Modeling the Dynamic Response and Establishing Post-buckling/ Post Snap-thru Equilibrium of Discrete Structures via a Transient Analysis

Abstract

Results of a transient analysis developed to model the dynamic response and establish post-buckling/post snap-thru equilibrium of discrete structures are presented. Three systems that exhibit unstable buckling characteristics are analyzed. The analysis consisted of first statically loading the structures up to there respective static limit loads. The structure is then perturbed from their critical state and a transient analysis is used to model the ensuing dynamic response. The transient formulation is first applied to two simple one-degree-of-freedom systems consisting of rigid links, springs, dampers, and lumped masses. The first of these systems was an arch with a point load applied at its vertex. This structure admits dynamic snap-thru response when loaded beyond its limit load. The second system was a model of a curved panel under an applied axial end-shortening. This system exhibited dynamic buckling behavior consisting of a large decrease in the resultant axial load when loaded beyond its limit load. The transient analysis was then applied to a finite element model of a cylindrical shell with a cutout under an applied axial compression load to model the dynamics of the global buckling response upon reaching its limit load. The results from this study illustrate the usefulness of the transient analysis in modeling the dynamics of an unstable structural response and establishing equilibrium beyond any points of instability.