Lightweight Body in White Design Using Topology-, … models was Inertia Relief (IR). The following...

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Lightweight Body in White Design Using Topology-, Shape-and Size Optimisation

Christophe Bastien1, Jesper Christensen2, Mike V Blundell3, Jakovs Kurakins41Coventry University, [email protected], Priory Street, Coventry, CV1 5FB, UK

[email protected]@coventry.ac.uk

[email protected]

Abstract

As focus on the world climate rises, so does the demand for ever more environmentally friendly technolo-gies. The response from the automotive industry includes vehicles whose primary propulsion systemsare not based upon fossil fuels. On this basis a Low Carbon Vehicle Technology Project (LCVTP), partlyfunded by the European Regional Development Fund (ERDF), has been completed. The project includeddesigning a lightweight Body In White (BIW), specifically tailored to suit the drive train and generalpackaging requirements associated with a Hybrid Electric Vehicle (HEV). The future opportunities foroptimising the new lightweight vehicle architecture have been investigated using a technique entitledtopology optimisation, which extracts the idealised load paths for a given set of load cases, followed bya shape- and size optimisation in order to provide local areas of the vehicle with more definition.An appropriate shape- and size optimisation process for frontal crashworthiness scenarios has been devel-oped by comparing and combining different point selection methods and applying various metamodellingtechniques.

Keywords: Hybrid Electric Vehicle (HEV), Electric Vehicle (EV), optimization

1 Introduction

The automotive industry is a very competitive in-dustry. In order to gain competitive advantagesit is imperative that innovative vehicles are de-veloped rapidly as well as economically. Fur-thermore, due to global awareness, concern, aswell as political- and legislative focus on en-vironmental protection and conservation signifi-cantly increases the design and engineering chal-lenges within the automotive industry. In gen-eral, vehicle manufacturers focus upon the devel-opment of lightweight vehicle structures, whichmust comply with stringent safety regulations.With reduction of mass as the main objective,it is imperative that the required functionalityof the vehicle structure is retained or perhapseven improved. Besides NVH and fatigue life,crash performance is one of the most important

attributes to be considered, partially due to thelegislative requirements. In order to meet thesedifficult challenges for lightweight vehicle de-sign and development; the use of emerging com-putational optimisation techniques is increasing.The first step of the “ideal”optimisation process,with respect to mass reduction, is therefore theuse of topology optimisation, providing defini-tions of load paths within the specified vehicledesign envelope, the design volume. This optimi-sation phase removes “surplus” material, whichdoes not efficiently contribute to the structuresability to react the applied loading. The post-processing of the topology optimisation resultsis a very important stage of the overall process.This is because the topology optimisation modelis not likely to have incorporated all potentialvariations of crash-scenarios. Hence sensitivitystudies of the topology are required in order to

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further ensure the structural integrity of the topol-ogy optimisation results. The definition, as wellas execution and post-processing of the topol-ogy optimisation results utilising NCAP equiv-alent load cases will be the focus of the first partof this paper. The second step of the proposed“ideal” optimisation process consists of generat-ing a metamodel, which is subsequently used toobtain a more refined / detailed vehicle structure,by determining the definitions of local areas, i.e.shape- and size optimisation of cross-sections.The metamodel based optimisation does howeverfacilitate a loss in “model accuracy”, as will beapparent from section 3.1. Furthermore, this stepis extremely CPU time and resource intensive,relative to the remaining steps of the overall op-timisation process. This is primarily due to thelarge number of test-models required to generatethe single metamodel, in addition to the complex-ity of these test-models. The necessity to cap-ture the highly non-linear behaviour of the crash-structure during certain load cases also adds sig-nificant complexity to the definition and use ofthe metamodel. In order to allow the sizing op-timisation to convert towards a robust and safedesign, it is important that the hyper responsesurfaces generated for the metamodel are simul-taneously smooth as well as accurate. The sec-ond part of this report will document step twopresented above, i.e. metamodelling. This willbe conducted by means of an investigating intoa proposed metamodel optimisation strategy, theobjective of which is to minimise the mass of thefront crash structure of a Hybrid Electrical Ve-hicle (HEV), when subjected to a 35mph frontimpact scenario. Several researches have investi-gated the potential for employing shape- and sizeoptimisation for crash structures, such as Mark-lund [1] Jansson et al. [2], Etman [3], Yang etal. [4] and Schramm and Thomas [5]. However,these investigations utilised individual responsesurface methodologies only. In contrast, Fors-berg and Nilsson [6] examined and comparedvarious metamodelling techniques implementedwithin LS-OPT [7], and their potential suitabilityfor crash structure optimisation. This paper willinvestigate these various sampling methods, anddraw conclusions on the most appropriate meta-model for minimising the mass of an HEV frontcrash structure subject to NCAP based loadingscenarios.

2 Topology Optimisation

The initial part of the paper presents how thestructural load paths were extracted from an ini-tial design volume, i.e. CAD model, by employ-ing FE based linear static topology optimisation.The design volume utilised is illustrated in Fig.1. The approximate maximum exterior dimen-sions of the design volume were: (x, y, z) 3865mm x 1850 mm x 1530 mm.

Figure 1: Design Volume

2.1 DiscretisationThe above illustrated design volume was meshedusing first order solid tetra elements, with an av-erage size of 25.0 mm. This led to the generationof approximately 103000 nodes and 527000 ele-ments.

2.2 Load casesThe load cases utilised in the optimisation pro-cess were intended to be representative of theworst case legislative and NCAP (35mph) rigidwall dynamic impact loading scenarios. There-fore, a total of six loading scenarios were de-fined, these are listed below, and have been con-verted into equivalent static loads based on crashpulse patterns of vehicles with equivalent mass(less than 1200 kg) [8]:

1. Front impact, Offset Deformable Barrier(ODB).

2. Pole impact.

3. Side barrier impact.

4. Roof crush: A-pillar.

5. Low speed centred rear impact.

6. High speed rear impact.

The approximate locations of the above definedloading scenarios are illustrated in Fig. 2.



Figure 2: Loading scenarios

2.3 MaterialThe material model used for the topology optimi-sation is linear elastic, utilising the material char-acteristics of a standard grade steel:

• Young’s Modulus, E: 210 GPa.

• Poisson’s ratio: ν: 0.3.

• Volumetric mass density; ρ: 7850 kg / m3

2.4 Material LawThe current state of the art topology optimisationmethods are based upon an implicit linear solv-ing algorithm which is very well suited for struc-tural stiffness design. These methods can how-ever not predict any non-linearity, let alone com-plex buckling events, such as the collapse of afront longitudinal member [9]. Within these lim-itations, it has previously been documented thatthe solution provided by this linear solver pro-vided a “reasonable” topology for the safety cell,roof and floor [10].

The employed linear static topology optimisa-tion algorithms were based on the Solid IsotropicMaterial with Penalisation (SIMP) interpolationscheme [11], stipulating that the relationship be-tween the stiffness matrix [k] and the volumetricmass density (ρ) was defined by the “power lawfor representation of elasticity properties”, equa-tion 1, [12]:

[k] (ρ) = ρp [k] (1)

In equation 1, [k] is the penalised stiffness ma-trix, and p is the penalisation factor, which isused to determine the “type” of relationship be-tween [k] and ρ. As long as p is equal to 1.0the two are directly proportional, as illustrated inFig. 3.

Figure 3: Relationship between [k] and ρ

This relationship can be adjusted, by varying pwith the effects as indicated in Fig. 3. The rea-son for adjusting this relationship is typically topenalise intermediate density values, in order toavoid “vague” definitions of topology, this is alsosometimes referred to as “checkerboard effect”.However, initial analyses revealed that this wasnot a widespread problem for the models in ques-tion. Therefore in the remainder of this paper thevalue of p will be 1.0, i.e. a linear relationship be-tween the stiffness matrix [k] and the mass den-sity ρ will exist.

2.5 Boundary ConditionsThe boundary condition used for the topologyoptimisation models was Inertia Relief (IR). Thefollowing information relating to IR is primarilybased upon Barnett & Widrick [13]. Inertia re-lief utilises a significantly different approach toobtain load equilibrium of an FE model. In thisapproach no Degree Of Freedom (DOF) of anynodes are constrained, due to Boundary Condi-tions (BC), as is the case with the “traditional”Single Point Constraints (SPC). Instead, iner-tia relief works by balancing the external load-ing with inertial loads and accelerations withinthe structure itself. This is specifically done by“adding” an extra displacement-dependent load



to the load vector: {F} in equation 2.

{F} = [k] · {u} (2)

In equation 2, [k] represents the stiffness matrix,and {u} represents the unknown nodal displace-ments. The additional terms of the stiffness ma-trix, due to IR can be appreciated by observingequation 3.

{F} = [kIR] · {u} =[[k] 00 [kADD]

]· {u} (3)

In equation 3 [kIR] is the stiffness matrix of theIR model, [k] is the “original” stiffness matrix,i.e. the one listed in equation 2, and [kADD] rep-resents the additional terms in the stiffness ma-trix, caused by the usage of IR. Thus by com-paring equation 2 to equation 3, the fundamen-tal difference between an SPC model and an IRmodel can be appreciated. With the descriptionof the general model setup complete, the fol-lowing chapter will present the outcomes of thetopology optimisation study.

2.6 Topology Optimisation ResultsFollowing the choice of material laws and (IR)boundary condition strategy, a resulting vehicleBIW topology optimisation was obtained, this isillustrated in Fig. 4.

Figure 4: Topology optimisation results

As previously explained, the post-processing ofthe topology optimisation steps is imperative, es-pecially with respect to variations of load cases,therefore a series of sensitivity studies were con-ducted in this connection.The topology optimisation study also includedinvestigation of the optimal centre of mass (CM)locations with respect to key HEV componentssuch as battery packs, feasibility and practical-ity of the CM locations, as well as vehicle dy-namics. Further information on the topology op-timisation study can be found in [10], [14] and[15]. The proposed vehicle structure in Fig. 4, is

“unconventional” when compared to most mod-ern day vehicles. This was particularly evidentfor the roof area, where the “traditional” roof-bows were replaced by a more triangular latticestructure. This was most likely caused by the us-age of a linear static solver. The safety cell doeshowever meet deformation targets [10] and rec-ommends bracings in the doors area, as indicatedin Fig. 4.

2.7 Front Structure DevelopmentThe development of the front structure could notbe developed using linear static topology opti-misation, due to the large and non-linear defor-mations anticipated in the crumple zone duringcrash scenarios. It was however concluded thatthe remaining topology optimisation results (in-cluding the safety cell) provide a good “startingpoint”, i.e. “BIW draft”, primarily because largedeformations, including non-linear behaviour isnot anticipated at these locations. For the de-velopment of the front structure, current state ofthe art crash structure designs were investigated[8]. The outcome of this investigation was usedto specify performance requirements, relating toe.g. pulse and intrusion. These were subse-quently used to define optimisation constraintsfor the development of the front crash struc-ture. The lightweight vehicle front crash struc-ture which served as the starting point for the de-velopment of the metamodel is illustrated in Fig.5.

Figure 5: Illustration of initial crash structure

The crash structure illustrated in Figure 5 wasoriginally engineered by Ravenhall [16]. It con-sists of six main parts:

1. Shotgun 1

2. Shotgun 2

3. Shotgun 3

4. Longitudinal top section



5. Longitudinal lower section

6. Longitudinal inner reinforcement

In essence, the structure utilises the bendingmode of the longitudinal beams to absorb the im-pact energy, thus creating the desired pulse pro-file [16]. The initial mass of the front crash struc-ture illustrated in Fig. 5 is 31.3 kg. During a 35mph front crash NCAP scenario the maximumintrusion was determined to be 542.5 mm, witha maximum crash pulse magnitude of 42.9·g oc-curring at approximately 60 ms. Fig. 6 illustratesthe deformed crash structure at 25 ms.

Figure 6: Crash structure at 25 ms exposed to a 35mph front crash scenario

The intrusion and pulse magnitudes as functionsof time during the 35mph front crash scenarioare visualised in Fig. 7. This particular modelutilised a total vehicle mass of 1200 kg. Thegraph of the pulse illustrated in Fig. 7 was beensmoothed using a C60 filter and is of “standardshape” [8].

Figure 7: Intrusion and pulse as functions of time,for a 35mph front crash scenario using the initial

front end structure

The pulse profile in Fig. 7 had an initial lowerpulse “plateau” with an averaged pulse of ap-proximately 20·g in the time interval between 0and 40 ms. The first pulse peak occurring at 5

ms was caused by the initial stress wave propa-gation throughout the crash structure. This origi-nated from the initial contact with the crash bar-rier, and should therefore not be taken into ac-count. The higher pulse “plateau” occurring be-tween 40 and 60 ms had a maximum pulse of42·g. These higher g values were caused by thefront end structure “locking up” towards the endof the crash scenario, this is caused by the limitedlength of the primary front end crash structure.

3 Shape- and size Optimisation

This part of the study was intended to evaluatethe potential for developing BIW crash structuresbased upon the outcome of topology optimisa-tion. The intention was to utilise shape- and sizeoptimisations to determine the “ideal” optimisa-tion process with respect to crash scenarios.Because of the large number of parameters as-sociated with such a study it was not feasible tofully consider all potential permutations, there-fore a simplified mathematical model was re-quired, a metamodel. A metamodel works bymeans of a multi-dimensional response surfacewhich is used to “estimate” the response of thefull model. In order to successfully create a re-sponse surface it is imperative to assess the in-fluence of the individual design variables againstthe objective, which in this case was to minimisethe mass. For the purpose of creating this sur-face a series of “key experimental models” wereneeded. The approach for selecting these was toutilise Design of Experiments (DOE), which canbe implemented in a variety of different ways.The potential for implementing individual sam-pling methodologies to obtain the above will bediscussed in the subsequent sections. Before thiswas conducted it was necessary to define the ac-tual design variables. This led to a series of com-plex challenges; one of which was parameterisa-tion. This was essential in order to enable theoptimisation of local areas of the crash structure,with respect to the individual design variables as-sociated with the metamodel. Consequently, avast number of computational permutations wererequired in order to complete the parameterisa-tion. This meant that a very large number of non-linear FE crash models had to be solved, whichin turn led to substantial CPU costs, as solving asingle model using 12 CPUs took approximately1 hour. Another important challenge was there-fore to balance the required CPU time with theaccuracy of the metamodel.

3.1 Design VariablesA total of six design variables were strategi-cally chosen, including two shape variables, allof which are illustrated in Fig. 8. The designvariables were selected based on their estimatedpotential for significantly affecting the overallcrashworthiness of the front end structure. Ap-propriate constraints were subsequently appliedto the individual design variables, such as mini-



mum (and maximum) thickness values, individ-ual distances etc.

Figure 8: Design variables

With the design variables specified the DOEstudies could commence.The following sectionswill discuss the potential for employing varioussampling methods for DOE, with respect to cre-ating the aforementioned metamodel for shape-and size optimisation in relation to crashworthi-ness and minimising mass.

3.2 Full Factorial versus HammersleyThe first DOE study involved the creation of 144design points using firstly Full Factorial Sam-pling (FFS) and secondly Hammersley Sampling(HS). All response surfaces were created for thetwo shape variables illustrated in Fig. 8, which inessence was the locations of the “recesses” along“shotgun 2” (V1) and the “longitudinal” (V2) re-spectively, Fig. 5, as well as the intrusion re-sponse. Initially Least Square Regression (LSR)approximation for both sampling methods wereused to create response surfaces. Not only didthe LSR create linear response surfaces, due tothe first order approximation, but it also createda fundamental difference between the respectiveresponse surfaces, as they had different angles inthe design space, as illustrated in Fig. 9.As indicated in Fig. 9, the first order LSR createdsignificantly different metamodels for the indi-vidual sampling methods, thus an accurate modelcould not be created or identified using this ap-proach.

Figure 9: LSR response surfaces using HS (upper)and FFS (lower)

Subsequently Moving Least Squares (MLS) ap-proximation for both sampling methods was usedto create a new set of response surfaces. Thesesubstantiated that the HS based approximationcreated accurate response surfaces, and that theresponse surfaces based upon FFS was renderedinsufficient, as shall be further discussed in sec-tion 3.4.Finally response surfaces were created usingthe Kriging interpolation method. As with theMLS approach, the response surface based onFFS combined with Kriging interpolation wasdeemed to be inadequate. It was found that krig-ing interpolation method combined with HS cre-ated a suitable response surface. However, theresults also indicated that issues regarding the ro-bustness for the subsequent optimisation wouldpersist, as the response range was very wide,and instable runs would be included in the meta-model.

3.3 Central Composite versus Hammer-sley Sampling

For the second DOE investigation, the rectangu-lar Central Composite Sampling (CCS) was com-pared to HS, this study consisted of 77 designpoints. The first step of this DOE study once



again consisted of creating LSR response sur-faces. As with the first study documented in sec-tion 3.2 these response surfaces were found to be“insufficiently shaped” for conducting accurateoptimisation. As a result, a substantial number ofsampling points would be required to ensure thatthe resulting metamodel was of sufficient accu-racy.Secondly, two response surfaces using MLS werecreated. Both were deemed to have “appropri-ate” shapes, as was previously found to be thecase for MLS, HS using 144 design points. Theresponse surfaces created using 77 design pointswere however found to have “insufficient” defi-nition in the vicinity of the actual design points.The use of the Kriging interpolation method inthis context was found to lead to non-smooth re-sponse surfaces, particularly in connection withHS. This was found to be especially evident atV1 = 1 and V2 = 1, as illustrated in Fig. 10, andwould thereby lead to a non-robust optimisationmodel.

Figure 10: Kriging response surface using HS, with77 design points

3.4 Combining FFS and HSBased on the above findings, an additional threeresponse surfaces were created. These werebased on the combined findings of the FFS andthe HS 144 design point samplings presented insection 3.2, and utilised 4th order LSR, 3rd orderMLS as well as the Kriging interpolation method.The rationale for this coupling approach was toinvestigate the potential for “stabilising” the re-sponse surfaces at the extreme points, a problempreviously highlighted by Fig. 10. The couplingapproach in combination with the above inter-polation methods should ensure a “reasonable”level of accuracy at the boundaries of the re-sponse surface, whilst simultaneously maintain-ing the accuracy within the design space. Thethree response surfaces created in this context areillustrated in Fig. 11.

Figure 11: Response surfaces based on combinedFFS and HS (144 runs), using 4th order LSR (top),

3rd order MLS (middle) and Kriging (bottom)

As illustrated in Fig. 11, all three response sur-faces have “similar” shapes, and adhere to the re-sponse surface initially generated from the MLSmetamodel using HS (144 runs). The responsesurface in Fig. 11 created using Kriging hadsharp edges and steep slopes. These character-istics of a response surface led to a non-robustoptimisation, and could thereby be disregarded.The error resulting from using the LSR and MLSmetamodels of Fig. 11 are presented in Fig. 12,as a function of the individual design points.



Figure 12: Percentage error of 4th order LSR (upper)and 3rd order MLS (lower)

Based on the results represented by Fig. 11 andFig. 12 it became evident that the MLS ap-proximation had the capability to form a smoothand simultaneously accurate response surface. Inaddition, the MLS model had the ability to ig-nore unstable runs, this does however result in ahigher percentage error of those specific designpoints, clearly visible in Fig. 12.

The higher order LSR also generated an “ade-quate” metamodel; however, when compared tothe MLS model the latter was found to “performbetter”. In addition, the CPU time required tocreate the MLS response surface was only a frac-tion of the CPU time required to create the LSRequivalent.

3.5 Combination of FFS CCS and HSFig. 13 presents equivalent response surfaces tothose illustrated in Fig. 11; the difference be-ing that Fig. 13 includes the contribution for therectangular CCS, consisting of 77 design points,initially presented in Fig. 10.

The response surfaces in Fig. 13 created using4th order LSR and 3rd order MLS were almost“identical” to the ones presented in Fig. 11. Thetwo Kriging surfaces evidently differed drasti-cally, as sharp slopes emerged at the edges of thesurface in Fig. 13.

Figure 13: Response surfaces based on combinedFFS (144 runs), HS (144 runs) and CCS (77 runs);using 4th order LSR (top), 3rd order MLS (middle)

and Kriging (bottom)

In order to determine the accuracy and indeedthe suitability of the metamodels for accuratecrashworthiness optimisation, it was necessary tomore carefully consider the effects of introducingthe CCS results. Fig. 14 represent the “cross-sectional” views of the three response surfaces inFig. 13, with the shape variable V1 set to zero.

The pink curve in Fig. 14 represents the meta-model created using MLS. As Fig. 14 reveals,this curve did not change significantly by the ad-dition of the CCS results. Hence, the “interior”points as well as the response surface boundarieswere already “adequately” determined, prior tothe addition of the CCS results, which did there-fore not improve the metamodel.Before the CCS points were taken into accountboth the LSR and the Kriging curves individually



Figure 14: Cross-sectional view of the combinedFFS and HS (upper) and with added CCS (lower)

deviated significantly with respect to the meta-model created by MLS, as illustrated in the up-per part of Fig. 14. When the CCS results, whichmainly defined the design points within the de-sign space, where subsequently considered, themetamodel generated by MLS became similar tothe other two. The metamodels created by LSRand Kriging moved towards the metamodel pro-duced by the MLS. Consequently, the MLS ap-proximation created “correct” metamodels withfewer design points as compared to the LSR andKriging approximations.

3.6 Variable ScreeningAs previously mentioned variable screening iscrucial for the identification and elimination of“unnecessary” variables within multi variableproblems; thus decreasing the amount of designpoints necessary to represent the actual system.In most cases regression coefficients are used todetermine dispensable variables. The samplingmethodologies and associated response surfacesdiscussed above were based on the two shapevariables V1 and V2 illustrated in Fig. 8. How-ever, Fig. 8 also contain the remaining 4 designvariables V3 to V6. Fig. 15 represents the maininfluences on the individual 6 variables upon theintrusion response using the FFS (144 runs) and aPlackett-Burman (36 runs) design. The Plackett-Burman can be interpreted as a “scaled down”version of the FFS run, it is a so-called fractionalfactorial design [12]. Fig. 15 was obtained usingANalysis Of Variance (ANOVA) [12].

Figure 15: Individual design variable influence uponintrusion response; FFS model (144 runs)(upper) and

Plackett-Burman(36 runs) (lower)

Fig. 15 thus provides an ANOVA; a graphic rep-resentation of the influence of each individual de-sign variable upon the intrusion response. AsFig. 15 reveals, the effects identified by use of theFFS design were very similar to those identifiedby the Plackett-Burman design. The Plackett-Burman did however have the obvious advantagethat the results were obtained by 36 runs as op-posed to 144, resulting in a significant decreasein CPU costs.

4 Optimised DesignBased on the findings and results presentedabove, it was concluded that the most appropriatemethodology for creating an accurate and smoothmetamodel for robust optimisation, with respectto crashwothiness and mass reduction, was themoving least squares method combined with HS.On this basis a combined shape- and size opti-misation of the crash structure illustrated in Fig.5, and the design variables illustrated in Fig. 8was conducted. The objective of which was, aspreviously mentioned, to minimise the mass ofthe structure; the load case consisted of a 35 mphfront crash scenario. The resulting optimised de-sign of the front crash structure is illustrated inFig. 16.



Figure 16: Optimised crash structure

When comparing Fig. 16 to Fig. 5 it was dif-ficult to notice any major differences. This wasnot unexpected, as the original structure of Fig.5 was already well engineered, and “fit for pur-pose”. Nevertheless, the optimised structure ofFig. 16 represented a mass reduction of 0,91kgor approximately 3% relative to the original val-ues. The pulse profile and intrusion are shown inFig. 17, which also contains the original profiles,previously presented in Fig. 7.

Figure 17: Intrusion and pulse as functions of time,for original and optimised crash structures

The two pulse profiles illustrated in Fig. 7 didnot display large differences; however, the pulsepeak value of the optimised model was slightlylower than that of the original. The intrusion re-sponses from both models remained unchanged,with identical maximum values.All of the above results show that the shape- andsize optimisation was successful, as the objec-tive of reducing the mass was met, in addition the“crashworthiness” constraints of pulse and intru-sion values were not violated, in fact the maxi-mum pulse magnitude was slightly reduced. Al-though the mass was only reduced by a mod-est 3%, which may not be of huge importanceconsidering the overall vehicle mass, the studyhas justified that the shape- and optimisation ap-proach worked, and provided results as intended,which is of significant importance with respect todeveloping structural optimisation algorithms ingeneral, and more importantly their potential forapplication to crashworthiness.

5 Conclusion and Next Steps

This paper has highlighted some of the key find-ings of a study into the potential for apply-ing structural optimisation algorithms within thefield of crashworthiness, given the objective ofminimising mass. The paper commenced witha study on HEV BIW architecture design usingtopology optimisation, followed by shape- andsize optimisation for developing the detailed ge-ometry of the front crash structure. It was foundthat topology optimisation on its own was ade-quate for safety cage development, but not forthe automatic generation of the front end crashstructure. The linear static topology optimisationcan be used for BIW development, however theengineering interpretation of the results are es-sential. To “automatically” develop crash struc-tures from design envelopes, thus minimising the“manual design work”, a topology optimisationalgorithm using non-linear FEA (currently notavailable in commercial software) could providean improved “starting point” for the shape- andsize optimisation. If this was to be achieved, the“originally engineered” structure in Fig. 5 couldtheoretically be replaced with the direct outcomeof topology optimisation. Research into the de-velopment of such an algorithm is presently on-going. The second part of the study demon-strated that shape- and size optimisation of crashstructure components can indeed be successfullycompleted. However, this process is very com-plex, due to various factors such as initial de-sign, design space, sampling method, metamod-elling technique, optimisation algorithm, meshand morphing strategy, which all need to be re-spected.The initial design was found to be a significantfactor which ultimately determined the successof the shape- and size optimisation. As men-tioned above, a non-linear topology optimisationalgorithm could “automatically” deliver an im-proved proposal for crumple zones, thus enhanc-ing the combined efficiency of the entire optimi-sation process, which potentially could signifi-cantly decrease the time used for the overall de-sign process.The shape- and size optimisation study con-cluded that the most appropriate methodology forcreating an accurate and smooth metamodel forrobust optimisation with respect to crashwothi-ness and mass reduction, was the MLS methodcombined with HS.This method can be used to efficiently and accu-rately optimise the cross sectional properties (i.e.shape and size) of a BIW crash structure, whilstmeeting NCAP requirements. This was substan-tiated by dynamic (explicit) FE modeling verify-ing the outcomes of the shape- and size topologyoptimisation.

6 Acknowledgements

The authors of this paper would like to thankcolleagues from Coventry University, Tata Mo-tors European Technology Centre (TMETC),



Jaguar Land Rover (JLR), Warwick Manufac-turing Group (WMG) and other contributors tothe Low Carbon Vehicle Technology Project(LCVTP) for supplying data leading to the op-timisation studies presented in this paper.

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[15] Christensen J, Bastien C, Blundell M V, Git-tens A, Tomlin O. Lightweight Hybrid Elec-trical Vehicle Structural Topology OptimisationInvestigation Focusing on Crashworthiness, In-ternational Journal of Vehicle Structures andSystems,ISSN 0975-3540, Volume 3, Issue 2,2011.

[16] Ravenhall N. Crash pulse analysis of currentvehicles and concept design analysis, CoventryUniversity.

AuthorsChristophe Bastien MSc, BEng(Hons), CEng, MIMechE, is aprincipal lecturer and the MSc Au-tomotive Engineering ProgrammeManager at Coventry University.He has over 15 years of indus-trial and academic experience withFEA and crashworthiness. He iscurrently leading the research intothe lightweighting of electrical ve-hicle architectures. He has filed 19patents in the field of vehicle andhighway engineering safety, and iscurrently undertaking a PhD in oc-cupant biomechanics.

Jesper Christensen MSc, BSc,CEng, MIMechE, is a Lecturer inStress Analysis at Coventry Uni-versity. The past 2 years of hiscareer has been spent focusing onstructural optimisation in connec-tion with crashworthiness, primar-ily in relation to HEV vehicles, forwhich he has published several re-cent papers. He is currently un-dertaking a PhD within the field ofstructural optimisation.



Professor Michael Blundell,PhD, MSc, BSc (Hons), FIMechE,CEng. Mike has over 30 yearsof experience in academia andalso in industry with companiesand institutions such as Boeingand the Ministry of Defence.Continuous experience throughouthis career on the developmentand application of CAE andVirtual Engineering in the marine,nuclear, automotive and aerospaceindustries.He has published morethan 95 papers, has authored anengineering textbook and is aregular reviewer of governmentfunded research proposals, reportsand publications.

Jakovs Kurakins Msc, Bsc, isa recent graduate from Coven-try University. His individualmasters project entitled: “Inves-tigation of Optimisation Strate-gies for Multi Variable Problemswith focus on Lightweight Ve-hicle Front Structure Develop-ment for LCVTP” was supervisedby Christophe Bastien and JesperChristensen.



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