Deformable body impact: dynamic plastic behaviour of a moving free–free beam striking the tip of a cantilever beam

Abstract

A theoretical model based on the rigid, perfectly plastic material idealization is proposed to simulate the dynamic behaviour of two deformable beams colliding with each other. The mid-point of a moving free–free beam is assumed to impinge on the tip of a cantilever beam with the beam axes perpendicular to each other. Complete solutions are obtained for various deformation mechanisms during the dynamic response process for the two deformed beams, and plastic shear sliding is taken into account. Attention is focused on the partitioning of the input energy between the two deformed beams after impact. A deformation map in a governing parameter plane is constructed to permit the calculation of the energy partitioning for a range of the beams’ parameters. This consists of nine regions corresponding to various deformation mechanisms. Typical numerical results are presented to demonstrate the influence of structural and geometrical parameters such as the ratios of the fully plastic bending moments of the two beams, of their fully plastic shear forces, of their masses per unit length and their length, on the energy partitioning after impact. Finally, the severance limit is given for the case of both beams having rectangular cross-sections. This indicates that shear sliding failure may happen in either of the beams if the initial kinetic energy is sufficiently large.