Crashworthiness design of functionally graded foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure has recently gained attention due to its excellent crashworthiness. Based on the previous study, a new kind of foam-filled thin-walled structure called as functionally graded foam-filled thin-walled structure has more excellent crashworthiness than the traditional uniform foam-filled thin-walled structure. Moreover, as far as we know multi-cell thin-walled structure has more excellent crashworthiness than the traditional single-cell thin-walled structure. As an integrator of the above two kinds of excellent thin-walled structures, functionally graded foam-filled multi-cell thin-walled structure (FGFMTS) may has extremely excellent crashworthiness. Based on our study, the crashworthiness of the FGFMTSs is significantly affected by the design parameter of the graded functional parameter m. Thus, in order to obtain the optimal design parameters, the FGFMTSs with different cross sections and different wall materials are optimized using the multiobjective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). At the same time, the corresponding uniform foam-filled multi-cell thin-walled structures (UFMTS) which have the same weight as these FGFMTSs are also optimized in our study. In the multiobjective design optimization (MDO) process, polynomial functional metamodels of SEA and PCF of FGFMTSs are used to reduce the computational cost of crash simulations by finite element method. The MDO results show that the FGFMTS with PCF in the initial period of its crash not only has better crashworthiness than the traditional UFMTS with the same weight but also performs superior balance of crashing stability. Thus, the optimal design of the FGFMTS with PCF occurring in the initial crash is an extremely excellent energy absorber and can be used in the practical engineering.     

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 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.     

Multiobjective crashworthiness optimization of multi-cornered thin-walled sheet metal members

Plastic deformation of structures absorbs substantial kinetic energy when impact occurs. Therefore, energy-absorbing components have been extensively used in structural designs to intentionally absorb a large portion of crash energy. On the other hand, high peak crushing force, especially with regard to mean crushing force, may lead to a certain extent and indicate the risk of structural integrity. Thus, maximizing energy absorption and minimizing peak to mean force ratio by seeking for the optimal design of these components are of great significance. Along with this analysis, the collapse behavior of square, hexagonal, and octagonal cross-sections as the baseline for designing a newly introduced 12-edge section for stable collapse with high energy absorption capacity was characterized. Inherent dissipation of the energy from severe deformations at the corners of a section under axial collapse formed the basis of this study, in which multi-cornered thin-walled sections was focused on. Sampling designs of the sections using design of experiments (DOE) based on Taguchi method along with CAE simulations was performed to evaluate the responses over a range of steels grades starting from low end mild steels to high end strength. The optimization process with the target of maximizing both specific energy absorption (SEA) and crush force efficiency (CFE), as the ratio of mean crushing load to peak load, was carried out by nonlinear finite element analysis through LS-DYNA. Based on single-objective and multi-objective optimizations, it was found that octagonal and 12-edge sections had the best crashworthiness performance in terms of maximum SEA and CFE.     

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.     

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.     

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.     

Mechanics of axial plastic collapse in multi-cell,multi-corner crush tubes

Quasi-static nonlinear finite element simulations are performed to study the energy absorption characteristics of axially crushed thin-walled aluminum tubes with different multi-cell, multi-corner configurations. By considering the kinematically consistent representation of plastic collapse as observed in the crush simulations, an analytical formula for the mean crush force is derived using the super folding element theory. In this model, the isotropic material is treated as rigid-perfectly plastic and the total internal energy is calculated by considering both bending and membrane deformation during the folding process. The simulation results show a strong correlation between the cross-sectional geometry and the crush response of the tubes. The analytical predictions for the mean crush force are compared with the FE results as well as other analytical models reported in the literature.     

Energy absorption properties of non-convex multi-corner thin-walled columns

In this paper, we proposed a strategy to improve energy absorption efficiency of thin-walled columns by introducing extra non-convex corners in the cross section. Several profiles of non-convex multi-corner thin-walled columns obtained through this strategy are presented and their energy absorption capacities under axial crush are investigated analytically and numerically. Explicit formulations for predicting the mean crushing force of non-convex multi-corner thin-walled columns are derived based on the theory of Super Folding Element method, and the predicting results of these formulations have good agreement with the numerical simulation performed by explicit non-linear finite element method. The comparisons of the non-convex columns with square column show that the non-convex multi-corner thin-walled columns have higher energy absorption capacity.     

New extruded multi-cell aluminum profile for maximum crash energy absorption and weight efficiency

New types of trigger and multi-cell profiles with four square elements at the corner are developed. In terms of the crash energy absorption and weight efficiency, the new multi-cell structure shows dramatic improvements over the conventional square box column. The optimization process with the target of maximizing the specific energy absorption has been successfully carried out, and the example of design process is provided. In the optimization process, the problem of stable progressive folding is also addressed. The analytical solution for calculating the mean crushing force of new multi-cell profiles is derived showing good agreement with the numerical results. Finally, the advantage of the new design over the conventional single or multi-cell profiles is discussed.     

Design optimization of cross-sectional configuration of rib-reinforced thin-walled beam

In this paper, a rib-reinforced thin-walled hollow tube-like beam (named as rib-reinforced beam) is presented for potential application in vehicle bumper. Through numerical simulation of the bending behavior under impact loads, the rib-reinforced beam is compared with thin-walled hollow tube-like beams filled with and without foam materials (empty beam and foam-filled beam) in crashworthiness. The effects of the shape of the reinforced rib are investigated and the shape optimization design is performed for increasing energy absorption and reducing the initial peak force. A multi-objective crashworthiness optimization formulation including maximum energy absorption, maximum specific energy absorption and minimum initial peak force is constructed based on the ideal point method (IPM). The optimum configuration of the reinforced rib is given with a normalized cubic spline function. Numerical example results show that, compared with the empty and foam-filled beams with same weights, the optimized rib-reinforced beam has higher energy absorption performance and lower initial crash force. It is found that for the rib-reinforced beam little rumple is formed around the compressed indention, which helps to retard the collapse of the side wall and means more energy absorption.     

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.     

A new method to investigate the energy absorption characteristics of thin-walled metal circular tube using finite element analysis

A numerical study is made to investigate the energy absorbing rule of thin-walled metal circular tube made of three different materials (steel, copper, aluminum) by using response surface methodology (RSM). At the same time, the application prospect of RSM in terms of the research on the energy absorption rule of energy absorption structure can be explored. The test result shows that, the compression process of thin-walled metal circular tube can be divided into three stages: elastic stage, yielding plateau stage, compact stage; To get the greatest value of average plateau force (APF) , a tube with a shorter height and thicker wall should be adopted; To get the greatest length energy absorption (LEA), a tube with thicker wall should be adopted and the ratio of its height and diameter should be as big as possible; To get the greatest specific energy absorption (SEA), a tube with a thicker wall should be adopted and the ratio between its height and diameter should be as big as possible. Thus, it can be seen that, RSM is an advanced experiment design method, and it can be widely used in the research on the energy absorption characteristics of thin-walled metal circular tube and has a promising application prospect in the development of new energy absorbing material and structure.     

某冷弯薄壁型钢结构住宅用钢量优化分析

结合某冷弯薄壁型钢结构住宅实例,采用大型通用有限元软件ANSYS建模,运用零阶法、一阶法对梁、柱构件截面进行优化分析。结果表明,与原设计相比,优化分析后工程的用钢量得到了大大的减少,这不仅有利于钢材的节约,带来可观的经济效益,而且有利于冷弯薄壁型钢结构住宅在我国的推广和应用。     

泡沫填充的薄壁圆柱壳体轴向压碎的分析模型

由于填充轻型泡沫的薄壁钢管有良好的耗能能力而被广泛地应用于工程中。当结构轴心受压时,钢管与泡沫芯之间的作用对吸收能量起到关键作用。已有理论研究的大部分对象为完全填充的钢管。本文提出了一个理论模型,用于分析部分填充的钢管的轴向对称压碎性能。采用改进的模型分析壳体,并考虑了泡沫芯的作用。由能量平衡原理得到极限压力的平均值。建议公式得到的结果与先前文献中的结果吻合。参数分析用于研究泡沫芯稳定时期的压力值(σf),以及填充的比例和壳体的径厚比对结构轴向受压性能的影响。为薄壁结构的吸能性能方面的设计提供指导。     

对钢管材料在液压膨胀试验中的应力—应变关系的测定

基于塑性膜理论和力平衡方程等,对试验数据进行曲线拟合,来确定在液压成形过程（THF）中薄壁管的应力一应变关系。由此提出一种简单实用的液压膨胀试验方法,并对不锈钢和低碳钢管进行自由膨胀试验,以得到所需的试验变形数据。而自由膨胀的有限元模拟同时也验证了该方法的有效性。结果表明：目前的做法是正确的,可用于对钢管材料的应力一应变性能进行界定,此外,由此法也可得到扩展的大应变流动应力曲线。     

剪切型铅阻尼器在高层钢结构中的应用

剪切型铅阻尼器是一种滞回性能稳定、构造简单、受环境影响较小的耗能减震装置,近年来逐渐得到工程界的认可和推广。在非线性有限元分析软件Midas/Gen中建立一实尺寸高层钢结构建筑物数值分析模型,分别采用纯框架结构、框架-支撑结构、剪切型铅阻尼器-框架结构3种不同方案,模拟其在多遇地震和罕遇地震作用下抗震行为并进行比较,探讨了支撑、剪切型铅阻尼器对于钢结构建筑抗震性能的不同影响,分析了剪切型铅阻尼器的布设方式及注意事项,验证了剪切型铅阻尼器的优良性能。     

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.     

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.     

高承载钢板剪力墙抗震性能试验研究

框架-阻尼框筒是以框架-钢板剪力墙代替框架-核心筒结构中的钢筋混凝土核心筒,通过钢板剪力墙提供阻尼和刚度,形成了新的减震体系。基于该体系在超高层建筑中应用需求,完成了2个足尺钢板剪力墙的低周往复加载试验,对比分析了剪力墙在循环荷载作用下的承载力、延性、刚度及耗能能力,并与相应有限元结果进行对比。结果表明,所提出的高承载钢板剪力墙具有优良的延性和耗能能力,屈服荷载和极限荷载分别超过3300kN和5500kN,满足相应抗震设计要求。同时,有限元分析结果与试验结果吻合较好,可用于后续钢板剪力墙的优化。