Experimental And Theoretical Study On Bending Collapse Of Dual And Triple Rectangle Thin-walled Tubes

Thin-walled tubes are widely used in automobiles,buses,aircraft and other areas as protective devices to absorb kinetic energy.Under impact such tubes usually buckle locally(axial crush and bending collapse)and their load-carrying capacity shows quite differently,which are characterized by large displacements,large localized strains and material nonlinear behavior.In order to predict the collapse behavior of such tubes with reliable accuracy,one could rely on the finite-element codes or experiments.These tools are helpful but not desirable in the conceptual design stage because of the high costs and extensive running times.A theoretical,quick estimate of the collapse behavior for such tubes is therefore useful and beneficial.On the one hand,many researchers have carried out a lot of detailed research on the axial crushing and pure bending collapse characteristics of various section thin-walled tubes.These theoretical results can be conveniently used for crash analysis of complex structures,greatly improving modeling and computational efficiency.On the other hand,there lacks of research on the bending collapse characteristics of thin-walled beams with multi-cell sections,especially related experimental studies.In this paper,an efficient theoretical method is proposed to predict the bending collapse characteristics of the dual rectangle thin-walled tube(DRTWT)and triple rectangle thin-walled tube(TRTWT)based on the experimental investigation and theoretical analysis.In the experimental investigation,the deformation process of the DRTWT and TRTWT aluminum profiles was studied by the three-point bending experiment.On the basis of the main characteristics of the true deformation,a theoretical model of the bending collapse of the profile is obtained.This essentially constructs a set of displacement fields that describe the deformation of the bending collapse,in which there exists undetermined parameters(half of the hinge length and rolling radius)in the displacement field.Since the deformation of the thin-walled tubes is concentrated in a small local area,it is assumed that all the deformed energy of the material is absorbed and distributed along the hinge lines and in the toroidal surfaces during the bending collapse,so the theoretical load-displacement formula of the thin-walled beam during the bending collapse can be obtained according to the conservation of mechanical energy.According to the upper bound theorem,there is a displacement field which make the ultimate load take the minimum value.By this condition,half of the hinge length and rolling radius of the displacement field can be determined.This means that one is selected from a set of displacement field which is closest to the true solution in a certain sense.After determining the maximum nominal stress of the material by uniaxial tensile test,the theoretical loaddisplacement formula is compared with experimental data for validation of the theory.However,the upper bound solution is not applicable to the initial stage of the bending collapse.To obtain the initial bending collapse moment of the thin-walled beam,stress analysis must be performed.According to the buckling theory of the compressed thin plate,the initial bending collapse moment formula of the thin-walled beam with the DRTWT and TRTWT section are derived.Combined with the previous displacement analysis,the theoretical relationship between the bending moment and the plastic angle of the cross section of the thin-walled beam is obtained.Then,the theoretical formula is compared with the experimental results and numerical simulation results to verify the proposed method.In terms of application,a software for analyzing the bending collapse characteristics of thin-walled beams with the DRTWT and TRTWT section is developed.Users only need to input the geometric parameters and material parameters of the beam to obtain the bending momentplastic angle curve.In addition,simplified finite element models of the curved beam and the front structure of the vehicle body are created by using the beam and the spring elements for crash analysis.In the simplified model,the bending moment-plastic rotation curve of the beam is given to the spring element to simulate the bending collapse characteristic.Compared with the detailed model,the accuracy of the simplified model exceeds 80%,as well as the calculation efficiency is improved by 99%.It is of great significance for the crashworthiness analysis of automotive structure at the conceptual design stage.