Optimization of the foam-filled aluminum tubes for crush box application

Axial impact crush tests on empty and foam-filled square aluminum tubes have been performed. Furthermore, in order to find more details about the crush processes, finite element simulations of the experiments have been done. In terms of finding more efficient and lighter crush absorber and achieving maximum energy absorption, multidesign optimization (MDO) technique has been applied for optimizing the square rectangular tubes. Based on practical requirements the optimum tube geometry, which absorbs maximum energy and has a minimum weight, has been determined. Results of previous work indicated that using high density honeycomb for filling the tubes will results more energy absorption but the weight efficiency has been lost [Zarei HR, Kröger M. Optimum honeycomb filled crash absorber design. Mater Des 2007;29:193–204]. Therefore, a comprehensive study has been performed in order to find out the crush behavior of tube filled with foam with different densities. The MDO procedure has been implemented to find an optimum filled tube that absorbed the same energy as an optimum empty tube can absorb.     

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.     

Theoretical prediction and crashworthiness optimization of multi-cell triangular tubes

The triangular tubes with multi-cell were first studied on the aspects of theoretical prediction and crashworthiness optimization design under the impact loading. The tubes׳ profiles were divided into 2-, 3-, T-shapes, 4-, and 6-panel angle elements. The Simplified Super Folding Element theory was utilized to estimate the energy dissipation of angle elements. Based on the estimation, theoretical expressions of the mean crushing force were developed for three types of tubes under dynamic loading. When taking the inertia effects into account, the dynamic enhancement coefficient was also considered. In the process of multiobjective crashworthiness optimization, Deb and Gupta method was utilized to find out the knee points from the Pareto solutions space. Finally, the theoretical prediction showed an excellent coincidence with the numerical optimal results, and also validated the efficiency of the crashworthiness optimization design method based on surrogate models.     

Axial crushing analysis of end-capped circular tubes

The paper investigates collapse mechanisms and energy absorption capacity during the axial compression of the end-capped thin-walled circular aluminum tubes which are hollow or filled with polyurethane foam. An experimental technique is used to evaluate the crushing behavior of the circular tubes under compressive quasi-static strain rate. A numerical model is presented based on finite element analysis to simulate the crushing of circular tubes considering nonlinear response due to material behavior, contact boundary conditions and large deformation. The validated model using existing experimental results is used to evaluate the dynamic response in order to determine the dynamic amplification factor relating the quasi-static results to dynamic response. The experimental and numerical results are used to determine energy absorption capacity due to the plastic deformation of thin-wall tube and crushable foam. The performance of end-capped tubes is compared with non-capped tubes and it is found that maximum initial peak load can be controlled and convenient crash protection systems can be obtained using end-capped circular tubes.     

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.     

New generation of energy dissipating systems based on biaxial buckling

This work proposes a new generation of energy dissipating system based upon an original patented mechanical assembly: the Absorption par Compression–Torsion Plastique (ACTP) presented in Abdul-Latif and Baleh (2005).¹ In fact, the ACTP transforms a uniaxial external loading into biaxial compression–torsion, where several degrees of biaxial loading paths complexity can be created within the loaded tubes. Such a concept which aims to enhance the strength properties of material is now extended to study the biaxial plastic buckling of different materials, and different cross sections under further severe loading conditions.The intention of this comprehensive experimental study is to further investigate a new severe loading configuration under quasi-static strain regime. Thus, five inclination angles (30°, 37°, 45°, 53° and 60°) are tested using circular and square tubes made from copper and aluminum alloy, respectively. An integrity measure of the mean collapse load and the corresponding energy absorbed shows that the higher the inclination angle (i.e., the higher loading complexity), the greater the rates of change of torsional component, and the greater the mean collapse load, and the corresponding energy absorbed in copper and aluminum tubular structures.     

Comparative analysis of energy absorption capacity of simple and multi-cell thin-walled tubes with triangular,square, hexagonal and octagonal sections

Energy must dissipate during a collision to prevent damage and injury. To reduce loss from collision, energy absorbers are used that dissipate energy upon deformation and folding to prevent damage to critical parts of a structure. In this paper, simple and multi-cell thin-walled tubes made from aluminum with triangular, square, hexagonal and octagonal sections were subjected to quasi-static loading. The experimental results were then compared with numerical simulations. The results showed that the energy absorption capacity of multi-cell sections is greater than for that of simple sections. Also, hexagonal and octagonal sections in a multi-cell configuration absorbed the greatest amounts of energy per unit of mass.     

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.     

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.     

Lateral compression of a square or rectangular tube between two parallel narrow width indenters placed non-orthogonally

Collapse behavior of aluminum tubes of square and rectangular cross-sections, when compressed between two identical narrow width indenters placed symmetrically in parallel alignment, is examined. Experiments were performed wherein the angle between the axes of tube and indenters was varied from 0° to 90°. Load compression curves and deformation histories of typical specimens are presented. The collapse of the tubes was seen to be generally symmetrical, though asymmetries were observed in some tubes. Considering only the symmetrical mode of deformation, an analysis is presented for constructing the load compression curves as well as the shape of the deforming tube. The analysis considers the energy, absorbed in stationary and rolling plastic hinges which are formed in the collapsing tube. Computed results thus obtained compare well with the experiments.     

Quasi-static and dynamic crushing behaviors of aluminum and steel tubes with a cutout

Tubular members are commonly used as an energy absorber in engineering structures and many such members have a cutout. In this study, the crushing behaviors of tubes with a cutout are characterized and the effects of cutout on the energy absorption capabilities of these tubes are quantified. Systematic parametric studies were carried out to study the effect of material properties, including yield and ultimate strength of material, strain rate effect, location of cutout, tube length and impact speed on the crushing behaviors and energy absorption capacity of aluminum and steel tubes. First, a numerical model was constructed with a commercial explicit finite element code. It will be first proven that the numerical simulation can produce sufficiently accurate results in an economic manner. Subsequently, the crushing behavior of aluminum and steel tubes with a cutout was experimentally characterized and their energy absorption capacity was evaluated in terms of mean crushing force, peak crushing force and specific energy absorption (SEA). Tubes of various lengths with a cutout located at different locations, subject to both quasi-static and dynamic impact loadings were considered. For steel tubes, the numerical simulation investigated the influence of the strain rate effect and variation in strain hardening ratio of the material. Empirical equations describing the mean and peak crushing forces of aluminum and steel tubes with a cutout were developed using linear and nonlinear regression methods applied to the results obtained from the numerical and experimental studies.     

Attempts to improve energy absorption characteristics of circular metal tubes subjected to axial loading

In this paper, experimental investigation of two new structural design solutions with the aim of improving crashworthiness characteristics of cylindrical metal tubes is performed. In the first design method, a rigid steel ring is press-fitted on top of circular aluminum tubes. When this arrangement of dissipating energy is subjected to axial compression, the rigid ring is driven into the cylindrical tube and expands its top area; then, plastic folds start shaping along the rest of the tube length as the compression of the structure continues. In the second design method, wide grooves are cut from the outer surface of steel thick-walled circular tubes. In fact, this method converts thick-walled tubes into several thin-walled tubes of shorter length, being assembled together coaxially. When this energy absorbing device is subjected to axial compression, plastic deformation occurs within the space of each wide groove, and thick portions control and stabilize collapsing of the whole structure. In the present study, several specimens of each developed design methods with various geometric parameters are prepared and compressed quasi-statistically. Also, some ordinary tubes of the same size of these specimens are compressed axially to investigate efficiency of the presented structural solutions in energy absorption applications. Experimental results show the significant efficiency of the presented design methods in improving crashworthiness characteristics and collapse modes of circular tubes under axial loading.     

Experimental optimization of composite collapsible tubular energy absorber device

A four-phase program to improve the specific energy absorbed by axially crushed composite collapsible tubular energy absorber devices was undertaken. In the first phase, examining of the crushing behaviour of non-triggered tubes was carried out. The second phase is aimed at obtaining the best position for the triggered wall. The third phase focuses on the effects of material sizing in order to understand the influence of triggered wall length on the responses of composite circular tubes to the axial crushing load. The results of these three phases of the study contribute to the fourth whose objective is to optimize the shape geometry of the cross-section area to further improving in tube energy absorption capability. The experimental results demonstrated the strong potential benefits of optimizing the material distribution. The sizing and shape optimization of composite collapsible tubes exhibited a pronounced effect on their capability to absorb high specific energy under axial compressive load.     

碰撞试验中泡沫填充铝管的最优化设计

对泡沫填充空心方铝管进行轴向撞击粉碎试验。此外，为获得更多有关撞击过程的信息，也对试验进行了有限元模拟分析。为找到更有效轻便的撞击减震器，并达到吸收最多能量的目的，在方矩形管的优化设计中采用了多元设计优化方法（MDO）。基于管的最佳几何尺寸考虑将具有最轻重量并且吸收能量最多作为设计目标。前期研究表明，使用高密度蜂窝材料填充会使管吸收更多能量，但重量不是最轻[Zarei HR，Kroger M．Optimum honey-comb filled crash absorber design．Mater Des 2007，29：193-204]。因此，为了解采用不同密度的泡沫填充管的撞击性能，进行了全面的研究，。采用MDO方法寻找一种优化填充管，使其吸收的能量与最优空心管吸收的能量一样多。     

轴压下金属圆管耗能特性的改善

为提高金属圆管的抗冲击性能,分别通过两种设计方法进行试验研究。第一种方法将刚性钢环压入铝质圆管端部。轴压下,首先,刚性环扩大圆管端部;接着,沿管长方向形成塑性褶层。第二种方法在厚壁钢管外表面开槽。这个方法实际是将厚壁管分解成几个同轴相连的薄壁短管。受压时,每个钢槽内将出现塑性变形,结构的倒塌取决于厚壁部分。采用两种方法进行了不同尺寸试件的受压试验,并与同尺寸的普通管轴压下的耗能试验对比。结果表明,本设计方法和提出的圆管轴压倒塌模型均很有效。     

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.     

Multiobjective optimization for tapered circular tubes

As more and more new functional requirements are placed, some novel development of sectional configurations of the structural members has been increasingly introduced. This paper presents the optimal design for tapered tubes of three different configurations, namely hollow single, foam-filled single and collinear double tubes. To represent complex crashworthiness objective functions, a surrogate model method, more specifically, response surface method (RSM), was adopted in this study. The design of experiments (DoEs) of the factorial design and Latin Hypercube Sampling techniques is employed to construct the response surface models of specific energy absorption (SEA) and the maximum impact load (MaxL), respectively. In this paper, the linearly weighted average, geometrical average and particle swarm optimization methods are utilized in the multiobjective optimization for these three different tapered tube cases, respectively. A comparison is made among the different tapered profiles with the different optimization algorithms, and the crashworthiness merits of foam-filled tapered tubes are identified.     

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.     

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.     

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.