Nonlinear Mathematical Model for Dynamic Buckling of Stiffened Orthotropic Shell Panels

Abstract

This presents a mathematical model proposed by the author for description of deformation process of a shell structure under the action of a load that depends linearly on time. Material orthotropy, geometric nonlinearity, transverse shifts are taken into account. A distinctive feature of the model is the use of a refined discrete method for taking into account stiffeners, proposed by the author earlier. Prior to this, the method was used only in static or isotropic dynamic problems. It is proposed to add correction normalizing factors, which makes it possible to obtain the most accurate values of critical loads. The methodology of the calculation algorithm under dynamic loading is based on the Kantorovich method and the Rosenbrock method, which allows solving rigid ordinary differential equation (ODE) systems. New numerical results for cylindrical panels are obtained. The influence of the number of stiffening elements on the values of the critical load is shown. A comparison with the classical discrete method of taking into account stiffeners is carried out. For the problems considered in this paper, the phase portraits of the system are shown.