Automotive Chassis Topology Optimization:a Comparison Between Spider and Coupe Designs

Marco Cavazzuti, Dario Costi, Andrea Baldini, Patrizio Moruzzi

Abstract—Weight reduction is a major issue for carmakercompanies due the need to comply with the emission regulationswithout reducing the vehicle safety. A classic trial-and-errorapproach to design in the automotive industry is becominginadequate and new means are needed to enhance the designprocess. A major improvement on the end product can beachieved by adopting suitable optimization techniques fromthe early design stage. In the present paper the problem ofautomotive chassis design in view of weight reduction is tackledby means of topology optimization. The design methodologyproposed is applied twice: at first addressing a chassis for spidervehicles, then for coupe vehicles. The two chassis, togetherwith some intermediate result are discussed and compared.The methodology has been proven to be successful in findinginnovative and efficient layouts for automotive chassis.

Index Terms—chassis design, topology optimization, multidis-ciplinary optimization, weight reduction, structural dynamics

I. INTRODUCTION

WEIGHT reduction has become a primary concern inautomotive industry. In fact, safety standards and

emission regulations impose conflicting performance targetsthat need to be satisfied at the same time. While the respectof the safety standards pushes the automotive design processtowards heavy weight solutions, environmental issues andhandling call for a resolute vehicle weight reduction.

Over the last twenty years the average vehicle weight hassteadily risen due to the improvements in safety and thegrowth in number of the vehicle features [1]. This broughtto the increase in the aluminum content of vehicles with theaim of restraining their weight, and also to a growing interesttowards composite materials, even though their applicationis still limited to parts of some high performance prototypevehicle for cost reasons.

Apart from the quest for better materials, remarkableweight saves can be also obtained by adopting a newapproach in design involving optimization techniques. Op-timization is a powerful tool for systematic design in me-chanics; it can lead to sensible improvements that could notbe achieved with a simple trial-and-error approach.

In order to apply these techniques a suitable parameteriza-tion of the investigated problem together with the definitionof the objectives and the targets which are sought are needed.The optimization algorithm iteratively generates new sampleswhich are tested through simulation.

Topology optimization [2] is a non-traditional optimizationtechnique, particularly suitable for solving structural mechan-ics problems at an early design stage using finite elementsanalyses. It aims at finding the optimum material distribution

Manuscript received March 23, 2011; revised April 7, 2011.M. Cavazzuti, D. Costi, and A. Baldini are with MilleChili Lab, Diparti-

mento di Ingegneria Meccanica e Civile, Universita degli Studi di Modenae Reggio Emilia, Modena, 41125, Italy e-mail: millechililab@unimore.it.

P. Moruzzi is with Ferrari SpA, Maranello, 41053, Italy.

within the domain given by a finite elements mesh. In adifferent way than more traditional algorithms, it has thepeculiarity that it can change the topology of the object byvirtually digging holes in the domain at locations where thealgorithm, from local gradient computations, thinks it is lessneeded. This is made possible by adopting a parameterizationbased on a fictitious element-by-element material density.Various ways for formulating such an optimization problemexist: according to the SIMP method, which is the mostsimple and well-known, the material density can vary withcontinuity between void and full density. The stiffness of thematerial varies nonlinearly with the density following theformula

E = E0

(ρ

ρ0

)p

where E is the stiffness of the material, ρ the density,p is called penalty factor, and the subscript 0 stands forthe properties of the full density material. Of course anintermediate density material has no physical meaning butaccepting its presence is an helpful stratagem that allowsthe optimization problem to be solved much more easily.Setting a penalty factor larger than unity makes the in-termediate density material unfavourable due to its largedensity-to-stiffness ratio, pushing the optimization processtowards “black-and-white” solutions. For more informationson topology optimization we refer the reader to the richspecialized literature over the topic (e.g. [3]).

Applications of topology optimization to mechanical prob-lems are numerous in literature, also with regard to theautomotive field in particular. Most of these applications arefocused on the optimization of small components, where thenumerical modeling of the components is relatively simple,and a small number of loading conditions are investigated.In these cases the complexity of the problem is limited, dueto the fact that a small number of optimization constrainsneed to be satisfied, and convergence is likely to be achievedquickly.

For instance, in [4] the optimization of hard drives sus-pensions is addressed by mean of topology and topographyoptimizations. The aim of the study is to maximize thetorsion, bending, and sway modal frequencies. [5] dealswith the topology optimization of an automotive suspensionaiming at the minimization of its compliance for a givenvolume under three different static loading conditions.

In [6] instead, an application of topology and size op-timizations of a body-in-white structure is presented, thusinvolving a larger and more complex domain than it isusually encountered in topology optimization applications inliterature. In fact, the domain is given by all the volumethat lies below the vehicle styling surface with the exclu-sion of the room needed for elements like the passengercompartment, the engine, the wheel, the boot, the doors,

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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the windshields, and so on. The vehicle skeleton obtainedthis way undergoes the optimization process under globalstiffness, local stiffness, and crashworthiness constraints.

In this paper a methodology for automotive chassis designin view of weight reduction based on topology optimizationis applied for creating two types of chassis layouts. Thefirst type regards the design of chassis suitable for a rear-engine spider vehicle, the other for a rear-engine coupevehicle. The setup of the two optimizations are discussed andthe outcoming solutions compared. The optimization processapplied is part of a more elaborated methodology alreadypresented by the authors in [7]. This methodology was basedon three optimization algorithms (topology, topometry, andsize optimizations) to be applied in cascade for refining stepby step the chassis layout.

II. SET UP OF THE OPTIMIZATION PROCESS

A typical optimization problem can be written in the form

minimizex∈D

f (x)

subject to c (x) ≥ 0

where x is the vector of the optimization parameters, D thedesign space or domain, f the objective function, c the setof optimization constraints.

In topology optimization, as already discussed, the choiceof the parameters is given by a fictitious density for eachelement of a finite elements domain. Thus, In order to set upthe topology optimization process, the following still needsto be defined:

1) the domain of the optimization (i.e. the finite elementmesh of the object to be optimized, suitably subdividedinto designable and non-designable areas),

2) the objective of the optimization,3) the performance targets the chassis must satisfy (given

in the form of optimization constraints), together withthe loading conditions needed for computing the tar-gets.

The definition of the objective of the optimization is quitestraightforward: since the goal of the study is the weightreduction of cars we aim at the minimization of the chassismass. On the other hand, the definition of the domain andthe performance targets are more sensitive issues and will bebriefly discussed in the following.

A. Domain of the optimization

The domains of the optimization are shown in Fig. 1.The two domains are the same except for the addition ofa solid roof model for the coupe case. They are thought forleaving a large freedom in choosing the optimum layout tothe optimization process. In fact, the massive solid blocks inFig. 1 leave room just for the passenger compartment, theengine, and the gearbox. Room for other components (suchas trunk, fuel tank, and so on) is less critical and can beaccounted for a posteriori when interpreting the topologyoptimization results into an actual chassis. The chassis meshis made of 1.97 million four-nodes tetra elements, while theroof mesh is made of 1.97 hundred thousand eight-nodeshexa elements.

The only constraints in the choice of the domain aremainly given by the provisional vehicle dimensions:

1) the wheelbase and track are fixed,2) the suspensions layout is fixed and the suspensions

non-designable,3) the suspension, seats, engine, and gearbox joints are

fixed and non-designable areas,4) all the rest of the finite element mesh (including the

roof for the coupe case) is designable,5) the whole structure is made of aluminum.

B. Performance targets

An automotive chassis must comply with both handlingand safety performance standards. In the present studythese structural requirements are set according to FerrariSpA internal regulations. Their fulfilment is ensured byimposing optimization constraints in terms of admissiblenodal displacements, or modal responses. These quantitiesare measured from finite elements simulations. In particular,the performance requirements used in this work regard:

1) the global bending stiffness of the chassis structure:an elevated structural stiffness, both bending and tor-sional, ensures a better handling vehicle performance.For evaluating the bending stiffness the four wheelcentres are constrained in the finite elements modeland the sills are loaded vertically. It is required thatthe displacement in the loaded area remains below agiven threshold.

2) the global torsional stiffness: three wheel centres areconstrained and the fourth wheel centre is loadedvertically. It is required that the displacement of theloaded wheel centre remains below a given threshold.

3) the crashworthiness in case of front crash: for beinggranted the homologation approval, vehicles must showa good performance in case of several crash conditions(e.g. frontal, rear, lateral crash, and so on) accordingto the various safety standards such as Euro NCAPor US NCAP. In the present work the frontal crashalone is taken into consideration. However, due to theinherent restrictions of the topology optimization soft-ware employed, it is not possible to include dynamicand non-linear load cases into the optimization process.Thus, the crash analysis had to be simplified into astatic linear loading condition. The front surface of thedomain is constrained while concentrated loads alongthe rear-to-front direction are applied to the locationswhere the main vehicle hanging masses are connectedto the chassis structure: wheel centres, seats, engine,and gearbox joints. It is required that the passengercompartment undergo limited deformations under theseloads. In particular, the displacements are monitored atseveral locations along the seats and engine joints, theA-pillar, the pedal area, the flame-shield, the dashboardunder the windshield. An additional constraint is addedfor monitoring the overall compliance of the structure,since it has been seen that elevated compliances cancause difficulties to the finite elements analyses. Sincea proper regulation for such a loading condition ismissing, the threshold values for the allowable defor-mations are set equal to the displacements found byapplying the same loading condition to a referencechassis model. A check will be needed a posteriori to

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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(a) (b)

Fig. 1. Topology optimization domains: (a) spider vehicle chassis, (b) coupe vehicle chassis.

ensure that in case of dynamic non-linear simulationsthe behaviour of the vehicle in the event of crashrespects the performance standards.

4) the modal analysis: the natural frequencies inherentto global structural modes are directly related to thestructural stiffness. For this reason, another way forenforcing an elevated stiffness and a good handlingperformance, is by ensuring elevated natural frequen-cies. It is required that the first bending and torsionalnatural mode frequencies remain above a given thresh-old.

5) the local stiffness at the suspension, engine, and gear-box joints: the sills are constrained while selectedpoints are loaded along the coordinate axes. In par-ticular the load are applied to the front and rear wheelcentres along the three coordinate axes, and to theengine and gearbox joints along the vertical directions.It is required that the displacement of the loadedpoints remains below a given threshold. Since a properregulation for these eight loading cases is missing, thethreshold values are set equal to the displacementswhich are found by applying the same loading condi-tion to a real Ferrari chassis chosen as reference model.Ferrari internal regulations would actually require aninertance analysis over a wide range of frequencies forlocal stiffness evaluation at each joint in the structure,but the high CPU requirements that such an analysiswould involve makes of it a non viable option to beimplemented in a topology optimization task.

The numerical values of the optimization constraints differedbetween the spider and the coupe cases since a coupe layout,due to the presence of the additional roof structure, issupposed to be stiffer. The chassis domain is symmetrycalalong the spanwise direction, and so is the mesh. It isrequired that the topology optimization process mantains thesymmetry in the solution.

III. RESULTS

The model set up and the topology optimizations wereperformed using the software suite Altair HyperMesh 10 andits embedded optimization tool OptiStruct.

The optimizations on the two models were performedby increasing step by step the complexity of the process,i.e. adding the optimization constraints one at a time, andrepeating the optimization. This made it possible to check theconsistency of the solutions, and have a better understanding

Fig. 2. Trend of the chassis mass as constraints are added to the topologyoptimization process; the mass is normalized over the mass of case 1. Themasses for cases 5 and 6 include the mass of the roof.

TABLE IACTIVE CONSTRAINTS AFTER TOPOLOGY OPTIMIZATION:

3 = ACTIVE, 7 = INACTIVE, – = NOT APPLICABLE.

Active CasesOptimization Spider CoupeConstraints 1 2 3 4 5 6

Global bending stiffness 3 7 3 3 3 3

Global torsion stiffness 3 3 3 3 3 7

Crash seat joints displacement – 7 7 7 3 7

Crash engine joints displacement – 3 3 7 3 3

Crash A-pillar displacement – 3 3 3 3 3

Crash pedal displacement – 7 3 7 7 7

Crash flame shield displacement – 3 3 7 7 7

Crash dashboard joints displacement – 7 7 7 7 3

Crash compliance – 3 3 3 3 3

First natural mode – – 3 3 3 3

Local front wheel stiffness along x – – – 3 – 3

Local front wheel stiffness along y – – – 3 – 3

Local front wheel stiffness along z – – – 3 – 3

Local rear wheel stiffness along x – – – 3 – 3

Local rear wheel stiffness along y – – – 3 – 3

Local rear wheel stiffness along z – – – 7 – 7

Local engine joint stiffness along z – – – 3 – 3

Local gearbox joint stiffness along z – – – 3 – 7

Total 22

59

810

1218

710

1218

of the results. Six test cases are taken into consideration andtheir relative set up is resumed in Fig. 2 and Tab. I whichshow the trend of the chassis mass as optimization constraintsare added, and the active optimization constraints at the endof the process.

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

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(a) (b)

(c) (d)

(e) (f)

(g) (h)

Fig. 3. Topology optimization results: figures (a) to (f) refer to cases 1 to 6 respectively; (g) and (h) are the roofs obtained for cases 5 and 6. Thedifferent colours stand for different material relative densities with blue being 10% and red 100%. Elements with relative density lower than 10% arenot shown.

It can be seen that despite the growing number of con-straints from case 1 to case 6, a relatively large fraction ofthem is still active at the end of the optimization processes(73% on average). This also negatively affects the conver-gence of the optimizations which is not always obtainedstraightforwardly when the problem is over-constrained. Im-portant constraints, which are always found to be active,regard the A-pillar displacement and the compliance of thestructure in the event of crash, and the first natural mode.Most critical are also the local stiffness constraints since mostof them are always active, and they heavily affect the finalmass of the topologically optimized chassis.

Figure 3 shows the results of the six optimizations per-formed. Case number 1 (Fig. 3(a)) involve global stiffness

constraints alone. As a consequence, the seats, engine, andgearbox joints, as well as some suspension joints, not beingloaded, are not connected to the rest of the structure. Theloads between the front and the rear are transferred boththrough the sills and the central tunnel.

In case number 2 (Fig. 3(b)) due to the addition of thecrash loading conditions, bumpers in the front and connec-tions to all the junctions appear, this allows the load acrossthe central tunnel to be slightly lower.

The inclusion of the modal constraint (Fig 3(c)) brings toa slightly simpler structure and to a significant reinforcementof the bumpers support area.

Case number 4 (Fig. 3(d)) gives rise to a much morecomplex and different chassis layout. The whole structure

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

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is thickened and the number of beams on the rear part ismuch larger. It must be considered that loads along thelengthwise and the vertical directions in the suspensionareas were already included also while evaluating the globalstructural stiffness and the frontal crashworthiness. Thus, itwas expected that the most critical loading conditions duringthe assessment of the local stiffness of the suspension jointswould have been those along the spanwise direction. In fact,in Fig. 3(d) a large spanwise structure connecting the frontsuspension joints appears on the upper part of the domain,and the transversal beams linking the suspension joints areato the central tunnel on the lower part of the domain aredoubled in size. The tunnel itself disappears and is substitutedby a web of beams going from the front end of the formertunnel up to half the way along the sills. Such a sensiblechange in the layout and such an increase in weight forwhat it should have been a “local” stiffness issue must beconsidered carefully. In fact, it can be argued that such abehaviour is mainly due to the loading condition chosenfor the evaluation of the local stiffness which involves theclamping of the sills, so that the lines of force must gothrough the sills, thus making the central tunnel superfluous.However, this is not a loading condition to which a vehicle isactually subject while on the road. Other loading conditionshave been tried in substitution of the inertance analysis,but all of them are prone to similar issues. On the otherhand, it is out of doubt that the previous structure (Fig. 3(c))lacks reinforcements along the spanwise direction, which areproperly included in the solution proposed in Fig. 3(d).

The cases 5 and 6 (Figs. 3(e) and 3(f) for the chassislayouts, and Figs. 3(g) and 3(h) for the roof layouts) arecoupe versions of the cases 3 and 4 respectively. In thesecases, the beams are much thinner compared to their spiderversions, as a consequence of the fact that a portion of theload is carried upwards through the roof of the vehicle.This also allows the final structure to be much simpler (alower number of beams is found in the solutions), and thecentral tunnel to disappear completely. Despite the fact that incase 5 (Fig. 3(e)) local stiffness load cases are not included,spanwise structures appears both on the front and on the rearof the chassis. These structures converge towards the areasin which the roof is connected to the rest of the chassis andserve to transfer the loads between the chassis and the roof.The spanwise structures are still present and even reinforcedin case 6 (Fig. 3(f)) due to the local stiffness loads. It isinteresting to notice how the bumpers in both the copueversions are more distant from the ground level, are notparallel to each other but slightly converging, and their twosupport beams are less slanted and meet nearer to the carfront. These things suggest that the lines of force in the eventof front crash are going to remain higher on the level groundand be pushed towards the sides of the car in order to gothrough the roof structure.

The two roof layouts (Figs. 3(g) and 3(h)) are similar inthat apart from having two sets of beams running all the wayacross the left and the right side of the car, they have anelongated “X” shape on the top with some reinforcementsto the rear. The structure in Fig. 3(h) is thinner and hasa reticular front doorpost as a result of having assumed arelatively thick topology domain around the doorpost area.

IV. CONCLUSIONS

The methodology adopted for automotive chassis designby means of topology optimization has been proved to beeffective, being able to trace an optimum draft design forthe chassis by itself, by simply starting from a massivedesign space. It must be considered that the problem setup phase must be addressed carefully since the outcome ofthe optimization can be significantly affected by the choiceof the optimization objective, constraints, and simulationsmeans. This makes no exception, since every optimizationproblem is always deeply and intrinsically dependent uponthese aspects.

The methodology has been applied in order to designchassis for both spider and coupe vehicles. Different layoutshas been found by topology optimization and have beencompared and discussed in the present work. The resultsare consistent with the loading conditions applied and theperformance targets imposed which are derived from FerrariSpA internal regulations. The comparison made, allowed abetter understanding of the way the chassis works and onthe way in which the lines of force are transported acrossthe structure.

Addressing a coupe vehicle, it was found that a suitableexploitation of the presence of the roof from a structural pointof view allows a remarkable stiffnening of the chassis, whichis always a welcomed characteristic in view of improving thevehicle handling. The other way round, for given stiffnesstargets, significant savings in terms of structural weight canbe achieved. Thus, a joint approach to design, able to addressthe structural role of the roof and of the chassis at thesame time, aided by collaborative optimization techniques, isrecommended, and can lead to innovative and more efficientsolutions.

REFERENCES

[1] R. Borns and D. Whitacre, “Optimizing designs of aluminum suspen-sion components using an integrated approach,” SAE 05M-2, 2005.

[2] M. P. Bendsøe and N. Kikuchi, “Generating optimal topologies instructural design using homogenization method,” Computer Methodsin Applied Mechanics and Engineering, vol. 71, pp. 197–224, 1988.

[3] M. P. Bendsøe and O. Sigmund, Topology optimization: theory, methodsand applications. Springer, 2004.

[4] S. Kilian, U. Zander, and F. E. Talke, “Suspension modeling andoptimization using finite element analysis,” Tribology International,vol. 36, pp. 317–324, 2003.

[5] G. Chiandussi, I. Gaviglio, and A. Ibba, “Topology optimization of anautomotive component without final volume constraint specification,”Advances in Engineering Software, vol. 35, pp. 609–617, 2004.

[6] C. Reed, “Applications of optistruct optimization to body in whitedesign,” 2002.

[7] M. Cavazzuti, A. Baldini, E. Bertocchi, D. Costi, E. Torricelli, andP. Moruzzi, “High performance automotive chassis design: a topologyoptimization based approach,” Structural and Multidisciplinary Opti-mization, article in press.

Proceedings of the World Congress on Engineering 2011 Vol III WCE 2011, July 6 - 8, 2011, London, U.K.

ISBN: 978-988-19251-5-2 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)

WCE 2011