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.     

Numerical analysis of slender elliptical concrete filled columns under axial compression

This paper presents a non-linear finite element model (FEM) used to predict the behaviour of slender concrete filled steel tubular (CFST) columns with elliptical hollow sections subjected to axial compression. The accuracy of the FEM was validated by comparing the numerical prediction against experimental observation of eighteen elliptical CFST columns which carefully chosen to represent typical sectional sizes and member slenderness. The adaptability to apply the current design rules provided in Eurocode 4 for circular and rectangular CFST columns to elliptical CFST columns were discussed. A parametric study is carried out with various section sizes, lengths and concrete strength in order to cover a wider range of member cross-sections and slenderness which is currently used in practices to examine the important structural behaviour and design parameters, such as column imperfection, non-dimension slenderness and buckling reduction factor, etc. It is concluded that the design rules given in Eurocode 4 for circular and rectangular CFST columns may be adopted to calculate the axial buckling load of elliptical CFST columns although using the imperfection of length/300 specified in the Eurocode 4 might be over-conservative for elliptical CFST columns with lower non-dimensional slenderness.     

Bending collapse theory of thin-walled twelve right-angle section beams

The present paper focuses on the bending collapse behavior of the twelve right-angle section (TTRS) beams. This paper presents the theoretical bending collapse mechanism of the TTRS beams around two axes based on the kinematic approach, and derives the expressions of the bending moments. The accuracy of the theoretical calculations are validated respectively by performing 36 groups finite element simulations including three kinds of materials, three different section dimensions and four different thicknesses. The results show that for 17.5<c/h<48.6, the theoretical bending collapse mechanism of the TTRS beams presented in this paper can describe the collapse process accurately, and the moment–rotation curves calculated by theory show a good consistency with simulation results.     

框架结构不同倒塌模式的数值模拟与分析

基于离散单元法和杆端多弹簧模型的思想,引入适用于任意加载路径的弹簧恢复力模型,考虑混凝土轴向弹簧与截面剪切弹簧的耦合效应,建立了合理的弹簧破坏准则,并对单元失效后的碰撞问题进行了有效的处理,在此基础上开发了能够模拟强震作用下钢筋混凝土框架结构倒塌全过程的计算机仿真程序CSPF 1.0。以汶川地震灾区一实际建筑为例,利用CSPF 1.0程序模拟了地震作用下该结构响应的全过程,得到了该结构可能产生的强梁弱柱型倒塌模式。另外在增大原结构的柱截面尺寸及配筋的基础上,程序进一步模拟了强柱弱梁型的倒塌模式。通过对仿真结果的论述和分析,说明了程序CSPF1.0的可靠性和离散单元法在钢筋混凝土框架结构倒塌分析中的可行性,并在一定程度上揭示了框架结构的破坏机理和倒塌机制。     

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.     

The vibration behaviour of thin-walled regular polygonal tubes

This paper addresses the free vibration behaviour of single-cell thin-walled tubes with regular convex polygonal cross-section (RCPS) and provides an extensive analysis of the resulting natural frequencies and associated vibration mode shapes. A semi-analytical approach is adopted, which is based on the generalised beam theory (GBT) specialisation for RCPS recently proposed by Gonçalves and Camotim (2013) [1] and subsequently employed to obtain insightful conclusions concerning the buckling behaviour of RCPS tubes (Gonçalves and Camotim (2013) [2], [3]). This approach makes it possible to obtain closed-form analytical solutions and also acquire in-depth knowledge concerning the mechanics of the vibration problem, through the well-known GBT modal decomposition features. Attention is paid to local (plate-like), extensional, torsional and distortional vibration modes, as well as their interaction.     

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.     

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.     

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.     

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.     

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.     

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.     

On the fracture possibility of thin-walled tubes under axial crushing

Thin-walled tubes are widely used as energy absorption components in vehicle crashworthiness design where axial crushing is one of the most typical loading conditions. Lightweight materials such as high-strength steel, aluminum and magnesium have been applied for thin-walled tubes for weight reduction. Meanwhile, most of these lightweight materials are more brittle and easily fractured than traditional steel. Distribution and history of stress triaxiality and equivalent strain in the thin-walled tubes under axial crushing have been analyzed in this article with finite element simulation, as these two parameters of stress and strain states are commonly used for constructing fracture locus of materials. It is observed that both stress triaxiality and equivalent strain are transferring along the tube length like waves. Analysis results show that fracture is more likely to take place on the edge than the other positions of square thin-walled tubes. For identical axial crushing stroke, there is little difference of stress and strain states inside the square thin-walled tubes with initial impact velocity varying from 6 m/s to 24 m/s. Influence of geometrical parameters on the stress and strain states have also been analyzed, including the shape of cross-section corner, the wall thickness and the shape of cross-section, respectively. Analysis results in this article may offer references for design of thin-walled tubes and the necessary experimental characterization of mechanical properties for lightweight materials.     

Ultimate load-carrying capacity of cold-formed thin-walled columns with built-up box and I section under axial compression

The use of cold-formed thin-walled steel structures has increased in recent years, and some built-up section members are motivated and also widely used for their excellent structural behaviors. In this paper, a series of axially-compressed tests on built-up box section members composed of two C-section by self-drilling screws at flanges are conducted. The differences of global, local and distortional buckling behaviors between members with built-up and single sections are investigated at first. Then the effects of installation error and fastener spacing on ultimate load-carrying capacity of built-up members are analyzed. A strength estimation method for built-up members under axial compression is proposed based on the experimental investigation in this paper, as well as some existing experiments, and corresponding numerical analysis studies. Finally, the predicted capacity obtained by using the proposed strength estimation method is compared with experimental results and the nominal axial strength determined according to the AISI provisions, by which the suitability and accuracy of the proposed strength estimation method have been established.     

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.