Energy absorption of axially compressed thin-walled square tubes with patterns

The paper suggests the introduction of patterns to the surface of conventional thin-walled square tubes to improve the energy absorption capacity under axial compressive loads. A quasi-static axial crushing analysis has been conducted numerically by the nonlinear explicit finite element code LS-DYNA. Two types of patterns constructed using the basic pyramid elements were introduced. Type A pattern was aimed at triggering the extensional mode for relatively thin square tubes whereas type B pattern was intended to develop new collapse mode capable of absorbing more energy during collapse. A total of 30 tubes with a length of 120 mm, thickness 1.2 mm and widths of 40 or 60 mm were simulated. Numerical results showed that all tubes with type A patterns developed the extensional collapse mode instead of the symmetric collapse mode and absorbed about 15–32.5% more energy than conventional thin-walled square tubes with a mass increase less than 5%. Meanwhile, a new collapse mode named octagonal collapse mode was observed for tubes with type B pattern and the energy absorption of tubes developing this mode increased by 54–93% compared with the conventional tube. The influence of various configurations of the patterns on the deformation and energy absorption of the tubes was also discussed. The paper opens up a new avenue in design of high energy absorption components.     

Finite element simulation of the axial collapse of metallic thin-walled tubes with octagonal cross-section

The present paper deals with the implementation of the explicit FE Code LS-DYNA to simulate the crash behaviour and energy absorption characteristics of steel thin-walled tubes of octagonal cross-section subjected to axial loading. The collapse procedure is successfully simulated and the obtained numerical results are compared with actual experimental data from small-scale models and useful concluding remarks pertaining to the design requirements of the crushing process are drawn.     

Bending collapse of thin-walled circular tubes and computational application

This paper focuses on describing the bending collapse behavior of thin-walled circular tubes. In this paper, global energy equilibrium theory is applied to derive the relationship between the applied moment and the bending angle of circular tubes. A general bending collapse mode of circular tubes is referenced for the derivation, and it is assumed that during bending crush, all impact energy is absorbed and distributed along the hinge lines. After obtaining the relationship, it is compared to a published theory of tubular structure's bending resistance, which was obtained from analytical and experimental studies. The derived bending resistance is then applied to generate simplified circular tube models, which have different cross-sections and are made of different materials. Crashworthiness analyses are performed on these simplified models as well as detailed tube models, and the crash results are compared to verify the efficiency of the generated simplified model and the accuracy of the derived tube's bending resistance. All the problems involved in this paper are solved by means of LS-DYNA.     

Computer simulation and energy absorption of tapered thin-walled rectangular tubes

Tapered thin-walled tubes have been considered desirable energy absorbers under axial loading due to their relatively stable crush load and deformation response compared with straight tubes. This paper compares the energy absorption response of straight and tapered thin-walled rectangular tubes under quasi-static axial loading, for variations in their wall thickness, taper angle and number of tapered sides. Overall the study highlights the advantages of using tapered tubes as energy absorbers. In particular, the peak load required to crush the tubes decreases with the introduction of a taper, and as the taper angle increases. This is desirable for minimising the impact loads transmitted to the protected structure. The practical outcome of the study is design information for the use of tapered thin-walled rectangular tubes as energy absorbers in impact loading applications. Analysis has been undertaken using a finite element model, validated using existing theoretical and numerical models.     

Energy absorbtion and mean crushing load of thin-walled grooved tubes under axial compression

In the present study, crashworthiness characteristics of thin-walled steel tubes containing annular grooves are studied. For this purpose, the grooves are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube. The aims are controlling the buckling mode and predicting energy absorption capacity of the tubes. To do so, circumferential grooves are cut alternately inside and outside of the tubes at predetermined intervals. Quasi-static axial crushing tests are performed and the load-displacement curves are studied. Theoretical formulations are presented for predicting the energy absorption and mean crushing load. It is found a good agreement between the theoretical results and experimental findings. The results indicate that the load-displacement curve and energy absorbed by the axial crushing of tubes could be controlled by the introduction of grooves with different distances. Also, grooves can stabilize the deformation behavior and thus, the proposed method could be a good candidate as a controllable energy absorption element.     

Analysis of failure mechanisms observed in axial collapse of thin-walled circular fibreglass composite tubes

Theoretical analysis of the failure mechanism of the stable mode of collapse of thin-walled fibreglass composite tubes under static axial compression, based on experimental observations and taking into account all possible energy absorbing mechanisms developed during the process, is reported. Crushing loads and the energy absorbed are theoretically predicted. The proposed theoretical model was experimentally verified for various composite materials and tube geometries and proved to be very efficient for theoretically predicting the energy absorbing capacity of the shell.     

Experimental and numerical investigation of static and dynamic axial crushing of circular aluminum tubes

A comprehensive experimental and numerical study of the crash behavior of circular aluminum tubes undergoing axial compressive loading is performed. Non-linear finite element analyses are carried out to simulate quasi-static and dynamic test conditions. The numerical predicted crushing force and fold formation are found to be in good agreement with the experimental results. A summary of available analytical solutions is presented in order to estimate the mean crushing load and establish a comparison between these analytical loads and the experimental one. Some observations are made on the influence of geometrical imperfections and material strain rate effect.     

Numerical modelling of the axial compressive behaviour of short concrete-filled elliptical steel columns

This paper investigates the axial compressive behaviour of short concrete-filled elliptical steel columns using the ABAQUS/Standard solver, and a new confined concrete stress-stain model for the concrete-filled elliptical steel hollow section is proposed. The accuracy of the simulation and the concrete stress-strain model was verified experimentally. The stub columns tested consist of 150 × 75 elliptical hollow sections (EHSs) with three different wall thicknesses (4 mm, 5 mm and 6.3 mm) and concrete grades C30, C60 and C100. The compressive behaviour, which includes the ultimate load capacity, load versus end-shortening relationship and failure modes, were obtained from the numerical models and compared against the experimental results, and good agreements were obtained. This indicated that the proposed model could be used to predict the compressive characteristics of short concrete-filled elliptical steel columns.     

Torsional collapse of thin-walled prismatic columns

Torsional collapse of thin-walled prismatic columns is studied analytically and numerically. Simple torsional collapse models are developed to predict the collapse behavior of square columns under large plastic rotation using energy method. By considering the combined effect of geometry and material, the onset of the sectional plastic buckling is predicted and the critical twisting rotation for sectional buckling is obtained. Next, an analytical expression is derived for the moment-rotation relation valid for rotation up to 180°. The analytical solution is shown to compare well with the numerical results. The solutions are then extended for rectangular and hexagonal thin-walled columns. Numerical simulations for rectangular and hexagonal columns are also carried out and the results are presented in this paper for the purpose of comparison.     

A study of the influence of diameter and wall thickness of cylindrical tubes on their axial collapse

Axial compression experiments on aluminium cylindrical shells of diameter to thickness ratios (D/t) between 11.5 and 31.49 were conducted on a gravity drop hammer set up and Zwick machine. Typical histories of their deformation, variation of shell thickness along the fold length, inner and outer radii, folding parameter and size of fold, load–compression curves, energy absorbing capacity, initial peak load, and mean collapse loads obtained from the experiments are presented. Influence of the D/t values of the shell on their modes of collapse and energy absorption capacities are discussed. The shells are numerically simulated and analysed in detail by using the finite element code FORGE2. The material was modelled as rigid-viscoplastic. The experimental and computed results are compared. Typical contours of equivalent strain, equivalent strain rate, different stress components and velocity distribution are presented. The impact response of the shells is compared with their static response.     

Effects of openings of the buckling of cylindrical shells subjected to axial compression

Experimental and numerical methods are used to study the stability problem of cylindrical shells with cut-outs. The paper presents parametric research of the shape (square, rectangular, circular), the dimensions (axial and circumferential sizes, diameter) of the hole. The effect of the location and the number of the holes are also studied. The analysis indicates that the critical load is sensitive to the opening angle or circumferential size of the hole. The function (critical load-opening angle) is linear for large openings and independent of the geometrical imperfections of the shell. However for small openings, it is necessary to take into account the coupling between the initial geometrical imperfections and the openings. The linear approach does not fit because of the importance of the evolution of the displacements near the openings. These results will be used for the development of European rules.     

Calculation of the deep bending collapse response for complex thin-walled columns: I. Pre-collapse and collapse phases

The increasing complexity of transport vehicles means that more powerful finite element models are needed to simulate their crash behaviour. As existing models' calculation times are long and cannot effectively optimize structures in terms of peak moment and energy management, they should only be used as a final verifying tool. Distinct analytical models have been developed to determine the resistance to collapse of thin-walled structures subjected to a bending load. Part I of this paper concerns the theoretical prediction of bending strength in the pre-failure range for thin-walled structures of relatively complex geometry. Two types of buckling are considered: elastic and plastic.     

Collapse behavior of square thin-walled columns subjected to oblique loads

The crush behavior of a square column subjected to oblique loads, which is undergoing both axial and bending collapses, is analyzed. Oblique load conditions in numerical simulations are realized by means of impacting the column on a declined rigid wall with no friction. Mean crush loads corresponding to load angles are investigated with such geometrical parameters as thickness, width and length. Results show that there is a critical load angle at which a transition takes place from the axial collapse mode to the bending collapse mode. The dimensionless mean crush load is employed by normalizing the mean crush load with the analytical axial mean crush load and bending moment equations. It is expressed as a function of only one variable, the load angle. Finally, the formulation for the mean crush load is developed in terms of geometrical parameters and the critical load angle. The equation of the critical load angle is expressed as a function of the ratio of l/b. The value of the mean crush load drops to about 40% of the mean crush load in pure axial collapse after the critical load angle. Some cases of thin-walled columns are examined to verify the formulas of the mean crush load, and the results of numerical simulations are in good agreement with the predicted mean crush loads.     

Plastic collapse analysis of thin-walled circular tubes subjected to bending

Circular tubes have been widely used as structural members in many engineering applications. Therefore, its collapse behavior has been studied for many decades, focusing on its energy absorption characteristics and collapse mechanism. In order to predict the collapse behavior of members, one could rely on the use of finite element codes or experiments. These tools are helpful and have high accuracy but are costly and require extensive running time. Therefore, an approximate model of tubes collapse mechanism is an alternative especially for the early step of design. This paper is also aimed to develop a closed-form solution to predict the moment–rotation response of circular tube subjected to pure bending. The model was derived based on the principle of energy rate conservation. The collapse mechanism was divided into three phases. New analytical model of ovalisation plateau in phase 2 was derived to determine the ultimate moment. In phase 3, the Elchalakani et al. model [Int. J. Mech. Sci. 2002; 44:1117–1143] was developed to include the rate of energy dissipation on rolling hinge in the circumferential direction. The 3-D geometrical collapse mechanism was analyzed by adding the oblique hinge lines along the longitudinal tube within the length of the plastically deformed zone. Then, the rates of internal energy dissipation were calculated for each of the hinge lines which were defined in terms of velocity field. Inextensional deformation and perfect plastic material behavior were assumed in the derivation of deformation energy rate. In order to compare, the experiment was conducted with a number of tubes having various D/t ratios. Good agreement was found between the theoretical prediction and experimental results.     

薄壁钢约束方木柱轴心抗压性能有限元模拟

为探究合理有效薄壁钢约束方木柱轴心受压有限元分析模型,以及预应力对该薄壁钢约束方木柱轴心受压性能的影响;采用ABAQUS有限元软件建立了薄壁钢约束方木柱模型,采用"静摩擦-动摩擦指数衰减"接触模拟了薄壁钢与方木柱的相互作用,采用自定义场输出转换器单元实施了预应力的施加.基于合理有效有限元分析模型,进行预应力度k(钢材表面拉应力σcon与钢材屈服强度fy比值)=0、0.1、0.15、0.2和0.25对薄壁钢约束方木柱轴心抗压性能影响分析.分析结果表明,数值模拟结果与试验结果吻合良好,k=0相较于k≠0的试件屈服荷载、极限荷载和残余强度都更低,且更早进入塑性阶段,残余强度随着k的增加而下降;但k并非越大越好,过大的k会造成钢材部分区域屈服,削弱主动围压的效果;由于预应力的存在,预应力薄壁钢约束方木柱具有更好的承载力性能和延性.     

Experimental investigation on the axial collapse of expanded metal tubes

Expanded metal sheeting is widely used around the world for catwalks, granting, and decorative purposes. In the literature, little information can be found regarding the behavior of structural elements made of expanded metal. This paper is aimed at studying the axial collapse of squared and round tubes made of expanded metal sheeting under compressive loading. When expanding the metal a diamond-like cell pattern is formed in the metal sheets, then these patterns are characterised by two geometrical axes. A set of experimental tests was conducted to investigate the influence of the angle formed between the major axis of the expanded metal and the compressive load. From the results, three types of collapse response were mainly observed depending on the orientation of the axes: (1) Mode 1 characterised by a plastic collapse mechanism; (2) Mode 2 local buckling of the individual cells; and (3) Mode 3 global buckling of the tube walls.     

An analysis of axi-symmetric axial collapse of round tubes

Different size tubes of aluminium and mild steel were subjected to axial compression in an Instron machine. The tubes chosen were such that they collapsed in axi-symmetric concertina mode. Typical load-compression curves and deformed shapes of the collapsed tubes are presented. These reveal that the axi-symmetric folds formed in the deforming specimens extend both inside and outside of the line of original tube radius, and the ratio of the inside to outside fold lengths depends on the tube dimensions.

Considering the tube collapse mechanism as observed experimentally, an analysis is presented in an attempt to predict the mean collapse load and the post collapse load-compression curve. The computed values of the mean collapse load and the load-compression curve during a load oscillation, are presented and compared with the experiments, as well as with some existing theoretical results.     

Mathematical modeling of axial crushing of cylindrical tubes

Different aspects of mathematical modeling for the axial crushing of cylindrical tubes with straight fold have been discussed. The variation of circumferential strain during the formation of a fold has been taken into account. The present paper tries to answer questions such as (a) how great is the inside and outside folding, and (b) how the crushing load varies. In the present paper, the influence of the consideration of the conservation of mass on the mathematical formulation has been studied. The results of average and varying circumferential strain have also been compared.