Anomalous elastic–plastic responses to short pulse loading of circular plates

Abstract

It is shown that a circular plate with fully fixed boundary may exhibit anomalous nonlinear elastic, perfectly plastic response behaviours of the same type that have been shown to occur in a beam whose ends are fixed against both axial and transverse displacements. “Anomalous” here means that the final deflection may be either in the direction of the applied external force during the pulse, or in the opposite (“negative”) direction. When the plate is modelled with two or more degrees of freedom the response may be chaotic and the final deflection unpredictable because of extreme sensitivity to parameters. In this paper results are shown of calculations by the general purpose finite element code ABAQUS and by Galerkin models of one, two, three, and eight degrees of freedom. For simplicity the assumption of sandwich plate behaviour is adopted, but comparisons are also shown for plates of uniform section.