Some problems in modelling a rigid-plastic cantilever beam subjected to impact loading

A rigid-plastic model is used in this paper to analyse the behaviour of a cantilever beam subjected to impact loading. It is well known that deformation localisations in such a model are represented by plastic hinges during its transient response. These plastic hinges, including bending and shearing hinges, are basically discontinuity interfaces of the generalised displacements. By assuming a convex yield function of bending and shear, continuity conditions at a moving or stationary plastic hinge are herein examined, with particular reference to the presence of shear deformations at the hinge. Then, some interesting works of existing literature about this theme are discussed and a more general kinematic mechanism for the beam under study is proposed. The numerical procedure carried out in this paper is referred to an early stage of motion, characterised by two stationary hinges, at the root and at a some point between the root and the free end. The results of this analysis are illustrated and discussed in comparison to the results from other authors.