Modeling the dynamics of reinforced shallow shells made of nonlinear elastic materials

The problem of dynamic behavior of flexible reinforced shallow shells made of nonlinear elastic materials of the composition phases is formulated. The geometric nonlinearity of the problem considered in the Karman approximation, and the weakened resistance to shear is taken into account in the framework of non-classical Reddy theory. The numerical integration of the formulated initial-boundary value problem is carried out on the basis of the method of steps in time with the involvement of an explicit "cross" scheme. Specific calculations of the dynamic behavior are carried out for relatively thin and thick shallow spherical shells and plates having an annular shape in plan and with the rigid inner insertion which are under the pressure caused by the blast air wave. Thin-walled structures are clamped on the outer edge and axially reinforced by logarithmic spirals in the plan. The influence of the angles of reinforcement on the flexibility and stress-strain state in the materials of the phase of the composition of elastic plates and shallow shells is studied. It is obtained that on the set of considered structures of reinforcement, the reinforcement in the radial (meridional) directions is rational, as this structure provides the minimal flexibility and the minimal stressed state in the material of the binder matrix of compositions. It is shown that because of the geometric and physical nonlinearity of the studied problem, the dynamic response of composite shallow shells essentially depends on which front surface (convex or concave) the overpressure of the explosive type is applied.