Dynamic Buckling Estimates for Discrete Systems under Step Loading

Abstract

AbstractThis paper deals with nonlinear dynamic buckling analysis of imperfection sensitive or more generally limit point discrete systems under suddenly applied loads of infinite duration. Static and dynamic stability conditions and respective buckling estimates for such systems without or with damping are properly established. It was shown that the static stability criterion associated with zero total potential energy and negative definite second variation leads always to exact dynamic buckling loads for one‐degree‐of‐freedom systems if damping is ignored, and to lower bound buckling estimates if this effect is included. It was also found that such a static criterion leads always to lower bound dynamic buckling estimates for multi‐degree‐of‐freedom systems with or without damping. Moreover, it was established that dynamic buckling associated with an unbounded (damped or undamped) motion occurs for that magnitude of the load for which the velocity of the phase point corresponding to any one of the generalized coordinates of the system vanishes for the first time.