Dynamic modelling of elastic-plastic beams under impact

This study is aimed to investigate the dynamic response of a fully clamped beam subjected to impact loadings by a rigid mass. First, the analytical formulae are derived for predicting the quasi-static force-deformation relations of an elastic-plastic beam during loading and unloading. For a particular impact scenario in which the striker with a heavy mass impinges the mid-span of the beam at a low speed, it is assumed that the dynamic deformation mode remains identical to the quasi-static one. By employing energy method, the quasi-static characteristics are utilized to develop an elastic-plastic theoretical model of the beam under impact loadings so as to predict its dynamic behaviour during the loading, unloading and subsequent elastic vibration stages. Validation and comparison are conducted against numerical simulations using the commercial software package ABAQUS and it is shown that the proposed elastic-plastic theoretical model is capable of providing a good prediction of the overall dynamic behaviour of the beam under impact. In parallel, comparisons between the predictions of the current elastic-plastic model and those of the rigid-plastic analysis are carried out to highlight the elastic effect on the accuracy of modelling an elastic-plastic beam under impact.