NONLINEAR DYNAMIC BUCKLING OF DISCRETE DISSIPATIVE OR NONDISSIPATIVE SYSTEMS UNDER STEP LOADING

Nonlinear dynamic buckling of nonlinearly elastic, nondissipative or dissipative, multimass systems under step loading of infinite or finite duration is thoroughly discussed. Attention is restricted to discrete structural systems that under the same loading applied statically experience snapping or bifurcational instability associated with an unstable branching point lying either on a trivial or a nontrivial primary equilibrium path. Considering the stability of motion in the large the mechanism of dynamic instability and the nature of the dynamic critical point are properly investigated. Dynamic buckling criteria leading to exact dynamic buckling loads, as well as a simple static buckling criterion yielding lower bound buckling estimates of practical importance, are established. Finally, error estimates of the lower bound buckling loads obtained by the static buckling criterion are also assessed.