An Energy Approach to Anomalous Damped Elastic-Plastic Response to Short Pulse Loading

In beams with full-end constraints, loaded transversely by short pressure pulses, the effect of extensional plastic deformation is to make possible instabilities related to snap buckling in the elastic-plastic recovery after the first peak displacement (Symonds and Yu, 1985). In the present paper we make use of a damped, Shanley-type model to study the calculation of the final displacement, reached asymptotically. We show that plots of the elastic strain energy and of the total energy as functions of the displacement help to guide thinking. They provide clarification of previously observed phenomena (Genna and Symonds, 1988) that appear complex at small damping, and lead to lower and upper bounds on the load parameter such that anomalous responses are observed. The response is calculable with the usual accuracy in problems where bifurcations are concerned.