studied for very short, short and long fibrous cylindrical shells of different relative thicknesses for different reinforcements. It is found that under dynamic loading of such structures by internal pressure, Reddy theory can lead to inadmissible results. The difference in the calculations of the Reddy theory and the refined theories increases with the increasing time interval. It is shown that for the dynamic calculations of very thin cylindrical reinforced shells, it is necessary to take into account the change of their metrics on the thickness of the structure. It is shown that due to the geometric and physical nonlinearity of the formulated problem, the maximum deflections in thin shells can occur after several tens of oscillations of the fibrous structure, and not only the neighborhood of the initial moment of time when the cylindrical shell is under short-term intensive dynamic loading.