Newinsightsintothecollapsingofcylindrical thin-walledtubesunderaxialimpactload€¦ · · 2010-12-30Newinsightsintothecollapsingofcylindrical thin-walledtubesunderaxialimpactload

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New insights into the collapsing of cylindricalthin-walled tubes under axial impact loadM Shakeri∗, R Mirzaeifar, and S SalehghaffariDepartment of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnics), Tehran, Iran

The manuscript was received on 25 November 2006 and was accepted after revision for publication on 8 May 2007.

DOI: 10.1243/09544062JMES562

Abstract: The current paper presents further investigations into the crushing behaviour of circu-lar aluminium tubes subjected to axial impact load. Experiments prove that in order to achievethe real collapsing shape of tubes under axial loads in numerical simulations, an initial geomet-ric imperfection corresponding to the plastic buckling modes should be introduced on the tubegeometry before the impact event. In this study, it is shown that the collapsing shape of tube isaffected by this initial imperfection and consequently it is shown that by applying an initial geo-metric imperfection similar to the axisymmetric plastic buckling mode, the tubes tend to collapsein a concertina mode. This phenomenon is studied for circular tubes subjected to axial impactload and two design methods are suggested to activate the axisymmetric plastic buckling mode,using an initial circumferential edge groove and using one- and two-rigid rings on the tube. Ineach case the broadening of the concertina collapsing region is estimated using numerical sim-ulations. Experimental tests are performed to study the influence of cutting the edge groove onthe collapsing mode.

In order to optimize the crashworthiness parameters of the structure such as the absorbedenergy, maximum deflection in axial direction, maximum reaction force, and mean reactionforce, a system of neural networks is designed to reproduce the crushing behaviour of the struc-ture, which is often non-smooth and highly non-linear in terms of the design variables (diameter,thickness, and length of tube). The finite-element code ABAQUS/Explicit is used to generatethe training and test sets for the neural networks. The response surface of each objective func-tion (crashworthiness parameters) against the change of design variables is calculated and bothsingle-objective and multi-objective optimizations are carried out using the genetic algorithm.

Keywords: axial crushing, circular tubes, plastic buckling modes, neural networks, geneticalgorithm

1 INTRODUCTION

Due to the day-to-day increasing of the transportvehicles speed, traffic accidents unfortunately havebecome a common occurrence nowadays. In order todecrease human sufferings and financial burdens, overthe last decade more focus has been paid to design thetransport structures with taking the crashworthinessrequirements into consideration. Many experimen-tal and theoretical studies have been carried out

∗Corresponding author: Department of Mechanical Engineering,

Amirkabir University of Technology, 424 Hafez Avenue, Tehran,

Iran. email: [email protected]

on designing devices to dissipate the kinetic energyduring an accident by converting this energy intoanother form of energy. These devices are usuallycalled mechanical energy absorbers. Energy absorbersare classified into two major categories, the reversibleenergy absorbers, like the hydraulic dashpots or elas-tic dampers, and irreversible or collapsible energyabsorbers, like energy dissipation in plastic deforma-tion of members of the structure.

There are numerous types of irreversible energyabsorbers, like circular tubes, square tubes, tubularstructures, octagonal cross-section tubes, sphericalshells, frusta, tapered tubes, S-shaped frames,honeycomb cells, composite tubes, foam-filled, andwood-filled tubes.

JMES562 © IMechE 2007 Proc. IMechE Vol. 221 Part C: J. Mechanical Engineering Science

870 M Shakeri, R Mirzaeifar, and S Salehghaffari

Thin-walled tube-like structures with circular cross-section, because of their efficiency in energy absorp-tion and ease of manufacture represent the mostcommon shape of collapsible energy absorbers. Thekinetic energy of the accident can be dissipated inplastic deformation of tube in several forms, like inver-sion, splitting, mushrooming, lateral indentation, andaxial crushing. Among these mechanisms, the axialcrushing of circular tubes provides the best device forabsorbing the kinetic energy of impact loads becauseof the greater amount of material participating in theplastic deformation and energy absorption. Further-more, in the axial crushing mechanism, the reactionforce is reasonably constant and the stroke length isrelatively high compare with the other mechanisms ofcollapsing of tubes.

Circular tubes under axial quasi-static or impactload may crush in different modes, including: con-certina or axisymmetric, diamond, Euler, and mixedmode. Many experimental and numerical studies havebeen carried out on finding the parameters that con-trol the collapsing mode of tube under axial load.Among the performed researches, a great percentinvestigate the influence of geometric dimensionssuch as diameter, thickness, and length of the tube onthe collapsing mode [1, 2]. The purpose of such stud-ies is ascertaining ranges for geometrical dimensionsand then studying the collapsing mode of the tube foreach range. Other than the geometrical dimensions,the influence of many other parameters is studiedin the literature. For instance; the effect of mass andinitial velocity of impact on collapsing of tube is stud-ied in references [2] to [4]. Some experimental testresults are reported in reference [5] for collapsing oftubes made of three different materials and the effectsof material properties such as strain hardening andsensitivity to strain rate are studied. Controlling thecollapsing shape of tube by adding stiffener rings to thetube is studied in reference [6] by performing exper-imental tests. The influence of boundary conditionsat the tube wall ends and the friction coefficient isstudied in reference [7]. The influence of the inertiacharacteristics of the tube on the collapsing mode isstudied in reference [8] using a finite-element (FE)analysis. The phenomena of dynamic plastic buck-ling and dynamic progressive buckling are studiedfrom the viewpoint of stress wave propagation in ref-erence [9], and in reference [10] the FE method isused to investigate the influence of cutting a controlledsize chamfer at the edge of the tube on the collapsingmode.

As a general rule, when the tube length is greaterthan the critical length for the given diameter andthickness, it deforms in Euler or global bending mode,which is an inefficient and unreliable mode in energyabsorber designing and should be avoided in crash-worthiness applications. Among the other collapsing

modes besides global bending, diamond and mixedmodes are the most probable collapsing modes forthe common dimensions of tubes, but both of thesemodes have the potential ability of changing to globalbending by little changes in the load or boundaryconditions. Another disadvantage of collapsing in dia-mond or mixed mode is the high probability of mis-calculations in designing tubes as shock absorbers.Because the exact collapsed shape of tube in this caseis almost unpredictable even when all the externalconditions (like load and boundary conditions) areknown exactly. Contrary to the mentioned modes, theconcertina collapsing mode is the most desired designin crashworthiness applications because of its relia-bility and efficiency in absorbing the impact energy.The high efficiency in energy absorption for tubes thatcollapse in concertina mode returns to the great per-cent of material that contributes in energy absorption.In addition to the energy absorption performance, thereaction force for collapsing in concertina mode doesnot have sudden changes in contrast with diamondcollapsing. A summary of empirical relations for cal-culating the absorbed energy and mean reaction forcefor different collapsing modes is presented in refer-ence [1]. Experimental studies show that in the widerange of dimensions of tubes (that is shown with dif-ferent L/D and D/t ratios) there is only a limited regionthat the crushing of tube in concertina mode is guaran-teed. Unfortunately, this region is limited to the tubeswith relatively small L/D and D/t ratios that have alower ability in dissipating the impact energy com-pared with the larger tubes. Among the researchescarried out on designing aluminium tubes as collapsi-ble shock absorbers, almost no work is reported ondesigning methods to extend the region in which theaxisymmetric collapsing mode is guaranteed.

In the present study, the initial geometric imper-fection of plastic buckling modes in the postbucklinganalysis is introduced as a new factor that can extendthe concertina collapsing region.The prevailing theoryon the postbuckling analysis of tubes under axial load-ing is applying an initial imperfection proportional toa linear combination of all the plastic buckling modeson the tube and analysing the new structure underexternal loads. In this work, it is shown that by apply-ing only an initial imperfection, proportional to theaxisymmetric collapsing mode instead of the tradi-tional method, the concertina collapsing region willextend to a wider region. In order to show this effect,numerical simulations are carried out to specify thelimits of concertina collapsing mode region for tubesof various diameters, lengths, and thicknesses underaxial impact load and the extension of these limits byapplying the initial geometric imperfection propor-tional to the axisymmetric plastic buckling mode onthe structure is shown in the L/D–D/t diagram in therange of 20 < D/t < 100 and L/D < 6.

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New insights into the collapsing of cylindrical thin-walled tubes 871

In order to use the introduced parameter in applieddesign of energy absorbers, two methods are sug-gested to activate the axisymmetric plastic buck-ling mode: cutting an initial circumferential edgegroove outside the tube and using one- and two-circumferential stiffeners. Performing FE simulations,the extension of the axisymmetric collapsing regionafter using these methods is shown in the L/D–D/tdiagram.

Almost all of the reported works on designingthe cylindrical tubes as impact energy absorbers arejust carried out to satisfy the imposed crashworthi-ness requirements, whereas, nowadays, optimizationbecomes a necessary part of designing procedure. Theoptimization of the structure under crashworthinessrequirements is very complex and expensive from thecomputational point of view because the objectivefunction is often non-smooth and highly non-linearin terms of design variables. The optimization proce-dure requires repetitive and iterative validation of theselected objective function for various values of designvariables. To avoid the calculation of the objectivefunction in each iteration by computationally costlyFE simulations, approximated functions may be usedto simulate the crush behaviour of the structure. Theresponse surface methodology (RMS) [11], and neuralnetwork systems [12] are the most common devicesto reproduce the crush behaviour of the structure. Inthe present study, a system of parallel neural networksis developed to reproduce the structural behaviourduring the crush phenomenon. A limited numberof FE simulations are carried out to train and testthe neural network systems. The remarkable prefer-ence of the presented work to most similar studies isusing different neural network systems to return eachcrashworthiness parameter instead of using a globalnetwork to simulate all the parameters. After train-ing the neural network systems, the response surfaceof selected crashworthiness parameters against thedesign variables are calculated and shown in graphicalform. Finally, using the response surfaces developedby the neural network systems, the genetic algorithm(GA) is implemented to find the optimal configurationof tube dimensions for both single-objective (SO) andmulti-objective (MO) optimizations.

2 NUMERICAL MODEL AND VERIFICATION

2.1 Description of the FE model and materialproperties

Numerical simulations of axial crushing of tubes underimpact loading are carried out using the FE codeABAQUS/Explicit. In order to calculate the plasticbuckling mode shapes, the FE code ABAQUS/Standard

is used. Four-noded shell elements with reduced for-mulation (S4R), suitable for large strain analysis areused to model all the analysed tubes. Three integrationpoints are used through the shell thickness to modelbending. The shell thickness is set to t = 2 mm for allthe specimens except in the cases that another thick-ness is mentioned. After convergence, an element sizeof 3 mm is found to produce suitable results. Two rigidwalls are fixed to the ends of the tube. For simulatingthe impact load, a point mass (m = 250 kg) is attachedto the upper rigid wall and an initial downward veloc-ity (V0) is defined for the wall just before the impactevent. The quasi-static load is simulated by movingthe upper plate with a constant velocity downward.The tube is tied to the lower rigid wall and free at theother end. The lower plate is constrained in all degreesof freedom and the upper plate is fixed in all trans-lational and rotational degrees of freedom except theaxial displacement in order to avoid the twisting of theimpactor plate. The contact between the tube and rigidwalls is assumed to be frictionless, but a friction coef-ficient equal to 0.1 is used to model the self-contact ofthe inner and the outer surfaces of the shell.

The material properties are defined as linear elasticfollowed by non-linear work hardening in the plasticregion. The true static stress–strain curve of a typicalaluminium alloy obtained by a standard tensile test asshown in Fig. 1 is used to introduce the approximatedtrue stress-plastic strain data points in numerical sim-ulations. These points are shown in Table 1. Theelastic modulus of this material is 70 Gpa, the den-sity is ρ = 2700 kg/m3 and the Poisson ratio is ν = 0.3.The material is assumed to have only isotropic strainhardening and strain rate effects on the yield strengthare neglected.

Fig. 1 True stress–true strain characteristic of thealuminium alloy (experimental)

Table 1 True stress–plastic strain data points used foraluminium in numerical simulations

σ (N/mm2) 175 185 192 200 205 210

εp 0 0.01 0.02 0.03 0.04 0.05



Fig. 2 Collapsing of a tube under axial quasi-static load obtained from the experimental [5] andnumerical results. (a) The deformed shape, (b) the absorbed energy, and (c) reaction forceagainst the axial deformation

2.2 Verification of the FE simulation usingthe previously reported experimental results

Crushing simulation of a tube under quasi-static axialloading is carried out and the results are comparedwith the experimental results of Hsu and Jones [5]in order to evaluate the accuracy of the FE simula-tion in predicting the absorbed energy and the crushforce as well as the deformation mode of the tube. Thetube has a nominal outer diameter of 50.8 mm (2 in),length of 250 mm, and a wall thickness of 1.53 mm. Thetube is made of 6063-T6 aluminium alloy. The materialproperties of this alloy are described in reference [5].The specimen is sandwiched between two parallelhigh-strength steel plates and the upper plate movesdownward with a constant speed of 2 mm/min. Themaximum axial deflection is set to 150 mm. Figure 2(a)shows the deformed shape obtained from the exper-imental and numerical results. The absorbed energyand crush force against the axial deformation of thetube obtained by the numerical simulation and exper-imental test are compared in Figs 2(b) and (c), respec-tively. As it is shown, the numerical simulation predictsclosely the deformed shape as well as the absorbedenergy and crush force.

2.3 Quasi-static crush test to verify the FEsimulation

A quasi-static crush test is carried out to verify theaccuracy of the numerical simulation results. In this

test, an aluminium alloy tube of external diameter75.6 mm, length of 151.2 mm, and a wall thicknessof 1.4 mm is loaded quasi-statically in axial directionby using a compression testing machine at a nominalcross head-speed of 5 mm/min. In order to obtain thematerial data, a quasi-static material test is performedon a strip cut from a shell using a standard tensiletest machine and the resulting stress–strain curve isused to introduce the approximated true stress-plasticstrain data points in the numerical simulation. Thespecimen is placed between parallel steel plates ofthe test machine without any additional fixing. Themaximum axial deflection is set to 105 mm. Figure 3compares the experimental and numerical results ofthe deformed shape for the tube. Figure 4 shows theaxial load against the axial deformation obtained fromthe experimental and numerical results. It is obvi-ous that the numerical method simulates the crushingbehaviour of the tube with sufficient accuracy.

3 THE INFLUENCE OF THE PLASTIC BUCKLINGMODES ON THE COLLAPSING SHAPE OF THETUBE

3.1 The influence of initial imperfection on thecollapsing modes classification chart

Inasmuch as the tubes deformation under axial loadwill involve buckling, it is necessary to perturb theinitial geometry of the tube in the crushing analysisproportional to the buckling modes. By ignoring the



Fig. 3 The deformed shape of the tube under axial quasi-static load obtained from theexperimental and numerical results

Fig. 4 The reaction force against the axial deformationof the tube under quasi-static load obtained fromthe experimental and numerical results

geometrical perturbation, numerical methods onlypredict the axisymmetric collapsing mode for all casestudies because the geometrical model and load con-dition are both axisymmetric in collapsing of tubesunder axial load. However, the experimental tests showthat concertina collapsing happens only for a narrowrange of tube dimensions. This phenomenon can beexplained by considering an instantaneous bucklingjust before the crushing of tube. The effect of thisinitial buckling can be introduced in numerical simu-lation by applying an initial imperfection proportionalto the buckling modes on the tube in crushing analysis.Experimental results show that the best geometri-cal imperfection for applying on the tube model innumerical simulation is a linear combination of someof the first buckling modes, for example the first tenplastic buckling modes [13]. Typically, the magnitudeof the perturbation used for each eigenmode is afunction of the relevant structural dimension, such asshell thickness and the magnitude of the correspond-ing eigenvalue. Since the lowest eigenmodes are mostpertinent to the crushing behaviour of the structure,appropriate magnitudes may be found by obtaininga mesh imperfection of a few percent of the shellthickness for the first eigenmode and a decreasing

percentage as the corresponding eigenvalue of modesincreases. The magnitude of these imperfections arefound by a trial and error procedure and comparingthe results of numerical simulation with the experi-mental results. Note that the magnitudes related tothe modes change proportional to the change of eacheigenvalue related to the first eigenvalue, so the onlyunknown in each attempt of trial and error proce-dure is the imperfection proportional to the first mode.In this study, the magnitude for the first mode is setto 2 per cent of shell thickness that was previouslyreported in the literature too [13].

In order to perform the procedure of applying theseimperfections on the structure, in each numericalsimulation, the first ten buckling modes and theircorresponding eigenvalues of the tube are obtainedby running an eigenvalue buckling analysis usingABAQUS/Standard. As a sample, the first four bucklingmode shapes of a tube of D = 120 mm, L = 216 mm,and t = 2 mm are shown in Fig. 5. These modes arerelated to buckling of the tube placed between two

Fig. 5 The first four mode shapes of a tube subjected toaxial compression



rigid walls (the rigid walls are eliminated in Fig. 5 inorder to improve the clarity of picture), the back wallis constrained and an axial force is applied to the fronttube. The results of buckling analysis are stored, and inthe next step, the IMPERFECTION keyword is used inABAQUS/Explicit to read the buckling modes from thestored data, scale them by the defined magnitudes,and perturb the nodal coordinates of the FE modelbefore the crushing analysis.

All the previous studies in the literature concentrateon finding an initial geometric imperfection in numer-ical simulations in order to simulate the experimentalcollapsing shape of tube with a good accuracy. Thecontribution of this initial imperfection on the collaps-ing mode of tube and finding applied methods basedon this imperfection to control the collapsing modeis not studied yet. In this paper, initial imperfectionproportional to the plastic buckling modes is intro-duced as a new parameter that controls the collapsingshape of tube under axial impact load. By perform-ing numerical simulations for tubes of various L/Dand D/t ratios for the impact velocity V0 = 7 m/s, thelimits of the region in which the concertina crush-ing mode is guaranteed in the L/D–D/t diagram isobtained and shown in Fig. 6. The results of an exper-imental test in the case of quasi-static loading [1]

Fig. 6 The limits of the concertina collapsing region

are shown in this figure too. As it is shown, the lim-its of the concertina collapsing region for the crushsimulations are similar to the results of quasi-statictest. It is evident that, in both conditions of load-ing, only the tubes with relatively small L/D andD/t ratios that have a lower ability in dissipating theenergy, compare to larger tubes, collapse in concertinamode.

In the next step, the same numerical simulationsof tube crushing under axial impact load are per-formed, but solely the initial geometric imperfectionof the axisymmetric buckling mode (like mode 1in Fig. 5) is applied on the structure at the beginningof the crushing analysis. As it is shown in Fig. 6the limits of the concertina collapsing mode regionextend remarkably in the L/D–D/t diagram usingthis method, except for the tubes of relatively greatdiameters. This phenomenon reveals that by acti-vating the axisymmetric buckling mode of the tubeunder axial compression, the concertina collaps-ing mode takes place for a wider range of dimen-sions. The following sections, describe applied designmethods in order to activate the axisymmetric buck-ling mode.

3.2 Quasi-static crush tests to verify the collapsingmodes classification chart

Six quasi-static crushing tests are performed in orderto verify the classification chart presented in Fig. 6.According to this chart, numerical simulations predictconcertina collapsing mode for tubes of any 20 <

D/t < 75 and L/D of two or less and predict mixedmode for L/D of two or greater in this range of D/t .The main purpose of this section is evaluating thenumerical results for the classification chart in therange of 20 < D/t < 75, so the tests are carried outfor two different D/t ratios (D/t = 54 and 72) andthree L/D ratios for each D/t value. The test condi-tions and material properties are the same as the testin section 2.3. The dimensions of tubes and the axialdeflection for each test are shown in Table 2, note thatthe thickness of tube is set to 1.4 mm for all specimens.

Table 2 Results from the quasi-static experimental tests and numerical simulations

Fmax (kN) Fmean (kN) Modea

DeflectionTest # D/t L/D (mm) Expb Numb Exp Num Exp Num

1 54 1 50 47.2 48.1 19.9 18.1 C C2 54 2 105 47.4 47.2 18.3 17.6 M3 M33 54 3 190 48.4 49.3 18.0 17.4 M3 M34 72 1.1 85 59.9 57.6 23.0 19.8 C C5 72 2 140 66.0 63.2 22.1 20.1 M4 M46 72 3 200 62.7 64.1 21.2 20/3 M4 M4

aC, concertina; M3, mixed mode with three circumferential lobes; M4, mixed mode with four circumferential lobes.bExp, experimental; Num, numerical.



Fig. 7 Comparison of the results for tubes collapsing mode under axial quasi-static load obtainedfrom experimental tests and numerical simulations

The collapsed shape of tube obtained by FE simula-tion and experimental tests are compared in Fig. 7 forthese tests. It is obvious from the presented resultsthat numerical method can simulate the collapsingshape of tube with sufficient accuracy. Table 2 showsthe values of the maximum and mean collapsing forceobtained from FE simulation and experimental tests.It is obvious from Fig. 7 and Table 2 that the numericalsimulation can predict the collapsing shape and thecrashworthiness parameters with a great accuracy.

4 TUBES WITH A CIRCUMFERENTIAL EDGEGROOVE

As it is shown in Fig. 5, in the axisymmetric buck-ling mode the edge ring of the tube deforms out-wards. An applied design to activate this mode isweakening the edge ring of the tube by cutting a cir-cumferential edge groove outside the tubes to forcethis ring to deform outwards at the beginning of thecrushing.



Most of the previous reported works on design-ing the grooved tubes in order to control the col-lapsed shape under axial loading are restricted tothe tubes with grooves alternately cut outside [14] orinside and outside [15] the tube or the spirally slot-ted tubes [16]. The common weakness of all thesedesigns is in the reduction of the amount of materialparticipating in the plastic deformation and energyabsorption. However, in the presented design, as itwill be shown in the following sections, the amount ofmaterial that does not contribute in energy absorptionis so low that the groove have a negligible influ-ence on the energy absorption capacity of the struc-ture, on the other hand the presented design have aremarkable influence on the collapsed shape of thetube.

The edge grooves are of W = 3 mm wide and d =1 mm depth. The details of the specimen design aregiven in Fig. 8. In order to model the specimen, theshell thickness of the first row of elements in theFE model is changed to t = 1 mm and the OFFSETparameter is used in the SHELL SECTION keyword,to adjust the position of this row of elements likeFig. 8. The procedure of extracting the buckling modeshapes and their corresponding eigenvalues, and thecrush analysis is like before. Numerical simulationsfor tubes in the range of 20 < D/t < 100 and 1 <

L/D < 6, before and after cutting the circumferentialgroove are performed and the limits of the concertinacollapsing region are obtained. Figure 9 shows theremarkable extension of the axisymmetric collapsingregion after cutting a circumferential edge groove onthe tubes.

Fig. 8 Details of the circumferential groove design

Fig. 9 The limits of the concertina collapsing regionbefore and after cutting the circumferentialgroove

5 QUASI-STATIC EXPERIMENTAL TESTS ONTUBES WITH A CIRCUMFERENTIAL EDGEGROOVE

As explained in the previous section, cutting acircumferential edge groove on the tube activatesthe axisymmetric buckling mode and increases theprobability of forming axisymmetric folds in contrastwith diamond folds. In order to verify the numer-ical results, 16 experimental tests are carried out.These tests are performed on tubes with D/t = 49,t = 2 mm and four different L/D ratios. The mate-rial properties and test conditions are similar to thosegiven in section 3.2. For each L/D and D/t ratio, twospecimens with and without grooves are prepared.Figure 10 shows a specimen with the edge groove.The dimensions of groove are similar to that given

Fig. 10 A specimen with circumferential edge groove



in Fig. 8. Table 3 contains the properties of theseeight specimens. In order to guaranty the accuracyof the experimental tests, each test was carried outtwo times. Figure 11 compares the collapsing modeof tubes with edge groove and the initial tubes. It isobvious that cutting the edge groove increases thenumber of axisymmetric folds. In all the tests fortubes with circumferential edge groove, after form-ing two or three axisymmetric folds the collapsingmode changes to diamond. This phenomenon may bebecause of non-symmetric deflections that are gener-ated on the tube during cutting the edge groove. Asshown in Table 3, cutting the edge groove decreasesthe value of maximum reaction force that is a greatadvantage in designing tubes as mechanical shockabsorbers.

Table 3 Details of specimens used for studying theinfluence of cutting a circumferential edgegroove on the collapsing mode (as shown inFig. 11)

Number ofTest # L/D Fmax (kN) axisymmetric folds

A 1.75 64.1 1A-Groove 1.75 50.6 3B 1.85 64.5 1B-Groove 1.85 51.8 2C 1.80 64.3 1C-Groove 1.80 52.4 2D 1.70 64.1 1D-Groove 1.70 52.7 3

6 TUBES WITH ONE- ANDTWO-CIRCUMFERENTIAL STIFFENERS

As another design for broadening the concertina col-lapsing region, the circumferential stiffeners may beadded to the tube. In the first step, it is assumed thata stiffener ring is attached to the top ring of the tubeas shown in Fig. 12. In order to model the specimenwith the stiffener ring, a boundary condition thatconstrains the radial displacement of nodes on theedge of the tube is used. In the range of 20 < D/t < 100and 1 < L/D < 6, the collapsing mode classificationchart for the tubes before and after using the stiffenerring is depicted in Fig. 13. It is evident that the stiffenerring extends the concertina mode remarkably withoutinfluencing the energy absorption of the structure asit will be shown in the next section.

Another design to extend the concertina collaps-ing region is attaching two stiffener rings to the tube.The second stiffener is attached to the middle of thetube. The broadened limits of the concertina collaps-ing region for tubes with two stiffener rings are alsoshown in Fig. 13.

7 COMPARING THE CRASHWORTHINESSPARAMETERS OF THE PRESENTEDDESIGNS

The absorbed energy, maximum and mean reactionforces, and maximum deflection in axial direction arethe most important crashworthiness parameters in

Fig. 11 The influence of cutting a circumferential edge groove on the collapsing mode of tubesunder quasi-static axial load



Fig. 12 Tube with the stiffener ring

Fig. 13 Broadening of the concertina collapsing regionusing one- and two-stiffener rings

designing collapsible shock absorbers. These param-eters are calculated in all the performed numericalsimulations, as a sample these parameters are shownin Table 4 for tubes with D/t = 20 and three differ-ent L/D ratios. Table 5 contains the same results fortubes of D/t = 40. As expected, the absorbed energyfor grooved tubes is less than the energy absorbed bya tube of the same dimensions with the stiffener ring.This phenomenon can be explained due to the amountof material that participates in dissipating the impactenergy for these tubes. The amount of the absorbedenergy against the axial deflection is shown in Fig. 14for a tube of D/t = 40 and L/D = 2.3 with one stiffener

ring and with the circumferential edge groove, as it isshown, the absorbed energy of the grooved tube fallsdown during the formation of the first fold. It is evidentthat the difference between the absorbed energy forthese tubes is almost negligible and the designer maychose any of these suggestions depending on the easeof manufacture. Comparison of the maximum andmean reaction forces for tubes of relatively great D/tratios (D/t � 40) shows that using the circumferentialgroove can reduce the peak reaction force that hap-pens at the beginning of the crushing. The reductionof the reaction force can be considered as a remarkableadvantage for the grooved tubes design.

8 NEURAL NETWORK SYSTEMS TO REPRODUCETHE CRUSH BEHAVIOUR OF THE TUBE

The idea of using the artificial neural networksoriginates from the fact that all the biological neuralfunctions, including memory, are stored in the neu-rons and in the connections between them. In otherwords, learning may be defined as the establishmentof new connections between neurons or the modifica-tion of existing connections [17]. The artificial neuralnetworks are a simple set of computing units or neu-rons that can be trained to reproduce the behaviour ofa complex function.

The background work in the field of neural networksoccurred in the late 19th and early 20th centuries.Among different kind of problems, the idea of usingneural networks in engineering problems was firstdeveloped in 1940s byWarren McCulloch and Pitts [18]who showed that the neural network systems cancompute any arithmetic or logical function. Duringthe recent years, the application of neural networksystems is expanded to a vast range of problems inaddition to the engineering or mathematic fields, likebusiness, medicine, finance, and literature, inasmuchas the neural networks are not programmed to solve aspecific kind of problems. Indeed, the neural networksystems are not influenced by the physic equations of aproblem, they only work by training themselves usingthe past results of a problem and adapting their com-puting units to solve the new problems of the samekind.

In the present study neural network systems areused to reproduce the crush behaviour of thin-walledtubes. In the previous sections, all the results wereobtained from the FE simulations, but the final goalof the following sections is optimization of the tubedimensions under crashworthiness requirements. Inorder to achieve this, the optimization procedure, thatuses an iterative algorithm, needs the results of severalsimulations. Performing all these simulations by theFE method is very expensive and time consuming fromthe computational point of view. To challenge this



Table 4 Comparison of the crashworthiness parameters for tubes with one stiffener ring and grooved tubes ofD/t = 20

20-3 20-3.5 20.4

One stiffener Edge One stiffener Edge One stiffenerD/t–L/D Edge groove ring groove ring groove ring

Absorbed energy (J) 2270 2364 2991 3141 3435 3448δmax (cm) 8.39 8.3 11.03 10.9 12.24 12.21Fmax (KN) 54.31 46.15 59.86 46.24 46.07 46.06Fmean (KN) 27.06 28.21 27.11 28.8 28.12 28.21

Table 5 Comparison of the crashworthiness parameters for tubes with one stiffener ring and grooved tubes ofD/t = 40

40-2 40-2.3 40-2.5

One stiffener Edge One stiffener Edge One stiffenerD/t–L/D Edge groove ring groove ring groove ring

Absorbed energy (J) 4501 4704 5674 5914 6125 6125δmax (cm) 12.85 11.87 14.18 14.38 15.80 15.84Fmax (KN) 83.28 85.38 77.60 87.53 81.11 93.54Fmean(KN) 35.02 39.65 40.01 41.12 38.76 38.66

Fig. 14 Comparison of the absorbed energy for a tubewith one stiffener ring and a grooved tube

problem, a set of neural network systems is developedand trained by a limited number of FE simulations.

The response of the structure to impact load isoften non-smooth and highly non-linear with respectto the variables of the problem like the dimen-sions, boundary conditions, and impact velocity.Indeed, developing a single artificial neural networkto reproduce all the crashworthiness parameters ofthe structure simultaneously with sufficient accuracyis impossible, so in the present study different systemsof neural networks are developed in order to reproducethe crashworthiness parameters of the tube, sepa-rately. Furthermore, because the high non-linearityof the problem, the optimization algorithm is highlysensitive to the accuracy of the approximated results

obtained by the developed neural networks, so, inorder to achieve the desired accuracy, for some ofthe crashworthiness parameters two parallel networksare developed and the final value of the parameteris obtained by averaging the output values of eachcombination of networks.

In this work, only multi-layer perceptron (MLP) neu-ral networks are used [17]. The MLPs are currentlythe most widely used neural networks in engineeringproblems. A schematic of a two-layer perceptron net-work with one neuron in each layer is shown in Fig. 15.An MLP network can have an arbitrary number of lay-ers with different transfer functions in each layer, theoutput of each layer is the input of the next layer, andeach layer may have a different number of neurons. Foreach neuron, the input is weighted with an appropri-ate value that is shown in the figure by W . The sum ofthe weighted input and the bias (b) forms the input tothe transfer function f . Neurons may use any differen-tiable transfer function f to generate their output [19].The output layer has a number of neurons equal to

Fig. 15 Schematic of a two-layer perceptron network



the number of output variables. The MLP neural net-works are called the feed forward networks becauseas it is shown in Fig. 15 the signals always propagatefrom the first to the last line of neurons. Indeed, for anMLP network, the learning is performed by adjustingthe weights of the neurons such that the RMS errorbetween the known outputs of the training set and thenetwork returned outputs are minimized.

9 NEURAL NETWORKS DEFINITION

In the present study, the design variables are set to theL/D and D/t ratios, the aim of designing the networksystems is reproducing the most important crashwor-thiness parameters of the tube as a shock absorberthat are, the specific absorbed energy (the absorbedenergy per unit volume), the maximum axial displace-ment of the tube, the maximum reaction force andthe mean reaction force. Four different neural networksystems are developed in order to be used for theseparameters, furthermore some of these four systemscontain two parallel neural networks and the finaloutput for each parameter is calculated by averagingthe output of the parallel networks. The schematicof developed neural network system is shown inFig. 16.

The details of the neural network design, containingthe number of neurons and the transfer function ineach layer are explained in Table 6. The Levenberg–Marquardt algorithm is used for training all the neuralnetworks [17].

10 TRAINING AND TEST SETS

The final performance of the neural networks is highlysensitive to the settlement of the training sets in thedesign variables domain. A general rule for choosingthe location of the training sets in the design variablesdomain is not still achieved and there are several meth-ods like random allocation of sets [12, 20] or regulararrangement of sets.

Fig. 16 The designed neural network system for repro-ducing the crashworthiness parameters of thetube

In the present study, the training and test sets aredefined regularly in the range of 20 < D/t < 60 and1 < L/D < 4, that will be the optimization domaintoo. Neural networks are developed to reproduce thecrush behaviour of the initial tube and the tube withone stiffener ring. Total of 48 FE simulations are per-formed (24 for the initial tube and 24 for the stiffenedtube with one ring), among these, 40 runs are con-sidered as the training set and the test set containseight FE runs. The values of the most important crash-worthiness parameters of the tube, containing thespecific absorbed energy, the maximum axial displace-ment of the tube, the maximum reaction force andthe mean reaction force are calculated by FE sim-ulations. The normalized specific absorbed energywith respect to the maximum value of this param-eter in the training set domain that is 77 748 KJ/m3

is shown in Fig. 17(a) for a tube with the stiffenerring, and the normalized axial deflection of the stiff-ened tube with respect to the maximum deflection intraining set (that is 16.59 cm) is shown in Fig. 17(b).The values of the maximum reaction force and themean reaction forces for the training set of the stiff-ened tube are shown in Tables 7 and 8, respectively.The values of the crashworthiness parameters in the

Table 6 Details of the neural network system design

First layer Second layer Third layer

Transfer Transfer TransferNeurons function Neurons function Neurons function

Specific energy (e) Net1-a 4 tansig 4 tansig 1 purelinNet1-b 5 tansig 3 tansig 1 purelin

δmax Net2-a 6 tansig 4 tansig 1 purelinFmax Net3-a 6 tansig 3 logsig 1 purelin

Net3-b 6 tansig 4 tansig 1 purelinFmean Net4-a 8 tansig 7 logsig 1 purelin

Net4-b 4 tansig 4 logsig 1 purelin



Fig. 17 The normalized values of (a) the specific energy and (b) the maximum axial deflection forthe training set, the stiffened tube

Table 7 The training set for fmax, tube with the stiffenerring (KN)

L/D D/t = 20 D/t = 30 D/t = 40 D/t = 50 D/t = 60

1 46.74 69.27 85.59 110.24 129.162 46.26 68.58 85.38 122.65 135.383 46.15 68.03 88.67 111.45 127.564 46.06 68.09 91.20 112.66 133.82

Table 8 The training set for fmean, tube with the stiffenerring (KN)

L/D D/t = 20 D/t = 30 D/t = 40 D/t = 50 D/t = 60

1 29.99 33.56 39.56 42.31 48.092 28.88 35.68 38.24 42.72 45.293 28.82 36.00 36.90 42.58 46.204 27.28 34.79 38.28 40.63 43.55

training set of the initial tube are shown in Tables 9to 12.

After training all the networks, the test sets areused to find the error of each network. As a sam-ple, Fig. 18 shows the error between the maximum

Table 9 The training set for e, the initial tube (KJ/m3)

L/D D/t = 20 D/t = 30 D/t = 40 D/t = 50 D/t = 60

1 65 861 56 939 55 679 57 604 68 8442 66 856 72 580 55 832 49 736 34 4223 66 594 77 215 52 074 33 157 22 9484 66 777 70 030 39 055 24 868 17 211

Table 10 The training set for δmax, the initial tube (cm)

L/D D/t = 20 D/t = 30 D/t = 40 D/t = 50 D/t = 60

1 2.87 3.98 5.69 7.61 9.982 5.08 8.74 13.09 13.43 12.883 8.31 13.83 15.4 14.64 13.144 8.97 14.94 15.12 14.67 12.95

Table 11 The training set for fmax, the initial tube (KN)

L/D D/t = 20 D/t = 30 D/t = 40 D/t = 50 D/t = 60

1 48.64 69.93 92.65 110.68 137.182 50.05 67.84 90.14 122.54 139.223 48.49 67.44 88.16 112.68 131.404 45.08 68.73 61.86 111.29 135.52

Table 12 The training set for fmean, the initial tube (KN)

L/D D/t = 20 D/t = 30 D/t = 40 D/t = 50 D/t = 60

1 25.65 33.16 40.23 46.26 49.322 30.04 36.13 39.94 46.54 48.333 30.42 36.43 39.01 42.42 47.744 27.97 36.66 40.84 44.57 47.35

and mean reaction force obtained by the FE methodand the trained neural network system. As it is shownthe maximum error for the reaction forces is about5.5 per cent.

Fig. 18 Errors of the neural network for the reactionforces in test set, tube with the stiffener ring



11 THE RESPONSE SURFACES

Using the trained neural networks, the values ofthe crashworthiness parameters as a function of thedesign variables (L/D and D/t ratios) are calculatedfor the initial tube and the tube with the stiffenerring. Figure 19 shows the normalized values of theseparameters with respect to the maximum value of eachparameter in the training set for the stiffened tube with

one ring. The highly non-linear behaviour of the spe-cific absorbed energy is demonstrated in Fig. 19(a), butthe behaviour of the maximum axial deflection, themaximum reaction force and the mean reaction forceappears more regular and smooth. Figure 19(b) showsthat the maximum axial deflection of the tube underimpact load increases for the greater values of L/D andD/t ratios and then remains almost constant for theL/D and D/t ratios greater than 2 and 30, respectively.

Fig. 19 The response surfaces for the crashworthiness parameters of the tube with the stiffener ring

Fig. 20 The response surfaces for the crashworthiness parameters of the initial tube



It is evident from Figs 19(c) and (d) that the reactionforces are almost independent from the L/D ratio andincrease monotonically by increase of the D/t ratio.The same response surfaces for the crashworthinessparameters of the initial tube are shown in Fig. 20.

12 CRASHWORTHINESS OPTIMIZATION

12.1 Problem formulation

Several problems of crashworthiness optimizationmay be considered even for a simple structure underimpact load. Due to the variety of the parameters thatinfluence the response of the structure subjected todynamic loading, different classes of the optimizationproblems may be introduced. However, generally theproblem can be formulated as

optimize: {F (x)} (1)

subjected to: gi(x) � 0 i = 1, . . . , Nc (2)

within the design space: xil � xi � xiu

i = 1, . . . , Nd (3)

where F (x) is the objective or fitness function, gi(x) arethe constraint functions, and xi are the design vari-ables. The parameters xil and xiu are the lower andupper bounds of the design variable domain. In thepresent study the design variables are set to the dimen-sions of the tube or L/D and D/t ratios, the designvariable domain is 20 < D/t < 100 and 1 < L/D < 4.Both the SO problem and the MO optimizations areperformed by introducing different crashworthinessparameters as the objective function.

12.2 Genetic algorithm

The GA is an optimization method based on the pro-cess of evolution in biological population. In the GA,in the first step, a random population in the designvariable domain is generated and in the next steps,successively new populations are produced using theprevious individuals in such a manner that each newpopulation is modified and evolves towards an opti-mal solution. For the crashworthiness problems thatthe objective function is highly non-linear with respectto the design variables, unlike the other standardoptimization methods, the GA can be applied withsufficient accuracy.

In order to optimize the most important crashwor-thiness parameters of the structure that are the specificabsorbed energy, the maximum axial deflection andthe crush force efficiency, two different objective func-tions are generated by the weighted sum method

as

f1 =[

K1 ·(

Fmean

Fmax

)+ K2 ·

(EV

)](4)

f2 =[

n1 · δmax + n2 ·(

EV

)](5)

where k1, k2, n1, and n2 are the weighting parameters, Eis the absorbed energy, V is the volume of the tube, δmax

is the maximum axial deflection, and fmean and fmax arethe mean and maximum reaction forces, respectively.The parameter fmean/fmax is called the crush force effi-ciency. The high crush force efficiency allows the min-imization of the difference between the mean forceand maximum force and leads to limiting the peak ofthe acceleration. The final aim is maximization of thepresented objective functions with different values ofthe weighting parameters. The appropriate values ofthe weighting parameters are very problem dependentand depend on the requirements of the design. In eachof the presented objective functions, the SO problemcan readily be obtained by setting one of the weight-ing parameters to zero and the other parameter to one.The optimization procedure for both of the objectivefunctions for the initial tube and the stiffened tubeare carried out with different values of the weightingparameters and the results are presented in Tables 13and 14. It is evident that for the initial tube, in both ofthe objective functions the specific absorbed energydominates the other crashworthiness parameters andthe optimum point for different values of the weightingparameters is near the maximum point of the spe-cific absorbed energy. For the tube with the stiffenerring, by increasing the weighting parameter of the spe-cific absorbed energy and decreasing the weight of thecrush force efficiency in the first objective function( f1) the optimum point happens for the tubes of rel-atively greater D/t and L/D ratios. The optimization

Table 13 The optimization results for the objective func-tion f1, the initial tube and the tube with thestiffener ring

Tube with the stiffener ring Initial tube

Optimum Optimum Optimum Optimum

k1 k2 D/t L/D D/t L/D

1 0 20.02 3.48 40.49 3.980.9 0.1 20.12 3.55 40.18 3.840.8 0.2 20.3 3.63 35.90 3.620.7 0.3 26.13 3.67 35.76 3.590.6 0.4 26.66 3.66 35.81 3.560.5 0.5 26.83 3.64 35.46 3.550.4 0.6 27.19 3.64 35.67 3.550.3 0.7 28.35 3.55 35.49 3.480.2 0.8 27.42 3.62 35.55 3.550.1 0.9 27.75 3.63 35.55 3.530 1 27.65 3.63 35.46 3.56



Table 14 The optimization results for the objective func-tion f2, the initial tube and the tube with thestiffener ring

Tube with the stiffener ring Initial tube

Optimum Optimum Optimum Optimum

n1 n2 D/t L/D D/t L/D

1 0 37.29 3.31 39.93 3.290.9 0.1 35.43 3.46 35.80 3.560.8 0.2 34.19 3.49 35.69 3.540.7 0.3 33.40 3.51 35.68 3.550.6 0.4 32.24 3.54 35.67 3.550.5 0.5 31.52 3.55 35.62 3.540.4 0.6 30.53 3.54 35.67 3.540.3 0.7 29.32 3.59 35.46 3.580.2 0.8 28.69 3.61 35.53 3.530.1 0.9 27.89 3.63 35.47 3.540 1 27.80 3.63 35.46 3.56

results for the second objective function ( f2) show thatby increasing the corresponding weighting parame-ter of the specific absorbed energy and decreasing theweight of the maximum axial deflection, the optimumD/t ratio decreases, whereas the L/D ratio increases.The presented results in Tables 13 and 14 can be usedin designing the mechanical shock absorbers in theform of thin-walled tubes. The weighting parametersshould be chosen proportional to the requirements ofthe design.

13 CONCLUSIONS

The current paper introduces the initial geomet-ric imperfection proportional to the plastic bucklingmodes as a new parameter that can control the col-lapsing shape of the tube under impact loads. Numer-ical simulations are performed to find the influence ofthe presented parameter on the final collapsing shapeof tubes with different dimensions. Two applied designmethods use the presented parameter and numericalsimulations are carried out to find the broadening ofthe region in the L/D–D/t diagram in which the con-certina collapsing mode is guaranteed. Experimentaltests are carried out to verify the accuracy of thenumerical simulation.

Neural network systems are developed to reproducethe crashworthiness parameters of the structure andresponse surfaces of these parameters are portrayedusing the trained neural networks. There are severalparameters in designing neural network systems thatcan affect the accuracy of the results after trainingthe network. Some of these parameters such as theexact number of layers and the number of neurons ineach layer are obtained from an unavoidable error andtrial procedure. In this study, appropriate designs of

neural networks for reproducing the different crash-worthiness parameters are presented in detail thatcan be used in a design office. In addition, the pro-posed response surfaces can be used in designingprocedure directly.

In order to find the optimum L/D and D/t ratios,two different MO optimization problems are definedand designing tables are presented to find the opti-mum dimensions of the tube for different weight-ing parameters in the objective functions that canbe chosen depends on the requirements of thedesign.

REFERENCES

1 Guillow, S. R., Lu, G., and Grzebieta, R. H. Quasi-staticaxial compression of thin-walled circular aluminumtubes. Int. J. Mech. Sci., 2001, 43, 2103–2123.

2 Karagiozova, D. and Alves, M. Transition from pro-gressive buckling to global bending of circular shellsunder axial impact – part I: experimental and numer-ical observations. Int. J. Solids Struct., 2004, 41,1565–1580.

3 Al Galib, D. and Limam, A. Experimental and numer-ical investigation of static and dynamic axial crush-ing of circular tubes. Thin-Walled Struct., 2004, 42,1103–1137.

4 Karagiozova, D. and Jones, N. Dynamic buckling ofelastic–plastic square tubes under axial impact-2: struc-tural response. Int. J. Impact Eng., 2004, 30, 167–192.

5 Hsu, S. S. and Jones, N. Quasi-static and dynamic axialcrushing of thin-walled circular stainless steel, mild steeland aluminum alloy tubes. Int. J. Crashworthiness, 2004,9(2), 195–217.

6 Vafa, J. P. M. Theoretical and experimental analysis ofmetal tubes under axial loading. MSc Thesis, AmirkabirUniversity of Technology (Tehran Polytechnic), 2006.

7 Murase, K. and Wada, H. Numerical study on the tran-sition of plastic buckling modes for circular tubes sub-jected to an axial impact load. Int. J. Impact Eng., 2004,30(8/9), 1131–1146.

8 Karagiozova, D., Alves, M., and Jones, N. Inertia effectsin axi-symmetrically deformed cylindrical shells underaxial impact. Int. J. Impact Eng., 2000, 24, 1083–1115.

9 Karagiozova, D. and Jones, N. Influence of stress waveson the dynamic progressive and dynamic plastic buck-ling of cylindrical shells. Int. J. Solids Struct., 2001, 38,6723–6749.

10 Shakeri, M., Alibeigloo, A., and Ghajari, M. Numer-ical analysis of axi-symmetric collapse of cylindricaltubes under axial loading. In Proceedings of the SeventhInternational Conference of Computational StructuresTechnology (CST), (Ed. B. H. V. Topping) Civil-CompPress, Lisbon, Portugal, 2004, paper 250.

11 Kurtaran, H., Eskandarian, A., Marzoughi, D., andBedewi, N. E. Crashworthiness design optimizationusing successive response surface approximations.Comput. Mech., 2002, 29, 409–421.

12 Lanzi, L., Bisagni, C., and Ricci, S. Neural net-work systems to reproduce crush behavior of



structural components. Comput. Struct., 2004, 82,93–108.

13 Hibbit, Karlsson, Sorensen, Inc. Getting started withABAQUS/Explicit version 6.3, 2002 (HKS, USA).

14 Mamalis, A. G., Manolakos, D. E., Ioannidis, M. B.,Kostazos, P. K., and Kastanias, S. N. Numerical mod-eling of the axial plastic collapse of externally groovedsteel thin walled tubes. Int. J. Crashworthiness, 2003, 8(6),583–590.

15 Hosseinipour, S. J. Mathematical model for thin-walledgrooved tubes under axial compression. Mater. Des.,2003, 24, 463–469.

16 Kormi, K., Wijayathunga, V. N., Webb, D. C., andAl-Hassani, S. T. S. FE investigation of a spirally slot-ted tube under axially compressive static and dynamicimpact loading. Int. J. Crashworthiness, 2003, 8(5), 421–431.

17 Hagan, M. T., Demuth, H. B., and Beale, M. Neural net-works design, 1996 (PWS Publishing Company, Boston,MA).

18 McCulloch, W. S. and Pitts, W. H. A logical calculus ofideas immanent in nervous activity. Bulletin of Math-ematical Biophysics, selected papers on optical neuralnetworks, 1943, vol. 96(5), pp. 115–133.

19 Neural network toolbox, user’s guide. MATLAB 7, 2004(Math Works, Inc.).

20 Bisagni, C., Lanzi, L., and Ricci, S. Optimization ofhelicopter subfloor components under crashworthinessrequirements using neural networks. J. Aircr., 2002, 22(2),269–304.

APPENDIX

Notation

bi neuron’s biasD tube diameterE , e absorbed energy and absorbed energy

per unit volumeE0 maximum value of the absorbed

energy in the training setfi transfer function of the ith layerf0 maximum value of Fmax in the training

setf1 maximum value of Fmean in the training

setFmax, Fmean maximum reaction force and mean

reaction forcek1, k2, n1, n2 weighting parametersL tube lengtht wall thicknessW , d circumferential groove’s wide and

depthWi neuron’s weightxi design variables

δmax maximum axial deflectionδ0 maximum value of the axial deflection

in the training set


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