An improved energy criterion for dynamic buckling of imperfection sensitive nonconservative systems

Abstract

Abstract Imperfection sensitive, multi-degree-of-freedom, autonomous, structural systems under partial follower compressive loading, which lose their stability via divergence are investigated both qualitatively and quantitatively. Attention is focused on the global instability of that equilibrium state on the locally stable primary path, which at a certain level of the loading becomes globally unstable. Previous work valid for potential systems under step loading is extended here to nonpotential, imperfection sensitive systems. The serious difficulty of the lack of potential of the follower type of loading is overcome by formulating an appropriate energy balance equation, including loss of energy. Then, similar considerations to those for potential systems can be established, and geometric criteria can be formulated for an “equivalent energy” surface. Using the mean-value theorem for integrals one can obtain approximate dynamic buckling loads that are very good for structural design purposes. The efficiency and reliability of the proposed method is comprehensively demonstrated through numerous examples.