{'fraction_non_alphanumeric': 0.01642608262817322, 'fraction_numerical': 0.0, 'mean_word_length': 5.320754716981132, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
New insights into the collapsing of cylindrical thin-walled tubes under axial impact load

Abstract The current paper presents further investigations into the crushing behaviour of circular aluminium tubes subjected to axial impact load. Experiments prove that in order to achieve the real collapsing shape of tubes under axial loads in numerical simulations, an initial geometric imperfection corresponding to the plastic buckling modes should be introduced on the tube geometry before the impact event. In this study, it is shown that the collapsing shape of tube is affected by this initial imperfection and consequently it is shown that by applying an initial geometric imperfection similar to the axisymmetric plastic buckling mode, the tubes tend to collapse in a concertina mode. This phenomenon is studied for circular tubes subjected to axial impact load and two design methods are suggested to activate the axisymmetric plastic buckling mode, using an initial circumferential edge groove and using one- and two-rigid rings on the tube. In each case the broadening of the concertina collapsing region is estimated using numerical simulations. Experimental tests are performed to study the influence of cutting the edge groove on the collapsing mode. In order to optimize the crashworthiness parameters of the structure such as the absorbed energy, maximum deflection in axial direction, maximum reaction force, and mean reaction force, a system of neural networks is designed to reproduce the crushing behaviour of the structure, which is often non-smooth and highly non-linear in terms of the design variables (diameter, thickness, and length of tube). The finite-element code ABAQUS/Explicit is used to generate the training and test sets for the neural networks. The response surface of each objective function (crashworthiness parameters) against the change of design variables is calculated and both single-objective and multi-objective optimizations are carried out using the genetic algorithm.