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.     

Multiobjective crashworthiness optimization of circular aluminum tubes

This research deals with the development of circular aluminum tubes for crashworthiness. The dynamic crash responses of aluminum tubes are determined from the finite element simulation. In order to validate the FE results some dynamic impact test on aluminum tubes are performed. Multiobjective optimization technique is adopted to solve the problem of maximization of absorbed energy and specific absorbed energy of tubes. The D-optimal design of experiments [Atkinson AC, Donev AN, Optimum experimental designs. Oxford: Oxford Science Publications; 1992] and the response surface method are applied to construct an approximated design sub-problem and the optimization process is repeated until the convergence criteria are satisfied.     

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.     

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.     

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.     

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.     

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.     

A material and gauge thickness sensitivity analysis on the NVH and crashworthiness of automotive instrument panel support

This paper provides a finite element analysis of the effects of using alternative materials and gauge thickness on the weight and structural performance of the VN127 instrument panel support. Two types of analyses were performed, NVH and crashworthiness. The NVH analysis was used to determine the structure’s natural frequencies, whereas the crashworthiness analysis was used to examine the structure’s crash behavior under two different impact conditions. The materials used in this study included mild steel, aluminum and magnesium alloys. The thickness of the structure was varied from 0% to 40%, in increments of 10%. The results of different models were compared with the baseline model, i.e., the mild steel model with nominal thickness. It was found that by replacing mild steel with aluminum alloys, and increasing the gauge thickness of the structure by 40%, the NVH and crashworthiness performance of the structure was equivalent to the baseline model.     

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.     

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.     

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.     

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.     

Impact response of rectangular and square stiffened plates supported on two opposite edges

Experimental drop weight impact tests have been performed to examine the dynamic response of small-scale stiffened plates struck laterally by a mass with a spherical indenter. The laboratory results are compared with numerical simulations. The plates stiffened with a flat bar or L profile are supported at two opposite edges and impacted at different velocities and locations along the span. The impact scenarios could represent incidents in marine structures, such as load actions due to dropped objects on decks. The experiments are conducted using a fully instrumented impact testing machine. The obtained force–displacement responses show a good agreement with the simulations performed by the LS-DYNA finite element solver. The finite element model includes defining the experimental boundary conditions so as to simulate small axial displacements of the specimen at the supports. This representation can be used to analyze the structural crashworthiness of similar marine structures under collision scenarios. The strain hardening of the material is defined using experimental data of quasi-static tension tests and the strain rate sensitivity is evaluated using standard coefficients of the Cowper–Symonds constitutive model. The results show that the plastic response of the specimens is highly sensitive to the amount of restraint provided at the supports. Furthermore, it is found that in most of the specimens the contribution of the stiffeners to the impact response is insignificant, since the ends of the stiffener are free at the unsupported edges and the specimens experience small axial displacements at the supports.     

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.     

Experimental study on crashworthiness of tailor-welded blank (TWB) thin-walled high-strength steel (HSS) tubular structures

This paper aims to investigate the crushing behaviors of tailor-welded blank (TWB) thin-walled structures. A series of TWB high-strength steel (HSS) square tubes with different weld line locations is used to perform the crushing tests for evaluating the effects of different TWB parameters, such as weld line locations and material combinations, on crushing characteristics. These TWB specimens are fabricated through the laser welding process to ensure sufficiently narrow weld line. In the study, the center edge of TWB square specimens is not welded so that such special TWB structures have open cross section. The crushing test results exhibit excellent repeatability. The collapse modes and force–displacement relationships are compared with each other. It is found that the crushing behaviors of different material combinations are fairly significant for a given weld line location. Such key crushing characteristics as specific energy absorption (SEA), average crush force (F_avg), peak force (F_max) are also evaluated for understanding crashworthiness of these TWB structures. The experimental results provide us with some insightful guidance to crashworthiness design of TWB thin-walled HSS structures.     

A vehicle front frame crash design optimization using hole-type and dent-type crush initiator

The hole-type crush initiators according to various ratios of thickness to width (t/b) were studied. And the approximate equation to quickly predict the optimum size of the crush initiator by impact velocity for each ratio of thickness to width was introduced. Also, the simple rectangular and circular dent-type crush initiators of a front frame with non-uniform closed-hat section in a vehicle were studied for frontal crashworthiness according to various ratios of thickness to width (t/b).The optimum size and dent depth of a crush initiator, whose location is decided by the homogenization method, were studied by using design of experiment and response surface method. Design analysis results of the dent-type crush initiators were compared with those of the hole-type crush initiator of the same size as the dent-type crush initiators.The rectangular dent-type crush initiator absorbed more crash energy than the circular dent-type crush initiator. Dynamic mean crushing loads of a rectangular dent-type crush initiator of size equal to that of the hole-type crush initiator designed by the homogenization method were similar to those of the hole-type crush initiator.The trend curve of the optimum size rectangular dent-type crush initiator design is similar with the trend curve of hole-type crush initiator design. Therefore, the approximate equation used to predict the optimum size of the hole-type crush initiator can be applied to find the optimum size of the rectangular dent-type crush initiator.     

Design of thin wall structures for energy absorption applications: Enhancement of crashworthiness due to axial and oblique impact forces

This paper describes a computationally aided design process of a thin wall structure subject to dynamic compression in both axial and oblique directions. Several different cross sectional shapes of thin walled structures subjected to direct and oblique loads were compared initially to obtain the cross section that fulfills the performance criteria. The selection was based on multi-criteria decision making (MCDM) process. The performance parameters used are the absorbed crash energy, crush force efficiency, ease of manufacture and cost. Once the cross section was selected, the design was further enhanced for better crash performances by investigating the effect of foam filling, increasing the wall thickness and by introducing a trigger mechanism. The outcome of the design process was very encouraging as the new design was able to improve the crash performance by an average of 10%.     

锥形齿齿形参数及间距优化试验研究

镶齿滚刀已被广泛应用于多种开挖机械,如隧道掘进机、反井钻机、采掘机等。镶齿滚刀上合金齿的齿形参数以及齿间距、排间距的优化研究,对于提高机械掘进效率、降低施工成本有重要意义。设计并制作了不同齿形参数的锥齿,搭建了侵入试验平台,应用不同锥齿对北山花岗岩大块岩样(300 mm×300 mm×200 mm)进行了单齿侵入试验及齿间相互作用侵入试验。针对试验的北山花岗岩,试验结果表明,锥顶角为60°、锥顶半径为5.5 mm是其最优齿形参数。而齿间距和排间距分别在35 mm和40 mm左右为最优布齿参数。本研究可为开挖北山花岗岩地层的机械设备的刀具设计提供参考。     

A method for progressive structural crashworthiness analysis under collisions and grounding

Collisions and grounding always give rise to structural crashworthiness issues involving crushing, yielding, and fracture. For accidental limit state design and safety assessment associated with collisions and grounding, the resulting progressive structural crashworthiness characteristics should be analyzed to evaluate the energy absorption capability of the structure in the corresponding accidental event in conjunction with the associated criteria. The accidental energy absorption capability of a structure under collisions or grounding can be predicted by integrating the area below the reaction forces versus penetration curve until or after the accidental limit state is reached. For risk assessment associated with such accidents, the results of structural crashworthiness analysis are also used as a basis of the consequence analysis. The aim of the present paper is to present an efficient and accurate method which is useful for the progressive structural crashworthiness analysis of ships and ship-shaped offshore structures under collisions or grounding. Theoretical outline of the method is addressed. Application examples of the method to ship-shaped test structures are presented by a comparison with experimental results.     

Crashworthiness research on S-shaped front rails made of steel–aluminum hybrid materials

In the paper, crashworthiness of the S-shaped rail extracted from the frontal frame in a car is studied. In order to reduce the peak impact force while increasing the total absorbed energy, the hybrid materials are employed in that rail, where aluminum alloy is used for its front part and advanced high strength steel (AHSS) for its back part. By designing 16 experiments based on orthogonal experiment, the effect of five influence factors with four levels on the crash performance of the steel–aluminum hybrid S-shaped front rail is emphatically investigated. These influence factors include the different material types of aluminum alloy and AHSS, the sheet thicknesses of the two parts, and length proportion for the aluminum part. The AHSS includes dual-phase (DP) steel, transformation induced plasticity (Trip) steel and Mart steel; the aluminum alloy series include 5000 and 6000 series. The research result shows that the use of steel–aluminum hybrid materials can reduce the peak impact force and the total weight for the S-shaped front rail, while the total absorbed energy can be greatly increased, so the crashworthiness and lightweight of the S-shaped front rail are significantly improved.