Dynamic Buckling of Stiffened Shell Structures with Transverse ‎Shears under Linearly Increasing Load

Thin-walled shell structures are widely used in various fields of engineering, and the process of their deformation is essentially non-linear, which significantly complicates their analysis. The author presents a new mathematical model of shell structure deformation under dynamic loading, taking into account geometrical nonlinearity, transverse shears, and stiffeners. A distinctive feature of the model is the use of the refined discrete method to account for stiffeners, suggested by the author earlier. The method has previously been used only in static problems. It uses adjusting normalizing factors and makes it possible to obtain the most correct critical load values. A technique for numerically investigation of the process of deformation of such structures under dynamic loading is based on the L.V. Kantorovich method and Rosenbrock method for solution of a stiff ODE system. The proposed approach, in contrast to commercial software based on FEM, makes it possible to study in detail the supercritical deformation of structures, to identify patterns of influence of individual parts of the mathematical model on critical loads. Calculations for shallow doubly curved shells and cylindrical panels are provided. It is shown how the number of stiffeners affects the resulting buckling load values. A comparison with the classic discrete method to account for stiffeners is performed. Phase portraits of the system are given for all problems considered.