Crushing analysis and multiobjective crashworthiness optimization of tapered square tubes under oblique impact loading

In this paper, a class of axisymmetric thin-walled square (ATS) tubes with two types of geometries (straight and tapered) and two kinds of cross-sections (single-cell and multi-cell) are considered as energy absorbing components under oblique impact loading. The crash behavior of the four types of ATS tubes, namely single-cell straight (SCS), single-cell tapered (SCT), multi-cell straight (MCS) and multi-cell tapered (MCT), are first investigated by nonlinear finite element analysis through LS-DYNA. It is found that the MCT tube has the best crashworthiness performance under oblique impact regarding both specific energy absorption (SEA) and peak crushing force (PCF). Sampling designs of the MCT tube are created based on a four-level full factorial design of experiments (DoE) method. Parametric studies are performed using the DoE results to investigate the influences of the geometric parameters on the crash performance of such MCT tubes under oblique impact loading. In addition, multiobjective optimization design (MOD) of the MCT tube is performed by adopting multiobjective particle swarm optimization (MOPSO) algorithm to achieve maximum SEA capacity and minimum PCF with and without considering load angle uncertainty effect. During the MOD process, accurate surrogate models, more specifically, response surface (RS) models of SEA and PCF of the MCT tubes are established to reduce the computational cost of crash simulations by finite element method. It is found that the optimal designs of the MCT tubes are different under different load angles. It is also found that the weighting factors for different load angles are critical in the MOD of the MCT tubes with load angle uncertainty.     

Multi-Objective Optimization of aluminum hollow tubes for vehicle crash energy absorption using a genetic algorithm and neural networks

A numerical study of the crushing of thin-walled circular aluminum tubes has been carried out to investigate their behaviors under axial impact loading. These kinds of tubes are usually used in automobile and train structures to absorb the impact energy. A Multi-Objective Optimization of circular aluminum tubes undergoing axial compressive loading for vehicle crash energy absorption is performed for five crushing parameters using the weighted summation method. To improve the accuracy of the optimization process, artificial neural networks are used to reproduce the behavior of the crushing parameters in crush dynamics conditions. An explicit finite element method (FEM) is used to model and analyzed the behavior. A series of aluminum cylindrical tubes are simulated under axial impact condition for the experimental validation of the numerical solutions. A finite element code, capable of evaluating parameters crush, is prepared of which the outputs are used for training and testing the developed neural networks. In order to find the optimal solution, a genetic algorithm is implemented. With the purpose of illustrating optimum dimensional ratios, numerical results are presented for thin-walled circular aluminum AA6060-T5 and AA6060-T4 tubes. Multi-Objective Optimization of circular aluminum tubes has been performed in the basis of different priorities to create the ability for designer to select the optimum dimension ratio. Also, crush parameters of two aluminum alloys has been compared.     

Multi-objective crashworthiness optimization of tapered thin-walled tubes with axisymmetric indentations

In this paper, the effects of tapering and introducing axisymmetric indentations on the crash performances of thin-walled tubes are investigated. The crash performances of the tubes are evaluated using two metrics: the crush force efficiency (CFE, the ratio of the average crushing load to the peak load), and the specific energy absorption (SEA, absorbed energy per unit mass). The optimum values of the number of the axisymmetric indentations, the radius of the indentations, the taper angle and the tube thickness are sought for maximum CFE and maximum SEA using surrogate based optimization. In addition, multi-objective optimization of the tubes is performed by maximizing a composite objective function that provides a compromise between CFE and SEA. The CFE and SEA values at the training points of surrogate models (metamodels) are computed using the finite element analysis code LS-DYNA. Polynomial response surfaces, radial basis functions, and Kriging are the different surrogate models used in this study. Surrogate based optimization of the tubes showed that the tubes with indentations have better crush performance than tubes without indentations. It is found that maximum CFE requires large number of indentations with high radius, small thickness, and medium taper angle, while maximum SEA requires small number of indentations with low radius, large thickness and small taper angle. It is also found that the globally most accurate surrogate model does not necessarily lead to the optimum.     

Analysis and optimization of externally stiffened crush tubes

Nonlinear finite element analysis is used to investigate the quasi-static axial collapse response of cylindrical tubes which are externally stiffened by multiple identical rings. The rings divide the long tube into a series of short thin-walled tubes. It is assumed that the size and shape of integral stiffeners are controlled through a machining process. The effects of various geometric parameters such as wall thickness, ring spacing, ring thickness and width on the collapse response, crush force and energy absorption of monolithic, integrally stiffened steel tubes are studied and used as a general framework for a design optimization study. Through design and analysis of computer experiments, global metamodels are developed for the mean crush force and energy absorption, using the radial basis function approximation technique. Using both single- and multi-objective design optimization formulations, optimum designs for different response characteristics are found. The crush mode in the form of progressive collapse or buckling is found to heavily depend on the ratio of stiffener spacing to stiffener height as well as the ratio of wall thickness to stiffener thickness. The optimization results show the viability of externally stiffened tubes as efficient energy absorbers.     

Analytical and experimental studies on quasi-static axial crush behavior of thin-walled tailor-made aluminum tubes

In this paper, the crush behavior of segmented circular tubes, made of aluminum alloy 6061 and subjected to quasi-static axial loading, has been analytically and experimentally investigated. Crush behavior of these tubes was modeled by integrating available analytical models and superposition principle. In the certain overall length of segmented circular tubes, effects of changing the wall thickness and length of each segment on the energy absorption characteristics have been evaluated. One successful approach toward obtaining lightweight energy absorbers with high energy absorption capacity is the use of thin-walled Tailor-Made Tubes (TMTs). In these tubes, the thickness and mechanical properties of the wall vary along the length of the tube. Applying these tubes; crush force can be controlled by changing the length and thickness of each tube segment, improving the performance of energy absorbing systems. Results of this research showed that Tailor-made tubes have higher energy absorption capacity at identical crush lengths, and they can absorb more energy per unit weight compared to simple tubes with constant wall thickness and mechanical properties. Moreover, for the same specific energy absorption, the TMTs exhibit a considerable reduction in the magnitude of the mean and initial maximum crush forces. With the use of TMTs, the maximum crush force shifts to the end of the crush range, reducing the exerted deceleration on occupants and equipments. Comparing mean crush force and specific energy absorption obtained by analytical and experimental approaches, it was observed that combining current analytical models with superposition principle can prepare a set of analytical formulations to predict TMTs crush characteristics within an acceptable proximity.     

Optimal shape design of thin-walled tubes under high-velocity axial impact loads

In this study, the objective is to maximize the crashworthiness of thin-walled tubes under axial impact loads by shape optimization. As design variables, parameters defining the cross-sectional profile of the tube as well as parameters defining the longitudinal profile like the depths and lengths of the circumferential ribs and the taper angle are used. The methodology is applied to the design optimization of a crash-box supporting the bumper beam of a vehicle for the loading conditions in standard EuroNCAP crash tests. The crash event is simulated using explicit finite element method. While the crash-box is fully modeled, the structural response of the remaining parts during the tests is taken into account by developing a lumped-parameter model. A hybrid search algorithm combining Genetic and Nelder & Mead algorithms is developed. The results indicate significant improvement in the crashworthiness over the benchmarks designs.     

Experimental behavior of concrete filled double steel tubular (CFDST) members under low velocity drop weight impact

Thirty-one tests under low velocity drop weight impact were carried out to examine the residual failure modes and the time history of the impact forces, global deformations and strains of concrete filled double steel tubular (CFDST) members in this paper. The parameters varied in the testing program include the column type (straight and tapered), the boundary conditions (simply supported and fixed), the axial load level and the impact energy. The results showed that all CFDST members behaved in a ductile manner and the residual deformation consisted of local deformation at the impact section, as well as the overall bending deformation. Compared to hollow double steel tubes, the CFDST members under the same applied impact energy demonstrate superior impact behavior in terms of higher energy absorbed, smaller global deformation and local deformation due to the interaction of the sandwich concrete and double skin steel tubes. The influence of key parameters on the dynamic resistance ability of CFDST is discussed.     

Axial crush simulation of braided carbon tubes using MAT58 in LS-DYNA

This paper examines a composite damage constitutive model, MAT58, in LS-DYNA and its application for use in braided composite tube axial crush simulations. The constitutive response of MAT58 was investigated using single element simulations. It was found that MAT58 reproduced the softening behavior of the braided composite under monotonic compressive loading, but failed in subsequent unloading and tensile loading cycles. A deficiency in the damage law in MAT58 was identified. Unloading and reloading a volume of material that had suffered some degree of damage was a part of the process with the progressing of crush zone during the axial crush of composite tubes. Consequently, this deficiency hinders the success of MAT58 in such applications. In tri-axial braided composite tube axial crush simulations, although the predicted initial peak forces were within 20% of the experimental values, the predictions for the specific energy absorption (SEA) values were consistently low, particularly for tubes without a plug as crush initiator. These discrepancies are attributable to the deficiency in the damage law in MAT58.     

Multiobjective crashworthiness optimization of hollow and conical tubes for multiple load cases

Much attention of current design analysis and optimization of crashworthy structures have been largely paid to the scenarios with single load case in literature. Nevertheless the designed structures may often have to be operated in other load conditions, thus raising a critical issue of optimality. This paper aims to understand and optimize the dynamic responses and energy absorption of foam-filled conical thin-walled tubes under oblique impact loading conditions by using multiobjective optimization method. The crashworthiness criteria, namely specific energy absorption (SEA) and crushing force efficiency (CFE), are related to loading parameters and design variables by using D-optimal design of experiments (DoE) and Kriging model. To obtain the optimal Pareto solutions of hollow and foam-filled conical tubes, design optimization is first performed under different loading case (DLC) using multiobjective particle swarm optimization (MOPSO) algorithm separately. The optimal designs indicate that hollow tube has better crashing performance than the foam-filled tube under relatively high impacting velocity and great loading angle. To combine multiple load cases (MLC) for multiobjective optimization, a double weight factor technique is then adopted. It is found that the optimal foam-filled tube has better crashing performance than empty conical tube under any of overall oblique loading cases concerned. The study gains insights in deriving multiobjective optimization for multiple load cases, providing a guideline for design of energy absorber under multiple oblique loading.     

High strength thin-walled rectangular concrete-filled steel tubular slender beam-columns,Part I: Modeling

High strength thin-walled rectangular concrete-filled steel tubular (CFST) slender beam-columns under eccentric loading may undergo local and overall buckling. The modeling of the interaction between local and overall buckling is highly complicated. There is relatively little numerical study on the interaction buckling of high strength thin-walled rectangular CFST slender beam-columns. This paper presents a new numerical model for simulating the nonlinear inelastic behavior of uniaxially loaded high strength thin-walled rectangular CFST slender beam-columns with local buckling effects. The cross-section strengths of CFST beam-columns are modeled using the fiber element method. The progressive local and post-local buckling of thin steel tube walls under stress gradients is simulated by gradually redistributing normal stresses within the steel tube walls. New efficient Müller's method algorithms are developed to iterate the neutral axis depth in the cross-sectional analysis and to adjust the curvature at the columns ends in the axial load–moment interaction strength analysis of a slender beam-column to satisfy equilibrium conditions. Analysis procedures for determining the load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns incorporating progressive local bucking and initial geometric imperfections are presented. The new numerical model developed is shown to be efficient for predicting axial load–deflection and axial load–moment interaction curves for high strength thin-walled rectangular CFST slender beam-columns. The verification of the numerical model and parametric studies is given in a companion paper.     

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.     

外部加劲热轧钢管的分析和优化

利用非线性有限元法,分析了采用多种规格外部圆环加劲的圆柱形钢管的拟静力轴向破坏反应。加劲圆环将钢管沿竖向分为一系列的薄壁短柱结构。假定加劲肋的尺寸和形状由机械加工控制。研究了各种不同几何参数,如:钢管壁厚、环间距、环厚度和破坏时环的宽度,极限承载力和整体加劲钢管能量吸收的影响。将研究结果作为优化设计的基本原理。基于计算机模拟试验的分析,利用辐射函数,提出了关于平均承载力和能量消耗的后处理模型。运用单个对象和多个对象优化设计方程,得出不同反应特性的优化设计。根据渐进破坏屈曲得出的破坏模式依赖于加劲肋间距、加劲肋高度比、钢管壁厚以及加劲肋厚度比。优化结果显示,外加劲肋作为高效耗能构件是可靠的。     

Quasi-static response and multi-objective crashworthiness optimization of oblong tube under lateral loading

This paper addresses the energy absorption responses and crashworthiness optimization of thin-walled oblong tubes under quasi-static lateral loading. The oblong tubes were experimentally compressed using three various forms of indenters named as the flat plate, cylindrical and a point load indenter. The oblong tubes were subjected to inclined and vertical constraints to increase the energy absorption capacity of these structures. The variation in responses due to these indenters and external constraints were demonstrated. Various indicators which describe the effectiveness of energy absorbing systems were used as a marker to compare the various systems. It was found that unconstrained oblong tube (FIU) exhibited an almost ideal response when a flat plate indenter was used. The design information for such oblong tubes as energy absorbers can be generated through performing parametric study. To this end, the response surface methodology (RSM) for the design of experiments (DOE) was employed along with finite element modeling (FEM) to explore the effects of geometrical parameters on the responses of oblong tubes and to construct models for the specific energy absorption capacity (SEA) and collapse load (F) as functions of geometrical parameters. The FE model of the oblong tube was constructed and experimentally calibrated. In addition, based on the developed models of the SEA and F, multi-objective optimization design (MOD) of the oblong tube system is carried out by adopting a desirability approach to achieve maximum SEA capacity and minimum F. It is found that the optimal design of FIU can be achieved if the tube diameter and tube width are set at their minimum limits and the maximum tube thickness is chosen.     

Crashworthiness assessment of square aluminum extrusions considering the damage evolution

Combining the pivotal tests and FEM technology, crashworthiness of aluminum extrusions was studied for an automobile safety plan. Experiments under static axial loading conditions were carried out for square thin-walled tubes with different thicknesses, section dimensions, with various impact velocities were conducted as well. Crush behavior of this structure under axial static and dynamic loads was studied. FEM code was used for crash analysis, which gave deformation and load prediction. Geometric imperfection and damage model were introduced to simulation. Results show that experiment and numerical model have good agreement with each other.     

薄壁圆管的弯曲屈服和计算应用

采用整体能量平衡理论,推导出作用力矩与圆管弯曲角的关系。在推导一般性的圆管弯曲屈服模式中,假定弯曲破坏时,所有能量都能被吸收,并且分布在塑性铰线上。然后将作用力矩和圆管弯曲角的关系与数值分析和试验中得到的管状结构抗弯能力对比。推导出的抗弯曲性适用于简化圆管模型,这些模型有不同的截面和材料。不但对细化管状模型,而且对这些简化模型进行了耐撞性分析,碰撞结果的对比可以验证简化模型的有效性以及推导的管抗弯能力计算方法的精确度。文中的分析结果全部由LS-DYNA软件计算得出。     

往复荷载作用下矩形钢管混凝土构件力学性能的研究

以往 ,国内外学者对矩形钢管混凝土构件滞回性能的研究尚少见报道。本文以矩形钢管混凝土构件截面高宽比和轴压比为主要参数 ,进行了 3 0个构件滞回性能的实验研究。利用数值方法分析了矩形钢管混凝土构件的滞回性能 ,理论计算结果与实验结果吻合较好。利用数值方法 ,系统分析和考察了轴压比、长细比、含钢率、截面高宽比、钢材屈服强度和混凝土强度等参数对滞回曲线骨架线的影响规律 ,在此基础上 ,提出了矩形钢管混凝土构件弯矩 -曲率和P -Δ滞回关系模型 ,以及位移延性系数的简化计算方法。     

Axial crushing of thin-walled structures with origami patterns

Thin-walled tubes are a kind of popular design for the energy absorbing devices. However, when they are subjected to axial loading, there exists a large undesirable initial peak force, followed by fluctuation in the force–displacement curve. In this paper, the origami patterns are introduced to thin-walled tubes to minimize the initial peak and the subsequent fluctuations. Tubes of square, hexagonal and octagonal cross-sections with origami patterns are investigated by finite element analysis. Numerical results show that compared with the conventional tube, the patterned tubes exhibit a lower initial peak force and more uniform crushing load. The critical states are obtained under which the crushing mode follows the initial origami pattern. The parametric study shows the relationship between the pre-folding angle and the initial peak force as well as the mean crushing force for the tubes with different cross-sections. A prototype of the patterned tube is constructed and tested, showing much lower initial peak force and a smooth crushing process which agrees with the numerical results.     

Frusta structure designing to improve quasi-static axial crushing performances of triangular tubes

To improve quasi-static axial crushing performances of thin-wallled triangular tubes, frusta structures were designed and fabricated. Quasi-static axial compression experiments were carried out to reveal the collapse mode and energy absorption characteristic of the triangular frusta tube. Peak loads and mean crushing forces (MCFs) of tubes with different taper angles were compared. In-extensible and extensible collapse modes were suggested to predict the MCF of the triangular frusta tube with small and great taper angles, respectively. A new collapse mode, inward folding, was observed in the experiments. An energy absorption stability factor was defined to evaluate the anti-crushing efficiency of the triangular frusta tube. With greater taper angles, the energy absorption stability factor is much closer to 1, denoting more stable deformation style. It is concluded that frusta structures with taper angles effectively enhance the anti-crushing efficiency and stability of thin-walled triangular tubes.     

轴压下薄壁管断裂的可能性分析

在车辆的防撞设计中薄壁管作为耗能构件被广泛采用,轴压力是防撞部位承受的最典型荷载之一。为了减轻重量,薄壁管采用轻质材料诸如高强度钢材、铝和镁制成。然而,这些轻质材料中的大多数与传统的钢材相比更脆且易断裂。由于材料的应力、应变状态通常被作为判断其构造断裂点的依据,故对薄壁管的三轴应力分布和时程及其等效应变进行了有限元模拟。分析结果显示,三轴应力和等效应变沿着管长波动,方形薄壁管的断裂更可能发生在边缘而非其他位置。对于相同的轴压冲击,当初始冲击速度在6～24m/s变化时,方形薄壁管内部的应力、应变变化不大。对影响应力、应变状态的参数,包括横截面角的形状、壁厚和横截面形状分别进行研究。所得结果可为薄壁管的设计及轻质材料力学性能的试验特性研究提供参考。     

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.