Crashworthiness optimization design for foam-filled multi-cell thin-walled structures

Foam-filled thin-walled structure and multi-cell thin-walled structure both have recently gained attentions for their excellent energy absorption capacity. As an integrator of the above two kinds of thin-walled structures, foam-filled multi-cell thin-walled structure (FMTS) may have extremely excellent energy absorption capacity. This paper firstly investigates the energy absorption characteristics of FMTSs by nonlinear finite element analysis through LS-DYNA. Based on the numerical results, it can be found that the FMTS with nine cells has the most excellent crashworthiness characteristics in our considered cases. Thus, the FMTSs with cell number n=9 are then optimized by adopting a multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). During the process of multi-objective optimization design (MOD), four kinds of commonly used metamodels, namely polynomial response surface (PRS), radial basis function (RBF), Kriging (KRG) and support vector regression (SVR) for SEA and PCF, are established to reduce the computational cost of crash simulations by the finite element method. In order to choose the best metamodel for optimization, the accuracies of these four kinds of metamodels are compared by employing the error evaluation indicators of the relative error (RE) and the root mean square error (RMSE). The optimal design of FMTSs with nine cells is an extremely excellent energy absorber and can be used in the future vehicle body.     

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.     

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.     

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.     

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.     

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.     

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.     

Crashworthiness investigation of kagome honeycomb sandwich cylindrical column under axial crushing loads

For the classic thin-walled energy absorber, the energy dissipation during a collision is concentrated over relatively narrow zones. This means that a great deal of materials of the columns do not participate in the plastic deformation or not enter into the large plastic deformation stage. To expand the plastic deformation zones and improve the energy absorption efficiency, a new type of kagome honeycomb sandwich bitubal circular column is presented in this paper. This innovative impact energy absorber is made of two circular aluminum tubes filled with core shaped as a large-cell kagome lattice. The interaction effect, deformation mode and energy absorption characteristics of the composite structure are investigated numerically. Observing the collapsing process, it is found that the kagome lattices buckle first, which triggers the outer and inner skin tubes to fold locally. This behavior increases the plastic deformation areas. Moreover, the presence of the outer and inner tubes strengthens the buckling capacity of kagome cell. Furthermore, the folded tube walls intrude into the gap of the honeycomb cell, which further retards the collapse of the honeycomb cell. So the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. In addition, the effects of geometrical parameters of the kagome honeycomb on the structural crashworthiness are studied. It is found that the cell wall thickness and cell distribution (cell number in the circumferential direction) have distinct effects on the specific energy absorption. Besides, we also studied the foam-filled column with the same foam density as the kagome honeycomb and compared it with the kagome sandwich structure. It is found that the kagome sandwich column has higher mean crash force and better energy absorption characteristics.     

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.     

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.     

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.     

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.     

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.     

Comparisons of honeycomb sandwich and foam-filled cylindrical columns under axial crushing loads

For the conventional thin-walled energy absorber, the energy dissipation during a collision is concentrated in relatively narrow zones. This means that a great deal of material does not participate in the plastic deformation or enter the large plastic deformation stage. To expand the plastic deformation zones and improve the energy absorption efficiency, the authors presented a new type of honeycomb sandwich circular column. This innovative energy absorber is a composite structure composed of two circular aluminum tubes filled with core shaped as a large-cell honeycomb lattice. In this paper, six different honeycomb sandwich circular columns were investigated numerically. Comparisons of the interaction effect between tubes and filler, the deformation modes and the energy absorption abilities of these columns were conducted. The results were as following. The kagome sandwich column had the best energy absorption capability, followed by the columns sandwiched with triangle, hexagon lattices. In addition, foam-filled columns with different adhesive conditions were also simulated and compared with the honeycomb sandwich columns. It was found that increasing the adhesive strength improved the energy absorption and changed the deformation mode of the foam-filled columns. Furthermore, comparison showed that the honeycomb sandwich columns had higher specific energy absorption capability than the foam-filled tubes except for the strong bonded case. The kagome sandwich column performed best in crashworthiness, followed by triangle sandwich column.     

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.     

Crashworthiness of automotive steel midrails: Thickness and material sensitivity

The automotive midrail is the main load carrying/energy absorbing component in a frontal vehicle crash. Three separate midrails, from three different manufacturers, each of a different size class of vehicle, and each with different crush modes, were found to exhibit the same sensitivity to variations in material thickness and stress-strain properties. From the results it was determined that a general design guideline for crashworthiness could be stated as: For every 10% change in thickness there is approximately a 14% change in energy absorption capability for a crushing midrail, while for every 10% change in material strength there is approximately a 7·3% change in energy absorption capability. The proposed design guideline can be used to help determine suitable modifications to make a structure more crashworthy and, additionally, to determine how manufacturing variations may affect the crashworthiness of a vehicle.     

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.     

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。     

Experimental and numerical crashworthiness investigation of empty and foam-filled end-capped conical tubes

Foam-filled thin-wall structures exhibit significant advantages in light weight and high energy absorption. They have been widely applied in automotive, aerospace, transportation and defense industries. Quasi-static tests were done to investigate the crash behavior of the empty and polyurethane foam-filled end-capped conical tubes. Non-linear dynamic finite element analyses were carried out to simulate the quasi-static tests. The predicted numerical crushing force and fold pattern were found to be in good agreement with the experimental results. The energy absorption capacities of the filled tubes were compared with the empty end-capped conical tubes. The results showed that the energy absorption capability of foam-filled tube is somewhat higher than that of the combined effect of the empty tube and the foam alone. Finally, the crash performance of the empty and foam filled conical and cylindrical tubes were compared. Results from this study can assist aerospace industry to design sounding rocket carrier payload based on foam-filled conical tubes.     

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.