Nonlinear dynamic buckling of a cylindrical shell panel model

The dynamic buckling response of a spring-mass, geometrically imperfect, dissipative model with three degrees of freedom simulating a relatively deep cylindrical shell panel under step loading is comprehensively analyzed. The main feature of the real continuous structure and its corresponding model is that, under the same loading statically applied, both exhibit snapping. Energy, topological, and geometric considerations allow us to establish qualitative and quantitative criteria leading to dynamic buckling loads of both dissipative and nondissipative models without integrating the highly nonlinear equations of motion. An a priori knowledge of the accuracy of these buckling estimates is successfully obtained by discussing the geometry of the channel in which the motion takes place before reaching the escape passage through a saddle (or its neighborhood) with very small negative total potential energy. A comparison of the numerical results obtained by the proposed method with those of Runge-Kutta-Verner scheme shows the reliability and efficiency of the proposed method.