Optimization of composite structural components for energy

absorption

Marco Fontanamarco.fontana@tecnico.ulisboa.pt

Instituto Superior Tecnico, Universidade de Lisboa, Portugal

November 2019

Abstract

The aerospace and automotive industries have been pushing the boundaries of material innovationsas there is an ambition to develop ever-lighter vehicles, that are both safer and more fuel-efficient, to copewith ever-stricter emission regulations, in which composite materials represent one of the cornerstonesto solve the problem. Concerning safety, these materials represent an optimal alternative to metalsdue to their greater energy absorption capabilities at the expense of more complex failure behaviour.The present work aims to improve upon the aluminium impact attenuator (IA) currently used by theUniversity of Lisbon Formula Student team through a composite solution. Consequently, the influence ofgeometrical variations, particularly the use of curved walls, and the number of objectives considered forthe optimization are studied. To perform the optimizations, Abaqus is directly coupled with the DirectMultisearch (DMS) algorithm, the overall performance of the solutions is evaluated and the influenceof the introduction of curved walls on the energy absorption capabilities discussed. Additionally, tosimulate a more realistic situation, off-axis impacts are studied and the effect of curved walls in thatsituation analysed. Finally, an overview of the best configurations achieved is provided and one finalconfiguration selected, which is then extensively studied and a conclusion concerning the use of curvedwalls for energy absorption purposes presented.Keywords: Composites, Crashworthiness, Formula Student, Optimization

1. Introduction

In the recent years there has been a growing inter-est in the use of composite materials in the mostdiverse industries, mainly due to their ever-growingavailability and to the development of the knowl-edge concerning these, which have witnessed sig-nificant advancements that have allowed them todecrease the material and manufacturing costs, al-lowing for lighter and more complex structures tobe created. Energy absorption components are fre-quently used in the aerospace and automotive in-dustries in the form of impact attenuators (IA), inwhich it is being aimed to replace the aluminiumthat is currently being used with composite mate-rials, as it can lead to further weight savings whileincreasing the safety of occupants as these presenta higher specific energy absorption (SEA) [1]. Inthe realm of Formula Student, teams composed bystudents are challenged to develop a Formula-stylecar accordingly with a set of regulation, represent-ing an opportunity for innovative designs. As theteam belonging to the University of Lisbon is stillusing an aluminium honeycomb solution, this rep-resents the ideal opportunity to develop a new com-

posite solution. The main objective of the presentwork is to improve upon the work performed byCastro [2], developing a composite impact attenu-ator lighter than what currently used. Moreover,the influence of introducing curved surfaces will beextensively studied as far as the SEA capability ofthe IA is concerned, alongside other design param-eters, to achieve a better performing configuration.The work hereby presented constitutes a further de-velopment of the work initiated by Santos [3] andcontinued by Castro [2], in which a different ap-proach is enforced but the numerical models andthe material properties have remained unchanged.

1.1. Crashworthiness of composites

The use of composite materials in the aerospace andautomotive industries aims at reducing the overallweight of vehicles which results in the reductionof the fuel consumption and, consequently, meetthe increasingly stricter environmental goals whichlimit the emissions. As such, to make these ma-terials more widespread, these have to be studiedso that their crashworthiness can be assessed andthe safety not compromised as they are becomingthe norm in setups that were once the domain of

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metals, such as passive safety devices [4], which in-cludes impact attenuators. When conceiving vehi-cles aimed at passenger transportation, crashwor-thiness is a very important aspect as it is intrin-sically related to occupant safety. According toPoon [5], the goal of a crashworthy design of a ve-hicle is to prevent fatalities and minimize the ex-tent of injuries in survivable crash impacts. Eventhough composite materials present excellent prop-erties, the knowledge that concerns them is not verydeveloped, in particular, the fracture behaviour. Sothat these can be used more widely, extensive stud-ies concerning the fracture behaviour have been car-ried out and it has been concluded that these wouldoften fail in the form of fibre compressive kinking,fibre-matrix debonding and delamination [6, 7, 8].To study the influence of various design parame-ters, studies have been carried out concerning theuse of alternative geometries. This was the caseof the work performed by Feraboli et al. [9] who,when studying the behaviour of carbon fibre/epoxytubes realized that rounded specimens would allowfor a greater SEA, which was the same conclusionthat was drawn by Lescheticky et al. [10], whoalso noticed that curved sections should be incorpo-rated to increase the energy absorption capabilitiesof structures. Furthermore, to be able to performaccurate numerical simulations, extensive amountsof experimental testing for calibration are requireddue to the complex mechanical behaviour of com-posites, limiting the use of existing analytical andnumerical models to effectively simulate these. Bo-ria et al. [11] utilized a mathematical approach tostudy crashworthiness, studying the failure modesthrough an energetic point of view to obtain a modelthat is capable of estimating the energy absorptioncapability of a composite shell that was subjected toan axial impact. Regarding the delamination phe-nomenon, studies by Obradovic et al. [12] provedthat it can be neglected for crashworthiness applica-tions, as modelling the energy absorbers with multi-layered shell elements is a more efficient solution.To better evaluate the performance of various fi-nite element softwares, Melo [13] performed simu-lations of quasi-static crushing of coupons and thedynamic crushing of carbon fibre reinforced poly-mer (CFRP) tubes. From these simulations, it waspossible to conclude that the use of Abaqus [14]with the CZone [15] add-on constituted the mostreasonable approach as it presented a good compro-mise between accuracy and computational power.Moreover, the most accurate results were achievedthrough the use of Abaqus/Explicit [14] with a finemesh at the cost of lengthy simulations.

1.2. Energy absorption components

As far as energy absorption capabilities are con-cerned, Heimbs et al. [16] states that compositematerials are superior to metals as the crush oc-curs at a nearly constant crush load level. Thus,these materials have been increasingly used as en-ergy absorbers, utilising ever-more-complex geome-tries. Concerning the aerospace industry, a com-posite crash absorber has been developed by He-imbs et al. [16] to be used in z-struts of commercialaircraft with the use of Abaqus/Explicit [14], LS-DYNA and PAM-CRASH, which was then experi-mentally corroborated being the results within themargin of each other. Regarding the automotive in-dustry, Lesheticky et al. [10] performed simulationsutilizing Abaqus [14] with CZone [15], which led tothe conclusion that composite materials were capa-ble of meeting structural requirements at a lowermass than metals by analysing the performance ofthe front end of a car built using composite materi-als. Finally, as far as the Formula Student compe-tition is concerned, efforts by Obradovic et al. [12]resulted in the development of truncated pyramidalshape and considered the use of a trigger mecha-nism through the progressive reduction of the walls’thickness. To obtain the necessary crush stressparameters required by the CZone [15] add-on toprovide accurate results led Santos [3] to performquasi-static compression crush tests in carbon fibrecoupons. It was considered that the CZone [15] ap-proach constituted a reliable technique due to theacceptable results that were attained for compositetubes, predicting their behaviour with reasonableaccuracy. Initial optimization attempts concernedthe use of a structural nose, which proved unsuc-cessful and led to the optimization of the IA. Threesolutions were then manufactured and subjected toexperimental testing, in which these proved to beunable to safely stop the impact within the regu-lations established, thus constituting invalid solu-tions. To improve upon the results, Castro [2] em-ployed a numerical approach. As observed in in-vestigations by Obradovic et al. [12], the use oftruncated pyramidal shapes and a trigger mecha-nism would allow for better results to be achieved.As such, Castro [2] conducted geometrical studieson the influence of taper and the use of roundededges, in which it was concluded that greater ta-per angles would lead to lower accelerations at thecost of a greater final displacement, while the useof larger radii on the edges would increase the SEAand the post-impact length.

1.3. Multi-objective optimization

In order to design new components and improve onthem, optimization is a very useful tool, especiallywith the computational power that is today avail-

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able that allow for more complex systems and morecomplex optimization functions to be employed. Aconstrained non-linear multi-objective optimizationcan be formulated mathematically, according to Mi-ettinen [17], as the following:

min F (x) ≡ (f1(x), f2(x), ..., fm(x))T

s.t. x ∈ Ω ⊆ IRn(1)

In which are considered m objective functions fj :Ω ⊆ Rn → R ∪ +∞ , j = 1, ...,m to minimize. Itis important to notice that maximizing fj is math-ematically equivalent to minimizing −fj . The fea-sible region is represented by ∅ 6= Ω ⊆ Rn.

Furthermore, in the presence of m(≥ 2) objec-tive functions, the minimizer of one function is notcompulsorily the minimizer of another. In such asituation, a point that can be considered the op-timum for all objectives cannot be obtained [18].In this situation, a set of points that are obtainedthrough this is defined as the Pareto optimal or non-dominated set [17]. Additionally, given two pointsx1 and x2 in Ω, x1 is said to dominate x2 in thePareto sense, if and only if x1 is strictly better thanx2 in at least one of the objectives and point x1 isnot worse than x2 in any of the objectives. Finally,a set of points in Ω is non-dominated when no pointin the set is dominated by another one in the set.

DMS was developed by Custodio et al. [19] and isderivative-free solver for multi-objective optimiza-tion problems that does not aggregate any compo-nents of the objective function. It generalizes alldirect-search methods of the directional type fromsingle to multi-objective optimization. A list of fea-sible non-dominated points (from which the new it-erates or poll centres are chosen) is maintained byDMS. The search step is considered to be optionaland, whenever it is used, it aims at improving nu-merical performance. However, DMS tries to cap-ture the whole Pareto front from the polling proce-dure itself. At each iteration, the new feasible evalu-ated points are added to the list and the dominatedones are removed. Successful iterations correspondto changes in the iterate list, meaning that a newfeasible non-dominated point has been found. Oth-erwise, the iteration is classified as unsuccessful. Inthis method, the constraints are handled using anextreme barrier function, which can be representedas the following:

FΩ(x) =

F (x) if x ∈ Ω,

(+∞, ...,+∞)T otherwise.(2)

When a point is deemed as infeasible, the compo-nents of the objective function F are not evaluated,with the values of FΩ being set to +∞. This is what

allows to deal with black-box type of constraints,where only a yes or no answer is provided, as is thecase of the present work.

2. Design of a FST car impact attenuator2.1. Modelling aspectsThe numerical simulations were performed usingAbaqus [14] with the CZone [15] add-on, whichhas been directly coupled with the DMS algorithm.The IA was meshed using S4R elements, which aremulti-layered quadrilateral elements with reducedintegration and the impact wall was meshed usingR3D4 elements, which are quadrilateral rigid ele-ments. To validate the model, it was subjected to amesh convergence study, which allowed for the se-lection of the optimal element size. Concerning theboundary conditions, the IA was subjected to an en-castre at its built-in end and the impact wall had itsmovement constrained along the longitudinal axis.To mirror the experimental setup, the impact wall’smass was set to 300 kg and subjected to an initialvelocity of 7 m/s. It was then necessary to definecontact, which, at the crush front, was handled byCZone [15]. However, to obtain accurate results,self-contact needed to be modelled and handled byAbaqus/Explicit [14]. As far as material proper-ties are concerned, these were experimentally deter-mined [3] and the Tsai-Wu failure criterion used.

In this work, the geometries being studied canbe tapered and non-tapered, can have a flexiblenumber of curvatures in each of the walls, variableoverall dimensions, variable layup and zone distri-bution. As such, it was necessary to use a mod-elling technique that allows for such variety to beavailable. Abaqus [14] native scripting environmentwas considered to be the most powerful techniquethat would allow generating geometries at an ac-ceptable complexity as Python programming lan-guage is used. However, it is necessary to noticethat, given the required flexibility, multiple scripts(one per model) have to be used.

2.2. Summary of the key aspectsConsidering the solutions present in the literature,a summary of the main aspects that are tackled bythis work has to be made to define the key differen-tiators of this approach. These can be summarizedas the following:

• Delamination of the carbon fibre plies includedby the crush stress parameter;

• Use of progressive thickening of the walls alongthe IA;

• Tapered and non-tapered geometries are eval-uated;

• Use of curved-walls and study of its influence;

• Multiple configurations for the cross-sectionwill be tested;

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• Effect of off-axis impacts will be evaluated;

• Influence of the number of objective functionswill be studied.

3. Geometrical studiesThere was evidence that curved walls could have apositive effect on the energy absorption capabilitiesof composite materials [10, 16]. As such, prelimi-nary studies concerning the use of various numbersof curvatures on the walls of the IA were necessary.The overall dimensions are presented in table 1.

Table 1: Dimensions of the impact attenuatorCross-section dimensions [mm]

Length [mm]smallest largest

Non-tapered 200 x 100 - 220

Tapered 200 x 100 220 x 110 220

Firstly, the influence of the number of curvatureswas studied for a non-tapered configuration whichconsidered four models, which can be observed infigure 1. It was observed that two curvatures onthe side-walls constituted the minimum to achievea progressive impact as a lower number would of-ten result in instability phenomena. Furthermore,on the top and bottom walls, it was observed thattwo curvatures would lead to a better performingIA. The overall performance of non-tapered IAs ispresented in table 2.

Table 2: Performance of the non-tapered modelsModel 1 2 3 4

Mass [kg] 0.334 0.335 0.337 0.339Max. acc. [m/s2] 217.83 221.93 216.93 218.49Mean acc. [m/s2] 139.27 187.81 189.12 189.72

PIL [m] 0.002 0.083 0.083 0.089

(a) model 1 (b) model 2

(c) model 3 (d) model 4

Figure 1: Considered model configurations for pre-liminary testing

Secondly, as the use of curved walls on the IAproved successful for non-tapered geometries, itsuse for tapered geometries was studied as thesecould potentially improve upon the stability of theimpact, for which the geometries considered con-sisted on tapered variations of the ones presented in

figure 1. The results achieved mirrored the conclu-sions for non-tapered geometries, a minimum of twocurvatures on each wall addressed wall oscillationand positively impacted the energy absorption ca-pabilities. The overall performance of tapered IAscan be observed in table 3.

Table 3: Performance of the tapered modelsModel 1 2 3 4

Mass [kg] 0.352 0.353 0.359 0.357Max. acc. [m/s2] 260.46 275.47 274.58 262.00Mean acc. [m/s2] 159.49 210.06 215.54 214.34

PIL [m] 0.035 0.096 0.103 0.104

It can be observed that the masses of taperedconfigurations are higher than non-tapered ones,which is due to their overall larger dimensions. Fur-thermore, it is possible to notice that tapered ge-ometries exhibit higher maximum and mean accel-erations than what obtained with the use of non-tapered configurations. This is due to the greaterresistance offered by the tapered geometries thatresults in a greater post-impact length (PIL). Fi-nally, due to its satisfactory behaviour, it was de-cided that Model 2 - tapered would serve as thestarting point for the optimizations.

4. Optimization for Axial ImpactsAiming to achieve a manufacturable IA, several op-timizations were performed with a varying numberof design variables and objective functions, whoseinfluence will be studied throughout the followingsections.

4.1. Optimization of the cross-sectionIt was decided that the cross-section of the IA wouldbe the first to be optimized, in which the only de-sign variables were the amplitudes of the curva-tures. Furthermore, a total of two objective werefirstly used: mass (f1(x)) and maximum accelera-tion (f2(x)). However, with a fixed overall geom-etry that only considered variations of walls am-plitudes, the results were lacklustre, with just foursolutions being found with unremarkable results forthe objectives. As such, a third objective was intro-duced: mean acceleration (f3(x)). The increase inthe number of objective functions was implementedas this would allow for an increase in the number ofpossible combinations and ensure a greater varietyof solutions. The optimization was then initializedwith the results from the first attempt, which wouldallow for proper channelling of the results. The in-crease in the number of objectives proved successfulas the number of solutions rose to a total of 27 (upfrom a mere 4). Yet, it is necessary to note thatthis number of solutions corresponds to a three-dimensional Pareto front and has to be projectedon the desired axes to better evaluate the results.

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The solutions of this optimization can be observedin figure 2.

Figure 2: Pareto front resulting from the cross-section optimization considering 3 objectives

4.2. Optimization of the cross-section, layup andzones

The optimization of the cross-section provided veryfew distinct configurations and an adequate perfor-mance but there was no further room to improve-ment since a fixed model and layup was being used.As such, it was concluded that for further improve-ments additional design variables had to be consid-ered, which can be seen below:

• Amplitude of the curvatures;

• Layup of the zones;

• Length of the impact attenuator;

• Length of the zones.

Moreover, during the geometrical studies, a con-clusion concerning the use of tapered or non-tapered geometries was not reached as both con-figurations presented their advantages. So that abetter decision regarding the configuration can bereached both configurations have been studied. Theobjectives functions (OF) and constraints remainunchanged. To reduce the risk of geometry gen-eration problems, the dimensions of zones B and Cwere defined proportionally to the distance betweenzones A and D. The formulation used for this opti-mization can be seen below:

minx∈Ω

F (x) ≡ (f1(x), f2(x), f3(x))

s.t.

xi ∈ 203, 210, 217, 224, i = 1

xi ∈ 50, 55, 60, ..., 85, 90, i = 2

xi ∈ 20, 25, 30, ..., 85, 90, i = 3

xi ∈ 14, 21, 28, 35, i = 4

xi ∈ 0, 30, 45, 99, i = 5, . . . , 20

xi ∈ 5, 10, 15, i = 21, . . . , 28

max(A(x)) ≤ 35g.

mean(A(x)) ≤ 20g.

max(U(x)) < l + g′.

(3)

Parameters 1 to 4 correspond to the lengths of thezones where the length of zone A coincides with thelength of the impact attenuator. Parameters from 5to 20 correspond to the orientation of the layers ofeach zone, with each having a maximum of four lay-ers and three possible orientations (an orientationof 99 corresponds to a situation in which no furtherplies are created). Parameters 21 to 28 correspondto the amplitudes of the curvatures present on thefaces of the impact attenuator.

To reduce the necessary function evaluations forthe algorithm to converge, the initialization wasmade using the Pareto front of the cross-section op-timization with the proper adjustments. Throughthis procedure, it was possible to obtain good re-sults with an adequate number of simulations forboth tapered and non-tapered configurations.

Figure 3: Results for the non-tapered model opti-mization with 3 OF

For the non-tapered model, it can be observed infigure 3 that the variety of solutions has increasedwhen compared with the cross-section optimization,achieving lower masses and accelerations. However,upon closer inspection, it was observed that thesesolutions presented a very thin margin concerningtheir PIL, which was observed to be the strengthof tapered models. Therefore, a new optimizationconcerning these is performed.

Figure 4: Results for the tapered model optimiza-tion with 3 OF

Analysing the solutions attained for the tapered

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configuration presented in figure 4, it can be con-cluded that the number of non-dominated solutionsis greater and that the masses of tapered IAs canachieve lower values, much due to their greater ro-bustness which is also reflected in the greater accel-erations sustained. The higher number of solutionsobtained can be attributed to the increased likeli-hood to respect the safety margin imposed. Ad-ditionally, one important conclusion arose: higheraccelerations are associated with greater resistanceoffered by the material, resulting in a larger PIL.Thus, taper not only is it important to improve theimpact’s stability but also to increase the overallsafety of the design which, when combined with acurved-walled structure leads to an overall better-performing IA that present a progressive behaviour.

4.3. Optimization of the cross-section, layup with agreater number of zones

Even though the solutions obtained for taperedand non-tapered allowed for a progressive impactto be achieved with up to four zones, an attemptto achieve a smoother transition between the var-ious zones was considered. To ensure the pro-gressiveness of the impact a condition on the ac-celeration was enforced, which analysed the pres-ence of dips below a certain value. The ob-jective functions considered were the same three(m(x),max(A(x)),mean(A(x))) and the same con-straints enforced.

For this greater number of zones, two possibilitieswere considered: five and ten zones. Additionally,to compensate for the added zones, the number oflayers per zone was reduced to just two, reducingthe total number of variables. So that the resultsare channelled, the solutions obtained in the pre-vious section were adequately modified to be usedwith these new models and the optimization initial-ized on these.

However, this increase in design variables provedunsuccessful as the five and ten zone models pre-sented no improvements upon the results previouslyachieved. The great number of variables led tomany configurations using just up to three zonesout of the available (five and ten), with the remain-ing zones having most of the orientations set to 99,meaning that, effectively, they did not have any fur-ther layers. The variety of solutions achieved provedthat this alteration did not have the expected effecton the accelerations sustained by the IA, havinga very similar behaviour despite the much greaterdesign flexibility. It was concluded that this wasdue to the use of constant thickness plies, whichlimited the potential of using a greater number ofzones. Moreover, with so many design variables atstake, the overall shape of the cross-section sufferedclose to no alterations remaining roughly unchangedamong the best solutions. Nonetheless, this study

proved useful to better establish the foundations forthe subsequent steps of this work as some conclu-sions concerning the design variables were drawn.It was then concluded that a total of three zoneswith two layers each constituted a reasonable ap-proach. Furthermore, as the amplitudes around thecross-section did not vary significantly, symmetrywas enforced.

4.4. Optimization of the cross-section, layup andzones of a variable model

In the previous stages of this work, the overallmodel remained unchanged to assess the influenceof a variety of design parameters and the use ofmore objective functions. It was observed that theincrease in the number of objectives led to a greaternumber of possible combinations and, thus, in abroader range of possible solutions. The solutionsachieved up to this stage performed adequatelywhen accelerations and masses were concerned butlacked in the post-impact length (PIL) parameter,which is intrinsically related to the safety of theIA. As such, a fourth objective (PIL(x)) was in-troduced. Additionally, to better analyse whichmodel was the best performing, the optimizationembraced the possibility of having variable models.Therefore, the optimization performed at this stageconcerned variable tapered models with symmet-ric cross-sections, with a total of four objectives,which are the minimization of the mass of the im-pact attenuator (f1(x)), minimization of the max-imum (f2(x)) and mean accelerations (f3(x)) andthe maximization of the post-impact length (f4(x)).For the initialization, the dimensions and layup ofone of the best solutions was used with the propermodifications. The formulation for the optimizationcan be seen below:

minx∈Ω

F (x) ≡ (f1(x), f2(x), f3(x),−f4(x))

s.t.

xi ∈ 203, 210, i = 1

xi ∈ 70, 75, 80, 85, 90, i = 2

xi ∈ 70, 75, 80, 85, 90, i = 3

xi ∈ 0, 30, 45, 99, i = 4, . . . , 9

xi ∈ 2, 3, i = 10

xi ∈ 5, 10, 15, i = 11, 12

xi ∈ 2, 3, 4, i = 13

xi ∈ 5, 10, 15, i = 14, 15

max(A(x)) ≤ 35g.

mean(A(x)) ≤ 20g.

max(U(x)) < l + g′.

(4)

Concerning the parameters presented in formu-lation 4, parameter 1 corresponds to the length of

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zone A, coinciding with the length of the IA, whileparameters 2 and 3 correspond, respectively, to thepercentage of the difference between the length ofzone A and C and B and C. Parameters 4 to 9 cor-respond to the orientation of the plies of zones A toC. Parameter 10 correspond to the number of cur-vatures that are on the side-walls and parameter 13corresponds to the number of curvatures that areon the top and bottom walls. Finally, parameters11 and 12 correspond to the amplitudes of the cur-vatures on the side-walls and parameters 14 and 15correspond to the amplitudes of the curvatures ofthe top and bottom walls.

These new geometries were varied, as stated, withthe use of parameters 10 and 13 of the input vector,determining the overall shape of the cross-section.To better understand the geometries being mod-elled, these are presented in figure 5.

(a) model 22 (b) model 23

(c) model 24 (d) model 33

(e) model 34

Figure 5: Considered model configurations for flex-ible model optimization

As the number of objectives was increased onestep further, the number of possible combinationsgrew, meaning that proper channelling of the opti-mization was necessary to minimize the duration ofthe process and to perform a reasonable amountof function evaluations. Furthermore, as the al-gorithm can choose the best performing configura-tion it was expected that some of them would besubjected to more function evaluations than oth-ers. The solutions achieved are represented in fig-ure 6 and the results for the solutions highlightedpresented in table 4.

Figure 6: Results of the optimization for axial im-pacts considering 4 OF

Table 4: Optimal results of the optimization foraxial impacts considering 4 OF

Solution 1 2 3 4Model 33 24 23 34

Mass [kg] 0.179 0.183 0.187 0.218Max. acc. [m/s2] 227.12 218.99 203.33 179.93Mean acc. [m/s2] 184.08 181.60 177.68 167.67

PIL [m] 0.060 0.060 0.062 0.063

As can be seen from the results presented in table4, there is no significant difference between them.Apart from solution 4, the masses of the solutionspresented are within a margin of each other. Addi-tionally, the PIL suffers no significant alterationsmeaning that, in a situation of an axial impactthere is no substantial difference among the config-urations considered. Aside from Model 22, whoseresults are lacking, any of the other models con-sidered will present similar behaviour. The resultspresented up to this stage have proven that it ispossible to further optimize the IA in ideal condi-tions.

5. Optimization for Off-axis ImpactsWhen analysing the experimental setup used by theFormula Student team belonging to the Universityof Lisbon it became evident that the conditions inwhich the simulations were carried out hardly re-flected the real conditions. As such, it was con-sidered to be necessary to perform an optimizationthat included a certain degree of misalignment be-tween the IA and impact wall, aiming to achieve amanufacturable solution.

5.1. Off-axis preliminary testingTo better assess the inclinations that should be im-posed on the impact wall, preliminary testing hadto be carried out. Rotations along the horizontaland vertical axis of the impact wall were considered,ranging from 0.5 to 2 as these were estimated tobe reasonable values when analysing the test setup.This testing was carried out on the most fragile con-

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figuration (model 22) to better analyse the criticalangle.

From the studies carried out concerning the ro-tation along the horizontal axis, it was observedthat rotations of 2 did not significantly impact theresults, concluding that the inclinations along thisaxis were not very relevant as far as off-axis impactsare concerned (at least for smaller angles).

When analysing the results for rotations alongthe vertical axis it became clear that these rotationspresented much greater influence on the results. Forthe same configuration, the behaviour of the struc-ture can vary greatly with even the slightest vari-ations in terms of inclination. This aspect is sig-nificantly less dominant when rotations occur alongthe horizontal axis and much more dominant whenrotations along the vertical axis are enforced, whichcan be associated with the fact that the largest di-mension of the impact attenuator is in this direc-tion, thus bending moments are greater and thelikelihood of catastrophic damage increases.

Even though studies concerning the rotationalong one axis at the same time provided good re-sults, this situation corresponded to an ideal situa-tion as the impact is unlikely to have its initiationon an edge but rather on a vertex of the structure.As such, preliminary testing was conducted on asituation in which the impact wall was rotated by2 along both axes.

(a) Stage 1 (b) Stage 2 (c) Stage 3

Figure 7: Stages of the impact with rotation alongboth axes

For this setup, the acceleration sustained severaldrops that were a result of the failure of the IA.With these inclinations the extent of damage wasgreater than in previous studies, being the effect ofthe rotations along the vertical further accentuatedwhen combined with the rotations along the hor-izontal axis. The acceleration plot correspondingto the impact portrayed in figure 7 is presented infigure 8.

From analysing figures 7 and 8, it can be con-cluded that the rotation of 2 around each axis con-stitutes a more pessimistic (and realistic) approachto the problem. Thus, in the final optimization, aninclination of 2 about each axis will be used.

Figure 8: Rotation of 2along the horizontal andvertical axes - Acceleration plot

5.2. Optimization of the cross-section, layup andzones of a variable model

This optimization constituted a further attempt tooptimize the IA in more realistic conditions by hav-ing the impact wall rotated by 2 along each axis.The overall setup for this optimization remained un-changed from what presented in section 4.4. Theobjective functions were the same as previouslyused and slight variations were performed on theformulation (Model 22 was disregarded). Since thenumber of possible combinations was very signifi-cant, the optimization was run for a much longertime, which, when considering the channelling ofsolutions performed, allowed for a great variety ofsolutions to be achieved. For the bulk of the opti-mizations performed in this work, an element size of7 mm was used. However, to further increase accu-racy, an element size of 5 mm was used to validatethe results obtained. This strategy proved success-ful as the coarser mesh allowed for a significantlygreater number of function evaluations to be per-formed and, through re-running the Pareto points,more accurate results were achieved at a fraction ofthe time.

To better analyse the results, the four-dimensional Pareto front was projected on the massaxis, as this constituted the main objective of thiswork. In figure 9(a) one can observe the Paretofront concerning the two main objectives of thiswork, the mass and the maximum acceleration.However, for this final optimization, in which a saferconfiguration was being aimed for, another param-eter was considered to be equally significant: thepost-impact length. As such, the Pareto front forthis set of objectives can be observed in figure 9(b).

It is interesting to notice that the solutions arescattered around three major areas of the plots.Upon closer inspection as to why such a distribu-tion occurred, it was concluded that these were in-fluenced greatly by the number of layers, the left-most area corresponding to solutions with four lay-ers, the middle one to solutions with five layers and

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(a) Relationship between the mass and maximumacceleration

(b) Relationship between the mass and the PIL

Figure 9: Results of the off-axis optimization

the rightmost to six layers solutions.In table 5 are presented the solutions highlighted

in figure 9, in which three optimum solutions foreach were selected to be subjected to further stud-ies. As expected, the variety of optimum solutionsis greater for a situation in which the PIL is beingoptimized since there is a direct relationship be-tween the PIL and the mass. The safety margin isof the utmost importance given the fact that the IAis a major safety device of the FST car and can beconsidered as the leading criteria for the selectionof the final configuration.

Table 5: Optimum solutions of the off-axis opti-mization

Sol. ModelMass Max. acc. Mean acc. PIL[kg] [m/s2] [m/s2] [m]

1 23 0.190 210.81 159.40 0.0622 24 0.194 202.10 163.58 0.0613 23 0.219 181.01 155.97 0.0617 33 0.195 215.03 149.83 0.0688 24 0.263 273.43 156.01 0.1119 34 0.278 288.40 183.65 0.115

The best overall performance was achieved by So-lution 8 which sustained a higher maximum acceler-ation (albeit within margin of the upper limit), anacceptable value for the mean acceleration (withinmargin of the upper limit), a mass that representedacceptable savings regarding the aluminium IA and

a very good performance concerning the safety mar-gin. Ultimately, Solution 8 can be considered as theoptimum solution. The acceleration plot for thisconfiguration can be observed in figure 10, in whichit can be noted that the impact is fully progressive,being also possible to witness the consequence ofthe inclinations in the slopes of the plot which, inan axial situation, would be vertical lines. Further-more, the overall appearance of this configurationis of the Model 24 type, which is presented in figure5(c).

Figure 10: Acceleration plot of optimum solution 8

Finally, since a final configuration was achieved,it is then necessary to perform a general comparisonbetween this. The parameters whose data was notavailable are marked in table 6 with NA.

Table 6: Relative performance concerning the cur-rent solutions

Sol. Mass Max acc. Mean acc. PILAl. IA -63.5 % +38.9% +10.9% NA

Castro [2] sol. 2 -29.3% +9.6% NA -64.9%Castro [2] sol. 3 -17.9% +19.7% NA -94.6%

Concerning the mass, it can be noted that thesolution achieved is a very good performer in thisregard, being much lighter than the aluminiumIA and better, albeit to a lower extent, than theresults achieved in recent optimization attempts.Accelerations-wise, this configuration is less per-forming than the aluminium IA and the configu-rations proposed in previous studies, which couldbe considered the main caveat of this solution eventhough they are still within a reasonable marginthe limits of the regulations. More importantly, thePIL of Solution 8 is significantly greater than whatachieved by any of the configurations previously ob-tained, making it a better energy absorber.

6. ConclusionsThe work presented concerned the steps of designand optimization of a composite IA to be used in anFST car. To improve the performance, a multitudeof design variables were considered, including the

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testing of variable models, which allowed for a greatnumber of distinct configurations to be evaluated.

The importance of the use of curved-walled struc-ture was evident throughout the present work, as itwas observed that the energy absorption capabili-ties of composite structures were greatly improvedby these as a more stable impact was achieved andan impact attenuator that presented an excellentsafety margin (for its weight) was obtained.

Finally, it is important to reiterate that the re-sults presented in this work concern a less thanideal situation, making the results more significantas they are more likely to represent a real-world sit-uation, thus constituting a good starting point fora manufacturable impact attenuator that is capableof withstanding the rigorous testing required and beapproved.

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