The interaction between active aeroelastic control and structural tailoring in aeroservoelastic wing design

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The interaction between active aeroelastic control and structural tailoring in

aeroservoelastic wing design

Binder, Simon; Wildschek, Andreas; De Breuker, Roeland

DOI

10.1016/j.ast.2021.106516

Publication date

2021

Document Version

Final published version

Published in

Aerospace Science and Technology

Citation (APA)

Binder, S., Wildschek, A., & De Breuker, R. (2021). The interaction between active aeroelastic control and

structural tailoring in aeroservoelastic wing design. Aerospace Science and Technology, 110, [106516].

https://doi.org/10.1016/j.ast.2021.106516

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Contents lists available atScienceDirect

Aerospace

Science

and

Technology

www.elsevier.com/locate/aescte

The

interaction

between

active

aeroelastic

control

and

structural

tailoring

in

aeroservoelastic

wing

design

Simon Binder

a,b,

∗

,

Andreas Wildschek

c

,

Roeland De Breuker

b

a_Materials_X,_Airbus_Defence_and_Space_GmbH,_Germany

b_Section_of_Aerospace_Structures_and_{Computational}_Mechanics,_Faculty_of_Aerospace_Engineering,_Delft_University_of_Technology,_the_Netherlands c_Aircraft_Control_Domain,_Airbus_Operations_SAS,_France

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received5February2020

Receivedinrevisedform19August2020 Accepted13January2021

Availableonline18January2021 CommunicatedbyGrigoriosDimitriadis

Keywords:

Aeroservoelasticoptimization Compositetailoring

Feed-forwardgustloadcontrol Manoeuverloadalleviation

Thispaper presentsananalysisoftheinteractionand trade-offbetweenactiveaeroelastic controland passivestructuraltailoringonafree-flyingfullyflexible aircraftmodel.Bothtechnologiesareincluded in the preliminary design of a typical transport aircraft configuration with a conventional control surfacelayoutcontainingtrailingedgecontrol surfacesand spoilers.Thepassive structuraltailoringis facilitatedbyexploitingtheanisotropicpropertiesofcompositematerialstosteerthestaticanddynamic aeroelasticbehaviour.Activeaeroelasticcontrolisimplementedbyscheduledcontrolsurfacedeflections redistributing theaerodynamic loadsduringmanoeuvresto achievemanoeuvre loadalleviation and a feed-forward control lawfor gustload alleviation.The panel-based aerodynamicmodelling of spoiler deflections is improvedby acorrectionof the spatialdistributionof the boundarycondition derived fromhigherfidelitysimulationdata.Theoptimisationofactivecontrollawsrequires theconsideration ofconstraints ofthe actuationsystem, namelyrate and deflection saturation, inanonlinear manner. The interactionof manoeuvreload alleviation,gust load alleviationand passive structural tailoringis investigatedonthebasisofresultsofdifferentaeroservoelasticoptimisations.Thereforetheprimarywing structureis simultaneouslyoptimised withthe individualtechnologiesbeingactivated ordeactivated, resultingin eightdifferent wingstructures. The results oftheindividual and combined optimisations revealsignificantdesign differences.Thepotentials ofthe differenttechnologiescanonlybeoptimally exploited by simultaneous optimisation. The paper concludes with a study of the sensitivity of the majorfindings withrespect tothe knockdownfactorforfailure appliedto thematerial properties.A substantialshiftofeffectivenessfromactiveaeroelasticcontroltopassivestructuraltailoringisobserved withincreasedallowablesresultinginmoreflexibleandhencelessstiffwingdesigns.

1. Introduction

Theintroductionofcompositematerialswasanimportant mile-stoneinthedevelopmentoflightweightwingstructures.However, costlymanufacturing,highrepaircostsandcomplexrecycling pro-cessesputtheadvantagesofthehighstrengthtoweightratiointo perspective. In fact,full exploitation of the materialproperties is requiredforcompositematerialstocompetewithwellestablished metallic structures [1]. An important step in fully exploiting the anisotropic material properties ofcarbon ﬁbre reinforcedplastics hasbeentheindustrialutilisationofautomatedprocessesfor pro-ducingtow-steered composites.Whilethemethodallows improv-ing theaeroelasticbehaviour by introducingbeneﬁcial aeroelastic

*

Correspondingauthorat:Kluyverweg1,2629HSDelft,theNetherlands.

E-mailaddress:s.binder-1@tudelft.nl(S. Binder).

couplingspassively, theinteraction withactive control systemsis affected.Theanalysisthereofisthesubjectofthiswork.

Inaviation, the exploitation ofanisotropic material properties has its origin 70 years ago in the development of wooden pro-pellersinwhichthe fibredirectionwas utilisedto createthe de-siredaeroelasticbehaviour[2].Thismethod,alsoknownas struc-tural tailoring, is defined as the steering of the aeroelastic be-haviourby structuraldesignsothatitisfavourableforthe partic-ularperformance target.Intermsofwingdevelopment, structural tailoringby theembodimentofdirectionalstiffness promises var-iousenhancements of theaircraftperformance. The early studies haveconcentratedonthebeneficialeffectsoftheinducedstiffness cross-couplingonstatic anddynamic aeroelasticstability, control surface effectiveness andload redistribution for manoeuvre load alleviationandliftefficiency[3].Furtherstudiesalsorevealedthe positive influence of structural tailoring on the dynamic charac-teristics relevant for gust encounters [4], [5]. Motivated by the https://doi.org/10.1016/j.ast.2021.106516

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promisingresults,directionalstiffnesswasincludedasaparameter inthefieldofmultidisciplinaryaircraftwingoptimisations.While mostoptimisationstudiesaimtoreduce themassoftheprimary structure[6] [7],othersseektofurtherincreasethefuelefficiency ofaircraftbyadditionallyimprovingthelift-to-dragratioinstatic trimconditions[8]. Inrecentyears,theinvestigation ofthe influ-enceofdirectional stiffnessonthedynamic behaviourofbox-like wingstructureshasreceivedmoreattention[9],[10].

Stodiecketal.[11] recentlyinvestigatedtheapplicationof tow-steering inthe design of composite wing boxes. Withthe inclu-sionofcontrol surface effectivenessconstraints,itbecame appar-ent that depending on the design driving constraints, different mechanismsoccur.Whileloadalleviationformanoeuvreandgusts requires wash-out,control surface effectiveness andﬂutterspeed were raisedby inducinga wash-inbehaviour by structural tailor-ing.

Contrarytopassivemethodsforinfluencingtheaeroelastic be-haviour, active means have been investigated since decades. An importantdistinctionfrompassivemethodsresultsfromthe abil-ityofthe activecontrol methods toadaptto theparticular flight conditions such as fuel state, payload configuration or centre of gravityposition.Theactivecontrolsystemsconsideredinthiswork are Manoeuvre Load Alleviation(MLA) andGust Load Alleviation (GLA).

Both technologies have been applied to various aircraft [12] and target the alleviation of aerodynamic loads by control sur-facedeflectionsinawaythatisbeneficialforthestructuraldesign. ConcerningMLA, theredistributionofaerodynamic loadsby con-trol surface deflections mostly involves a shift of the centre of pressure inboard andthus closerto the wing rootresulting ina reducedbendingmoment.GustLoadAlleviationtargetsthe reduc-tion of the loads encountered during turbulent flight conditions by dynamic control surface deflections. Feeding back the signal of sensors as accelerometers to control surface actuators can ar-tificially increase the damping of specific aeroelastic modes and thereby lower the structural loads. Instead of modifying the re-sponse, these control surface deflection commands can also be computedbyfeedingforwardafilteredsignalofaturbulence mea-surementtakenupfronttheaircraft.Bothways,thecontrolsurface deflectionsleadtoredistributedaerodynamicloadswhen encoun-teringturbulence.

BesidestheinfluencethatGLAhasonthedynamicresponseof anaircraft,thesimilarityinthemechanismsofstructuraltailoring andMLA,aswell astheconflictingrequirementsonthe bending-torsioncoupling,suggeststhatstronginteractionisexpectedwhen usingbothtechnologiesonasinglewing.Weisshaarpredictedthat thedesignersofactivecontrolsystemsforcompositewingswould havenotonlytoexaminetheeffectofchangingthegainsbutalso theeffectsofstructuraltailoringontheresultingcontrollaw[13]. Theinteraction andtheassociatedissuesorsynergieshaveledto a variety ofstudies andprojects toaddress the so-calledfield of aeroservoelasticity. The general aspects of aeroservoelastic mod-elling,analysis andoptimisation,aswell asrelevant applications, aresummarisedin[14].

Dealing withaircraft wings on a simplified andgeneral level, the studies ofZeiler andWeisshaar [15], Librescu etal.[16] and WeisshaarandDuke[17] havebeen,amongstothers,pointingthe way. Inthe study performed by Zeiler etal. [15], thesynergistic potential ofintegratedstructuralandcontrol designwas revealed inawingoptimisationwiththeobjectiveofaeroelasticstability in-crease. Morespecifically, specific changesinthe structuraldesign showedanincreaseinthecontrollabilityofmodesthatwere oth-erwise nearly uncontrollable [15]. This beneficial effect was also observed by Librescu et al. [16] when extending the concept to anisotropic,compositewingstructures.Itwasshownthatthe com-binedoptimisationoutperformseitherstructuraltailoringoractive

controlalone[16].Weisshaar andDuke[18] investigatedthe com-bineduseofactivecontrolandstructuraltailoringwiththe objec-tive ofdrag reduction.Withcombined use,theinduced drag can beminimisedwithsmallercontrolsurfacedeﬂections,butthe de-termination of the deﬂections requires a combined optimisation withthestructure.

Over the years and as the tools and methods for integrated aeroservoelasticanalysisandoptimisationhaveevolved,many ap-plicationshavebeenpresentedthat targetthe integrated prelimi-narydesignoftransportaircraftwings.

Integratingactive manoeuvreandgustloadcontrolinthe pre-liminaryaircraftdesignwasshowntohaveadrasticimpactonthe resultingoptimaloverall design[19].Manystudiesexistinwhich transport aircraftwing structures with isotropicmaterial proper-tiesareoptimisedconcurrentlywithﬂuttercontrol,GLA,MLAand shapeadaptionbymorphing[20],[21],[22],[23],[24].

The interaction of structural tailoring and active control was studiedby Handojoetal.[25] usingthe exampleofoptimisation ofacomposite wingin thepresenceandabsenceofa ﬁxed con-trollawformanoeuvreandgustloadalleviation.However,inthe appliedsequentialoptimisation,theoptimisercouldn’tfullyutilize the directional stiffness properties asthe sensitivity ofthe loads withrespect tothe structuraldesign parameters was invisible to theoptimiser.Asaresult,theoptimiserwasunabletoexploitthe potentialofthedirectionalstiffness propertiestoredistributeand alleviatetheloads.

Integrated design of subsonic transport aircraft composite wingsemploying structuraltailoringandactivetrailingedge mor-phing for manoeuvre load alleviation has been presented by Werter[26] ﬁndingthatdesigndifference occurboth inthe stiff-ness distribution as well as the morphing induced camber dis-tribution whether or not the other technology is accounted for. Asimilar investigation was carriedout by Krupa etal.[27], who simultaneously optimised a wing structure including the control surface deﬂections for active manoeuvre load alleviation. As ex-pected, the wing employing both technologies outperformed the designsemployingoneofthetwo.

The previously given examples were focused either on single technologiesorcombinationsofstructuraltailoringwith manoeu-vre load alleviation or ﬂutter control. The interaction between active gust load alleviation and structural tailoring in the inte-grated optimisationof composite wingshas not beenstudied on theexample of transport aircraftconﬁgurations. The above-listed examplesthat includeactive control andstructuraltailoring con-sidereithersingle control surfacesordistributed controlsurfaces locatedatthetrailingedge.Thefollowingpoints differentiatethe presentworkfromthementionedstudies:

•

Insteadofindividualconsiderations orpairwisecombinations, ananalysisofthe interactionbetweenthethree technologies of structural tailoring, manoeuvre load alleviation, and gust loadalleviation ispresented asthe tailored utilizationof di-rectionalstiffnesspropertiesaffectsboth,manoeuvreandgust loads.

•

Insteadofsingle control surfacesoridealised layouts, a typi-caltransportaircraftconﬁgurationisusedwithaconventional controlsurface layout consistingofspoilers andaileronsthat iscompatibletothecurrentstateoftheart.

•

Theinﬂuence ofthestructuralﬂexibility on theobserved in-teractionsandthe trade-off betweenactive and passiveload alleviationisanalysedbya continuousvariationofthe mate-rial properties. Thisenables the assessment of the extent to whichtheresultsretainvalidityincaseofvariations.

Variousoptimisationsofthewingstructurearecarriedoutwith theindividual technologiesandtheir combinationstounderstand

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Fig. 1. Structuralmodelling approachusingTimoshenkobeamelementswith stiffnessandmasspropertiesobtainedbythecross-sectionalmodeller. Explanationofthe referenceangleorprincipalstiffnessdirection

φ

.

the mechanismsbehind thethreetechnologies. Optimisationsare carriedoutincludingstaticanddynamicaeroelasticconstraints in-cludingstrengthandbucklingconstraintsresultingfrom manoeu-vreandgust flight conditions.For theconsideration ofstructural tailoring,apredefinedlaminatelay-upisusedthat complieswith the usual composite design guidelines used in the industry.The actual parameterforincludingstiffness directioninthe optimisa-tionisthereferencedirectionoftheplies.TheMLAisincludedby scheduledcontrolsurfacedeflectionsduringthesteadysymmetric loadconditions,i.e.pull-uporpush-overmanoeuvre,and antisym-metric load conditions, i.e. rolling manoeuvres. A stack of finite impulse response filters is optimised alongsidethe other design parameters to emulate the presence of an optimal feed-forward gust load alleviation system. The paper concludes by answering theremaining questionwhethertheobservedinteractions are ro-busttovariationsintheselectedmaterialbyasensitivityanalysis ofthemajorfindingswithrespecttotheknockdownfactorapplied tothematerialproperties.

2. Aeroservoelasticmodel

The integrated aeroservoelastic design studies carried out in thisworkareperformedwiththeopen-sourcetoolchaindAEDalus that has been originally developed to investigate the effects of aeroelasticityonthehandlingqualitiesduringpreliminaryaircraft design[28].Among otherdevelopments,thecapabilityof numer-ical optimisation was included in the course of this work. The following introduces the models of structural dynamics, aerody-namicsandactivecontrolrequiredfortheaeroservoelastic optimi-sation.

2.1. Structuralmodel

The equationsofmotion ofthestructural dynamicsare based onthe ﬁniteelementmethod.Linear Timoshenkobeamelements areusedforthediscretisationoftheaircraftstructureonaglobal level. The stiffness and mass properties of the thin-walled wing cross-sectionsareobtainedbythecross-sectional modeller devel-opedby FeredeandAbdalla [29].Theimplementationusedinthe course of thiswork has been adopted from Proteus, a toolchain developedby WerterandDeBreuker[30] for thestructural opti-misationofaeroelasticallytailoredwingstructures.

Onthe cross-sectionallevel,thegeometryofthe cross-section isﬁrstdiscretisedwithtwo-dimensionalshellelements,asshown in Fig. 1.The outer dimensions ofthe cross-sections resultfrom predeﬁnedsparpositionsandairfoils.Theheightofthefrontand rearsparisassumedtobeequal.Onthelaminatelevel,thelayup

isspeciﬁed by the stacking sequence ofthe individual ply direc-tions.

Withthestiffnessandmassinformationobtainedonthe cross-sectionallevel,the Timoshenko beamelementstiffness andmass matrices are obtained. The global stiffness and mass matrix are thereafterassembled.The fullstiffness andmassmatrixare used forthe staticstructuralanalyses, whereas a representationbased on modal coordinates is employed in the dynamic structural model.Amean-axisapproach isutilisedfortherealisationofthe equations of motion of the free-ﬂying ﬂexible body, as used by Seywald[28].

2.2.Aerodynamicmodel

The steady aerodynamic model in dAEDalus is based on the well-knownVortexLatticeMethod(VLM)[31].Theunsteady aero-dynamicmodelisbasedonacontinuous-timestate-space formula-tionoftheUnsteadyVortexLatticeMethod(UVLM) thathasbeen firstdescribed byMohammadietal.[32] fortwo-dimensional air-foils,formulatedforthree-dimensionalliftingsurfacesbyWerteret al.[33],andextendedforarbitrarymotionandcontrolsurface de-flectionsbytheauthors[34].TheaerodynamicsolversindAEDalus are based on the well-known Vortex Lattice Method (VLM) [31] forsteadyaerodynamicsandtheUnsteadyVortexLatticeMethod (UVLM) [32] for unsteady aerodynamics.The latterhasbeen for-mulatedforthree-dimensionalliftingsurfacesbyWerteretal.[33], andextended forarbitrarymotionandcontrolsurface deflections bytheauthors[34].Inbothmethods,controlsurfacesarerealised bya modificationoftheboundaryconditionsimposed onthe re-spectivecontrolsurfacepanels.Themodificationisequivalenttoa rotationofthe panelsassociated withthecontrol surface around the hinge axis.The control surface deflection thereby leads to a differentflowfield inwhichmainly thecirculationnearthe con-trolsurfaceischanged.

Thecontrolsurfacelayoutusedinthisworkalsoincludes spoil-ersforwhichthistypeofmodelling,i.e.themere modificationof the boundarycondition imposed on the spoilerpanels, produces unsatisfactoryresults.The flowaroundadeployed spoiler,i.e. ex-hibitinglarge deflections, is highly dominatedby effects that are notaccountedforbypotentialflowmethods,e.g.regions of sepa-ratedflowbehindthespoiler.Inthefollowing,thederivationofa correctionmethodisshowntoimprovetheaccuracyofmodelling spoilers with the vortex lattice method. The boundary condition isthereforemodified forall panelsinthespanwise regionofthe spoilerinsteadofonlythespoilerpanels.

Thelinearityofthevortexlatticemodelallowsaninverse com-putationoftherequiredincrementalboundaryconditionbreqthat

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Fig. 2. Aerodynamicpanelmeshintheareaofaspoilercontrolsurface.The pan-els chosenfor the derivationfor a correctionlaw arehighlighted inbold. The dash-dottedlineindicatestheareainwhichtheboundaryconditionisvaried si-multaneously.

results in a given incremental pressure distribution cp,target by solvingthelinearsystemofequations:

∂c

p,i

∂

bj

(i=1..np,j=1..np) breq

=

cp,target (1)

with

∂

cp,i

/∂

bjbeingtheinﬂuencethatanincrementinthe

bound-arycondition ofthe j-thpanelhason thepressurecoefficient of thei-thpanel.Thesedifferentialsareobtainedbyatransformation ofthe influencecoefficientsthat are naturally availableusing the VLM.

Toprovidea correction thatis usablefordifferentshapesand positions of spoilers, the set of panels considered in the target pressuredistributionislimitedtoasetofpanelsintheareaofthe midspanofthespoilersurface,whicharetheboldpanelsinFig.2. Furthermore,theboundary condition isvaried simultaneouslyfor all spanwisepanelsofarowinchordwisedirectioninthe region ofthespoiler.Asanexample,thecombinationofthepanelsofthe thirdrow,resultinginthecombinedboundarycondition breq,3,is indicatedbythedash-dottedlineinFig.2.

The target pressure distribution used here is calculated from dataobtainedbyacommercialCFDsolverbasedonReynolds Aver-agedNavierStokes(RANS)equations.TheCFDcomputationswere carried out on the wing of the NASA Common Research Model (CRM [35])for one ﬂightcondition withand withoutspoiler de-ﬂectionandsubsequentlymappedtoanequivalentpanelmesh.

The chordwise distributedboundary condition that matchesa sectional pressuredistribution obtainedby the CFDcalculation is shown in Fig. 3 and is indicated by the adjective optimal. The boundaryconditionisnormalisedtotheequivalentboundary con-ditionobtainedby aconventionalrotation ofthepanelsresulting in theboundary condition factorsb

/

brot. Thechordwise distribu-tion of a conventional rotation of the panels associated to the spoilersurfaceisshownforcomparison.

A simpliﬁed distribution is obtained by an approximation of theoptimaldistributionbypiecewiselinearsegmentsbetweenthe fourchordwisestationsindicatedinFig.3bytheverticallines:

b(xle

)

= −

0

.

075brot

b(xh

−

csp

)

= −

0

.

2brot

b(xh

+

0

.

5csp

)

=

1

.

1brot

b(xte

)

=

0

.

5brot

(2)

Herein, xle,xte andxhdenotethe chordwisepositionofthe lead-ingedge,trailingedgeandspoilerhingeaxis,andcsp denotesthe chordofthespoilercontrolsurface.

Fig. 3. Comparisonoftheboundaryconditionrequiredtomatchthepressure distri-butionobtainedbyCFDsimulationwiththeconventionalboundarycondition.The piecewiselinearapproximationrepresentsthesimpliﬁedcorrectionthatisusable fordifferentshapesandpositionsofspoilercontrolsurfaces.

Theresulting integratedsectionalliftandmoment coefficients forvariousspoilerdeflections areshowninFig.4.The correction improvesthe otherwise poorperformance of the VLM,especially in calculating the moment coefficient. In the present case, CFD data were used for the correction at a moderate spoiler deflec-tion of 15 degrees, which is expected to be sufficient for load alleviation functions. Due to the linear nature of the VLM can-notaccountforthenonlineareffectssuchaslocalflowseparation that are observed in the CFD results for higher deflections. The derived correctionlawisimplemented forallspoilercontrol sur-facesintheaerodynamic modelsusedinthiswork.However, due tothelackofappropriate simulationdata,itwas notinvestigated, towhichextendthecorrectionmethodfoundisapplicablefor un-steadyaerodynamicmodels.

Before the integration withthe structuraland ﬂight dynamic equationsofmotion,thecomputationalcomplexityoftheunsteady aerodynamicstate spacemodelisreducedbymodelorder reduc-tion(MOR).The reducedorder modelisestablishedby amethod thatcombinesthebalancedproperorthogonaldecompositionwith theconcept of synthetic mode shapes[36]. The method is espe-ciallysuitableforthereductionofmodelsusedinaeroservoelastic optimisationasitrequiresnopriorknowledgeofthestructural dy-namics.

Couplingtheaerodynamicmodeltotheequationsofmotionof thefree-ﬂyingﬂexiblebodyrequiresthetransformationof aerody-namicloadstostructuralloadsandthetransformationofstructural motiontothemotionofthepanels.Thegenerationoftherequired couplingmatrices,aswellastheintegrationofthemodelsusedin thiswork,isdescribedbytheauthorsindetailinRef. [37].

2.3.Activeaeroelasticcontrol

ThepresenceofanMLAcontrollawissimulatedby command-ing control surface deﬂections

δ

MLA during the static analysisof themanoeuvreconditions.Forpush-overandpull-upmanoeuvres, thesecontrolsurfacedeflectionsaresymmetric,i.e.thedeflections ontherightwingequalthedeflectionsofthecontrolsurfaceson theleftwing.Incaseofasymmetricloadconditions,e.g.aroll ma-noeuvre,thesymmetricdeflectionsareadditionallysuperimposed byavectorofantisymmetriccontrolsurfacedeflections

δ

MLA,asym.

TheGLAcontrollawismodelledbythesecondaryfeed-forward paththatisshowninFig.5.Theverticalﬂowvelocityw issensed byanAngleOfAttack(AOA)sensorlocatedatthenoseofthe air-craft.Themeasuredvariationinangleofattack

α

meas ishighpass ﬁlteredtoprevent thefeed-forward controllers fromtryingto al-leviatethetrimangleofattack. Theresultingsignal

α

¯

meas isthen

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Fig. 4. Spoilerinducedincrementinsectionallift

clandsectionalmoment

cmforvariousspoilerdeﬂectionsobtainedbyCFD,theconventionalVLMwithoutcorrection

andthecorrectedVLM.

Fig. 5. Control scheme used to emulate the presence of an optimal gust load control law during the structural optimisation.

passed tothestackofFiniteImpulseResponse(FIR)filters associ-ated tothe individualcontrol surface pair. Thereby,one FIRfilter isusedper controlsurface pairconsistingofleftandrightcontrol surface. The z-transferfunctionofan FIRfilteroforderN canbe writtenas[38]: HFIR

(z)

=

N

n=1 hnz−n+1 (3)

withhnbeingthenth elementofthevectorofFIRﬁltercoeﬃcients

h.

Thesubsequentdelay tc accountsforthetime requiredby the

ﬁctitiouscontrollerforthecomputationofthecontrolsurface de-ﬂection commands

δ

c.The actuatorsforeach controlsurface pair

are modelled as nonlinear second-order systems with rate and deﬂectionlimits. After thecommandedsignals

δ

c havebeen

pro-cessed by the actuatormodels of the individual control surfaces, theresulting actualdeﬂections

δ

are forwardedto theaeroelastic model.

In parallel,the vertical ﬂowvelocity w is delayed beforeit is passedtothegustzoneinputsvgoftheaeroelasticmodel,seethe

lower path in Fig. 5. The different delays in the vector of time-delaystpdependontheﬂightspeedandthedistancebetweenthe

referencepoint,i.e.theaoaprobe,andtheaerodynamiccentresof theindividualgustzones.

It should be notedthat in this work, the assumption of one-dimensional turbulence proﬁles results inan exact measurement ofthegustvelocityatonlyonespanwisestation.Furthermore,no uncerntaintyinthedelaytc andpropertiesoftheactuatortransfer

function are taken into account. Under these circumstances, the feed-forward path used here can be considered as a highly ide-alisedgustloadcontroller.

3. Aeroservoelasticanalysisandoptimisation

Fortheoptimisationsrequiredinthiswork,staticanddynamic aeroservoelasticanalysesareperformedafterintegratingthe mod-els of aerodynamics, structure and control described in the pre-vioussection.Thissection describestheprincipalmethodologyof steadymanoeuvreanddynamic gust analysisaswell asthe gen-eralaspectsoftheoptimisationproblemformulation.

3.1. Analysis

Theanalysis ofquasi-steadymanoeuvre conditionsis done by finding the static equilibrium between inertial and aerodynamic forcesacting on the aircraft.The iterative search of therequired angle of attack, angle of sideslip and control surface deflections eliminatestheneedforthetrimparameterstobedesignvariables intheoptimisationproblem.Forsymmetriccases,theangleof at-tackandtheelevatordeflectionareusedastrimparameterstofind the longitudinal equilibrium between weight forces and the re-quiredlift.Theasymmetricrollmanoeuvreconditionalsorequires theequilibriumoflateralforces.Therefore,thetrimming parame-tersadditionallyincludeantisymmetriccontrolsurface deflections

δ

MLA,asymandthesideslipangle

β

.Asmultiplecontrolsurfacescan be used for rollcontrol, the weights of the individual deﬂection areusedasdesign variablesdeﬁning therollallocation

¯δ

MLA,asym. Asingle amplificationparameter r is then usedwithin the trim-mingroutinethatismultipliedwiththe vector ofweightstofind theactualindividualcontrolsurfacedeflections:

δ

MLA,asym

=

r

¯δ

MLA,asym (4)

For the dynamic analysis of gust encounters during horizontal flightconditions,thesimulationofthefree-flying flexible bodyis performedinthetimedomaininthreesteps:

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1. The discrete transfer functions of the FIR ﬁlters, compare Eq. (3), are transformed in the time domain by a bilinear transformation, andthe control surface commands

δ

c due to

thegustproﬁlesarecomputedasdepictedinFig.5.

2. Thecontinuous-timesignalofcommandedcontrolsurface de-ﬂections issubsequently used inthe nonlinear simulation of theactuator,includingactuatorratelimitationsanddeﬂection saturation.

3. The resulting actual control surface deﬂectionhistories

δ

are usedalongsidewiththegustproﬁles ina lineartime-domain simulationoftheoverallaircraftdynamics.

Subsequently,structuralfailureisassessed bythecomputation ofstrengthandbucklingreservefactorswiththewingdeformation resulting at the obtained equilibrium points of the steady cases and thetime historyof the dynamic analysis. Similar to the ap-proachusedby Werter[26],thestrengthfailurecriterionisbased on thework ofIJsselmuiden etal.[39],andthe buckling reserve factorsarecomputedbyabucklinganalysisbasedontheworkof Dillingeretal.[40].Itshould benotedthatonlylocalbuckling is takenintoaccountwiththebucklingpanelsbeingboundedbyribs andstiffeners.Forcomputationalreasons,thebucklingreserve fac-tors duringgust encountersare computedonlyforthemaximum principalstrainsobtainedinthedynamicanalysis.

3.2. Optimizationproblemformulation

Theobjectiveofalldesignoptimisationscarriedoutinthe cur-rent work isthe reduction of themass ofthe primary wing-box structure,i.e.theskinandspars.

The design parameters include structural and control design variables. Four variables are used for the thickness of skins and spars in each beam element, i.e. no chordwise variation of the thickness is allowed and the stringer thickness is held constant. The local minimum allowablevalue forthe material thickness is deﬁnedbasedonrequirementsresultingfrommanufacturing, han-dlinganduncontainedenginefailurecases.Whilethelayupisheld constant throughouttheoptimisationprocess, onlythe ply thick-ness is varied to ensure a continuous design space. Besides the laminate thickness variables, the laminate principal stiffness di-rectionisoptimisedintheformofadistributionofthereference angle

φ

forthe0◦ plydirectionasshowninFig.1.Thespanwise distributionoftheprincipalstiffness directionistherefore formu-latedasalinearcombinationofChebyshevpolynomials:

φ (

η

)

=

n

i=1 cφ,i

η

+

η

2

₋

₁

n−1

₊

_η

₋

_η

2

₋

₁

n−1 2 (5)

where n denotesthe number ofpolynomialsused. The vector of coeﬃcientscφ

= [

cφ,1

,

cφ,2

,

....,

cφ,n

]

T isusedasthestructural

tai-loringdesign variable.Asimilar approachbased onB-splineshas beenusedbyStodiecketal.[11] toensuresmoothproperty varia-tionsalongthespan.

The MLA design spaceis spannedby a vector ofcommanded controlsurfacedeﬂections

δ

MLA foreachloadcaseandadditionally therollallocation weights

¯δ

MLA,asym forasymmetricconditionsas roll manoeuvres. Finally, the GLA design variables consist ofone vectorofFIRﬁltercoeﬃcientsh foreachcontrolsurface pairthat isusedfordynamicgustloadcontrol.

Various constraints c

∈

R

>

0 are used to form the feasible regionthatisdeﬁnedasc

≤

1 inthedesignspace. Foreach com-ponent of the wingboxstructure, i.e. front spar, rear spar,upper skin,andlowerskin,onebucklingandonestrengthconstraintare formulated foreach beamelementandﬂight condition.The con-straints resulting fromthe time histories ofall gust analyses, i.e.

withthevarious gustgradients considered,areaggregatedtoone constraint using the Kreisselmeier-Steinhauser functions [41]. By this, the gust analysis results in one buckling and one strength constraintperbeamelementandwingboxcomponent.

The maximumand minimum control surface deflections used forMLAare boundedforsymmetric flightconditionsand formu-latedasconstrainsforrollconditions.Thecontrolsurfacerateand deflections occurring during gust encounters are limited by the actuatormodelsresulting inan alwaysfeasible GLA feed-forward path.Adampingconstraintisusedagustanalysisspeed,ensuring astable dynamic systemfornumericalpurposes during the time domaingustanalyses.

Itshould be notedthat ﬂuttermarginsandﬂuttercontrol are not considered in thecourse of thiswork. However, for numeri-cal reasons,the dynamic stability isconstrainedat thespeedsat whichthegustanalysesarecarriedout.

A single optimisation problem is formulated that consists of structuraland control design variables to minimise the wingbox structuralmasswithrespecttotheconstraintsdescribedabove.An activesetalgorithmisusedtoreducethecomplexityofthesearch fortheoptimalsolutionbyconsideringonlyasubsetofconstraints which are active atthe current designpoint. The gradient-based optimisationalgorithmrequiresthecomputationofaJacobian ma-trixat every optimisation iteration. The sparsity of this Jacobian isexploitedbyan eﬃcientprocedurethat runsonlytherequired analyses,e.g.astheGLAdesignvariablesdonotaffectmanoeuvre constraints,the respectivegradients are zeroanddo not needto becomputedbyﬁnitedifferentiation.

4. Analysisandresults

The previously described models and analysis procedures are now used for the optimisation of an aircraft wingstructure. Af-tera description ofthe test case, eight optimisations are carried outwiththeindividual technologies,i.e.MLA,GLA andstructural tailoring, being activated or deactivated. Based on the resulting designs, the interaction of manoeuvre load alleviation, gust load alleviationand passive structuraltailoring isinvestigated next. A study ofthesensitivity ofthemajor ﬁndings withrespect tothe knockdownfactorapplied to thematerial propertiesispresented attheendofthesection.

4.1. Testcasedescription

Theanalysesandoptimisationspresentedinthisworkare con-ductedon a generic long-haul transport aircraftmodel. The con-ﬁgurationbelongstocategory4E(ICAO/EASAaerodromereference code)andhasaMaximumTake-OffWeight(MTOW)ofmorethan 250,000kg.

TheairframestructureismadefromAS4/3501-6composite ma-terial.Theindividuallayersofunidirectionaltapeareplacedinan angleof0◦,90◦ and

±

45◦ relativetothereferencedirection.The layup isalso deﬁnedby ﬁxed percentagesof theindividual layer directions.Furthermore, onlysymmetric andbalanced layups are considered.Tailoringisexertedinthewingskinsonly,theprimary stiffnessdirectionofthesparscoincideswiththebeamaxis.This meansthatthe desiredbendingtorsioncouplingisonly achieved bymodifyingtheextensionshearcouplingintheskins.The max-imumnumberoftheChebyshevpolynomialsusedasshape func-tionsforthedistributionofthereferenceangle

φ

issettoﬁve.The wingstructureisdiscretisedusing34beamelements.

The employed conventional control surface layout consists of sixspoilercontrolsurfacesaswellasaninnerandanouteraileron asshowninFig.6.Allwingcontrolsurfacesareusedfor manoeu-vreloadalleviationandrollcontrolwhileforgustloadalleviation, onlytheouter threespoilersandtheaileronsare used.Whilethe

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Fig. 6. Schematicdrawingoftheusedconventionalcontrolsurfacelayoutconsisting ofsixspoilersandtheinneraswellastheouteraileron.

Table 1

SummaryoftheDesignSpace. Design Variables

Laminate Thickness (Skins and Spars; t) 4·17 Tailoring (Upper and Lower Skin; cφ) 2·5

MLA (δMLA+¯δMLA,asym) 4·8

GLA (h) 16·5

Total 190

actuationcharacteristics,i.e.maximumrate,naturalfrequencyand dampingarethesameforthespoilersandtheailerons,the down-ward deflectionlimitsdiffer.Ailerondeflections aresymmetric to thezeropositionwhereasspoilerscanonlybedeflectedupwards. An order of16 is used forthe FIR filter ofeach control surface usedforgustloadalleviation.

Theaerodynamic modelincludeswingandtailliftingsurfaces, andnoaerodynamic fuselage isconsidered.The panel mesh con-sistsofmorethan104panels.Theconﬁgurationisdividedinto10 gustzonestoaccountforthedelayoccurringwhenthegustmoves alongtheaircraft.

Theconstraintsareevaluatedatthree,previously selected rep-resentative manoeuvre ﬂight conditions:a 2

.

5g pull-up manoeu-vre, a

−

1g push-over manoeuvre and a roll manoeuvre with a predeﬁned roll rate at a load factor of 1

.

67g. The gust analysis iscarriedoutatthedesignspeedintheMTOWconfiguration.The analysis includes 15 discrete gust gradients analysed in a range from nine to 107 m as specified by the certification specifica-tions forlarge aeroplanes[42]. Updraughtanddowndraught gust conditionsare considered. Themodal basisused forthedynamic analysisconsistsof31modes,includingthesixrigid-bodymodes. Forthegiventest case,thedesign spaceresultsin190design variablesthat aresummarisedinTable1.Thestarting pointofall optimisations is an over-sized but feasible structure. The design variablesassociatedwithMLA,GLA orstructuraltailoringare ini-tialised with a zero value. Only the wing structure is optimised whiletheremainingairframeisfixedthroughouttheoptimisation. Theoptimisationsarestoppedwhenthechangeinthewingbox mass between two iterations is less than 0.01 kg, and the con-straintsaresatisfiedwithinatoleranceof10−4.

4.2. Individualandcombinedmethodsformassreduction

Various optimisations are carried out in which the different methods are active orinactive toinvestigatethe inﬂuenceof the different technologies on the primary wing structural mass. Ta-ble2showsthevariousperformedoptimisationstogetherwiththe active andinactive subsets ofthe designvariables. The reference

Table 2

Descriptionofthevariousoptimisationconﬁgurationswithactive()and inactive(-)subsetsofdesignvariablesandtheresultingmassreduction normalisedtothemaximumachievablemassreductionobtainedbythe concurrentoptimisationwithalldesignvariables(TMG).

Setup Design Variable Subsets Normalised WeightReduction Thickness Tailoring MLA GLA

N - - - -T - - 20.9% M - - 71.5% G - - 1.1% TM - 95.2% TG - 21.6% MG - 88.4% TMG 100%

Fig. 7. Normalisedmassreductionobtainedintheoptimisationsandthedifferences betweenthevariouscombinations.Theareaofthecirclescorrespondstothe nor-malisedmass reduction.100%signiﬁesthe maximumachievable massreduction combiningstructuraltailoring,MLAandGLA.

(N)isan optimization whereneither activecontrol, i.e.MLA and GLA, nor passive structuraladaptation is considered. Besides op-timisationsincludingthe differentmethods alone(T, M,G), their possiblecombinations are considered (TM, TG,MG, TMG). Inthe following, the achieved mass reduction relative to the reference caseisnormalised tothe reduction obtainedby theoptimisation inwhichall designvariables areactive (TMG).Theachieved nor-malisedmassreductionineach oftheoptimisationsisalsogiven inTable2.Asexpected,themaximumachievablereductionin pri-marywingstructuralmassisobtainedbytheTMGoptimisation.It canbeseenthatthesumoftheresultsoftheoptimisationswith theindividualmethodsissmallerthantheresultsofthecombined methods. For example, the sum of the results of the T, M and G optimisation yields a normalised massreduction of94% being sixpercentlower than theresultinthe concurrentoptimisation (TMG, 100%). This indicates that the various methods interactin asynergisticwaythat,ofcourse,isonlyrevealedinsimultaneous optimisations.

TheresultsareillustratedinFig.7inwhichtheareaofeach cir-clecorresponds totheobtainednormalised massreduction. Also, the differencesbetween the optimisation results are shown. The most synergistic effect is observed in the combination of active

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Fig. 8. Componentwisemassreductionobtainedintheoptimisationsnormalisedto theachievablemassreductionobtainedintheTMGoptimisation.

manoeuvreandgustloadalleviation.Whilethesumofnormalised mass reduction achieved by the separate use of the active con-trolmethodsresultsin73%(M+G),thecombineduseyieldsa15% higher mass reduction of 88% of the maximum achievable mass reduction.ThissigniﬁcantsynergisticeffectbetweenMLAandGLA has beenobserved before [19]. A similar though lessremarkable trend is visible in the combination of MLA with structural tai-loring resulting in a two per cent higher mass saving than the sum of the savings obtained in the optimisations with the indi-vidual technologies. In contrast,no synergistic effect isobserved by thecombinationofGLA andstructuraltailoring.Herethesum oftheeffectsobtainedinseparate optimisationsequals theeffect observedintheoptimisationwiththecombineduse.Itis further-more worth noting that, themass reduction obtained by MLA is underestimated whenoptimisedindividually comparedto a com-bination with GLA, structural tailoring or both. The same is ob-served forGLA where theeffectin theindividual optimisation is onlyanormalisedmassreductionofonepercentcomparedtofor exampleanaddedvalueof16%(MG-M)inthecombinedusewith MLA or only ﬁve per cent(TMG-TM) in the combined use with MLAandstructuraltailoring.Forstructuraltailoring,thisdoesnot hold.Theaddedvalueoftailoringis12%whencombinedwith ac-tivecontrol(TMG-MG)beingninepercentlowerthanobservedin theindividualoptimisation(T:21%).

To understandthe interaction, the normalised massreduction intheindividual wingboxcomponentsgiveninFig.8shows,that the main focus needs to be placed on the driving constraints in the skins. Although optimising the spars does not contribute to the overall mass reduction, their consideration in the optimisa-tion problem is still important because of their contribution to theoverallstiffnessdistributionofthewingbox.Theratiobetween manoeuvreandgustconstraintsintheskinsoverthespanwise po-sition isshownin Fig.9.Values of morethan oneindicate areas wheremanoeuvresarecritical,lessthanone wheregusts dimen-sion thewing. Whilethe wingresultingfromtheN optimisation is both, dimensioned by manoeuvres and gusts, the application of MLAin theM optimisationmakes most ofthewing structure gust-critical. In contrast to that, the applicationof GLA in the G optimisation results in a entirely manoeuvre driven design. The valuesatthetipareirrelevant,asthethicknessreachesthe mini-mumallowablethickness,resultinginalocallyoversizedstructure whereneithergustnormanoeuvreconstraintsareactive.

These resultsexplain the synergybetween MLAandGLA that can be observed in MG optimisation, as each of the two meth-ods allows more opportunities for the other. The application of structuraltailoring intheT optimisationis lessinﬂuentialto the constraintratiothantheactivecontrolmethodsbutincreasesthe manoeuvrecriticalityslightlycomparedtothereferenceN.This

in-creaseinmanoeuvrecriticalityduetostructuraltailoringexplains (i) that the application of GLA (TG vsT) can not result inmore beneﬁtsthanobservedintheindividualoptimisation(GvsN),and (ii)thesynergisticeffectinthecombinationofMLAandstructural tailoring.

Forfurtheranalysisofthemechanismofstructuraltailoringin thepresenceofactivecontrol,thenondimensionalbending-torsion couplingratioasdeﬁnedby[4] isused:

=

√

K

E I G J (6)

withE I beingthebendingstiffness, G J thetorsionalstiffnessand

K thebending-torsioncouplingstiffness.Positivevaluesof

indi-catea positive bending-torsion coupling,also known aswash-in, i.e. upward bending accompanied by a nose up twist. Negative valuesrelatetothedesiredwash-out,i.e.upwardbending accom-paniedbyanose-downtwistshiftingthecentreofloadinboard.

The characteristics of the distribution of tailoring induced bending-torsion coupling shown in Fig. 10 are similar with and withoutMLA (TvsTM), exceptforthetip, thatis lessimportant fortheoverallloadredistribution.Especiallynotableisthatinthe presenceofMLA,theoptimiserincreasestheamountofwash-out eventhoughthenegativebending-torsioncouplinghasanegative effectonthecontrolsurface effectivenessasshownbyWeisshaar [4].

With the addition of GLA, the optimiser reduces the amount ofnegative bending-torsion couplingin the outboardarea ofthe wing. In the TG optimisation, only the very outboard part is af-fected but comparing TMG and TM, the addition of GLA signif-icantly inﬂuences the characteristics of the bending-torsion cou-plingdistribution.

As the design resulting from the TM optimisation is mainly gust-critical,the application ofGLA requires the optimiser to in-creasetheeffectivenessofGLAbystrengtheningtheauthoritythe controlsurfaceshaveincontrollingthegustloads.Tosupportthis thesis,wedeﬁnethe

H

2 normofthetransferfunctionofacontrol surfaceinput toa bendingloadoutputasameasurefortheload control authority. The

H

2 norm is computed with and without structural tailoring,i.e.

φ

lo

,

φ

up are set to zero after the optimi-sation, tocharacterise the inﬂuence ofstructuraltailoringon the loadcontrolauthority.Therelativedifferenceisgivenby:

_H2

=

H

2

H

2,φ=0

−

1 (7)

The relative difference in the

H

2 norm of transfer functions from the ailerons to various spanwise load outputs is shown in Fig.11.In all cases,structuraltailoringreducesthe bendingload control authority of both ailerons with the outer aileron being moreaffected.Asinitiallyexpected, thestructuraltailoringinthe TMG optimisationhas lessdetrimentaleffecton the loadcontrol authoritycomparedtotheTMoptimisation.

Inaddition tothe described differencesinstructural tailoring, thedifferencesinMLAdesignare discussednext.As anexample, thecontrolsurfacedeflectionsgivenbytheoptimisedMLAduring thepush-overmanoeuvreareshowninFig.12.Inalloptimisations except for the M optimisation, the -1 g manoeuvre contributes to the critical loads, andthe optimiser uses MLA to redistribute the loads, reducing the level of constraints. Exceptfor the outer aileron, whichin all cases isdeflected downwardsto unload the wingtip, the characteristics of the MLA deflections are different betweenthe caseswith (TM andTMG)and without (MG) struc-turaltailoring.Without tailoring,the deflectionsincrease towards the tip whilewith tailoring,the deflections are reduced towards thetip.Thelatteristheexpectedpatternshiftingtheloadinboard andissimilartothepatternsfoundbyStanford[43] andKrupaet

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Fig. 9. Spanwise distribution of the ratio between manoeuvre and gust constraints.

Fig. 10. Spanwise distribution of the bending-torsion coupling parameter .

Fig. 11. Effectofstructuraltailoringonspanwiseloadcontrolauthority character-ized bytherelative differenceinthe H2 normofthe transferfunction froma controlsurfaceinputtoaspanwisebendingloadoutputwithandwithout struc-turaltailoring.

al. [27]. While ﬁnding the exact reasonforthe pattern observed intheMGoptimisationwouldrequirefurtheranalysis, the differ-entcharacteristicsjustifytheneedforanintegrateddesignofMLA together withthevariablesofthestructuraltailoringtomake op-timaluseofbothtechnologies.

Dueto thedynamic natureofgustencounters, thedesign dif-ferences in the GLA system are even more challenging to grasp.

Fig. 12. OptimisedcontrolsurfacedeﬂectionsforMLAduringthepush-over ma-noeuvre.

Table 3

Relativedifferenceintheﬁrstsymmetric bendingfrequencyoftheresultingwing structuresobtainedinthedifferent opti-misationscomparedtoN.

Optimisation FirstSym.Bending FrequencyDifference T -9.2% M -12.4% G -0.1% TM -25.2% TG -9.4% MG -15.8% TMG -25.9%

However,the primary influenceon thecontrol lawcanbe linked tothefirstsymmetricbendingmodefrequencythat,forthegiven typeofconfiguration,governsthedynamicgustloads[44].

ThefrequencyresponseoftheFIRfilterassociatedwiththefifth spoiler,includingthehigh-passfilteroftheAOAprobeisshownin Fig.13.Thefrequencyresponsecharacteristicsofthefilter,e.g.the peakposition,resultingfromthevariousoptimisations are differ-entduetothevariationofthestructuraleigenfrequenciesgivenin

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Fig. 13. Bode plot of the frequency response of the optimal FIR ﬁlter associated to the ﬁfth spoiler as optimised in the different setups including GLA.

Fig. 14. Relativedifferencebetweentheopenandclosedloopspanwisemaximum bendingmomentdistributionduringgustencounters.

The differencein theresultingGLA mechanismis analysedby a comparisonofthe relativedifferenceon themaximumbending moment around the longitudinal axis x between open loop and closedloopgustloadsdeﬁnedas:

Mx,GLA

=

max

(M

x,gust,open loop

)

max

(M

x,gust,closed loop

)

−

1 (8)

Therelativedifferenceinthemaximumbendingmoment distribu-tionisshowninFig.14forthedifferentcontrollersresultingfrom the optimisations G,TG, MGandTMG. Asigniﬁcant difference is visiblebetweenthecaseswithandwithoutmanoeuvreload alle-viation (GandTGvsMGandTMG). Duetothereducedstiffness, the controller ismuch moreeffective inreducing the gust loads. Anotherinterestingpoint isthatintheTGoptimisation,the opti-miser evenallows thecontrollerto increasethe bendingloadsat amid-wingpositionof60-70%ofthenormalisedhalfspan,asthis regionisnotdimensionedbygustloads,seeFig.9.Thismeansthe optimiseradoptsthemechanismtotheprevailingloadhierarchy.

In conclusion,only thesimultaneous designof GLA withMLA andstructuraltailoringcanexploitthefullpotential.

4.3.Sensitivityofmaterialpropertiesknockdownfactor

Inthe design ofsafety-critical aircraft structures, the nominal allowablesaresignificantlyreducedbyknockdownfactors account-ing forlow-speedimpact damage, material scattersand environ-mentaleffectsastemperature,moistandUVlight[45].Avarietyof knockdownfactors isinvestigatedbecause newdesignparadigms andmaterialsareenvisionedinthefuture.Theinclusionoffatigue models inthe optimisation problemcould replace therespective knockdown factors allowing formore flexible wingdesigns [46]. Also, the development of materials with significantly higher al-lowables,e.g.carbonnanotubes,canreducethestiffness offuture wingstructuresdrastically[47].

Whilemostoftheexampleslisted intheintroductiongive no informationontheappliedknockdownfactor,therearealso stud-ieswhichdonotconsideranyknockdownfactor[48],[49].Other studiesusemaximumstrainallowablesthataremoreconservative [27].

Theresultsshownintheprevioussectionwere producedwith aknockdownfactorof0.65appliedtothematerialstrength prop-erties,i.e.longitudinal/transverse tension/compressionstrength as wellasthein-planeshearstrength.Inthissection,theknockdown factorisgraduallychangedfrom0.35to0.95toinvestigatethe ef-fectofthematerialpropertiesonthemainﬁndingsoftheprevious section.

Fig.15showstheresultingprimary structuralmassforvarious knockdownfactorsnormalisedtotheprimarystructuralmass ob-tained in the N optimisation using a knockdown factor of 0.65. A reduction of the knockdown factor from 0.65 to 0.35 results in an increase of the optimised mass of100% inthe absence of active control and structural tailoring (N). The sensitivity is less pronouncedwhen all technologiesarepresent(TMG). Itis worth notingthat, anincrease inthematerialknockdown factorof0.01 corresponds to amass reduction of1.60% in theN optimisations compared to 0.75%in the TMG optimisations. The net beneﬁtof new material technologies should therefore always be assessed with takinginto account all system andtechnologies that inﬂu-encetheloadsonthewingstructure.

The inﬂuence of the material knockdown factor on the mass reductionachievablebytheindividualtechnologiesandtheir com-binations is given in Fig. 16. The mass reduction achievable by

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Fig. 15. Inﬂuenceofthematerialknockdownfactoronresultingobjectivefunction, namelyprimarystructuralmass,normalisedtotheobjectiveresultingfromtheN optimisationwithaknockdownfactorof0.65.

Fig. 16. Inﬂuence ofthematerialknockdownfactor onthe massreduction nor-malisedwithrespecttotheNoptimisations.

Fig. 17. Thedifferenceintheliftdistributionduringthe2.5 gmanoeuvredueto structuraltailoring(TvsN)fordifferentknockdownfactors.

structural tailoring is increasing with higher knockdown factors, i.e.moreﬂexible andhencelessstiffstructures. Theeffect ofthe knockdownfactor onthetailoring-induceddifference inthe pull-up manoeuvre liftdistribution (T vs N) isgiven in Fig. 17. With higherknockdownfactorsandlessbendingstiffness,the bending-torsioncouplinginducedbystructuraltailoringisresultinginmore wash-outbyhigherdeﬂecitons.

The potential of MLA is, as expected, negatively affected by higher knockdown factors asthe higher ﬂexibility has detrimen-taleffectsonthecontrolsurfaceeffectiveness.

Forthe investigated rangeof knockdown factors, the individ-ualapplicationofGLAisnotleadingtoanymassreductionasfor allNoptimisationsthegust constraintsarebelowthemanoeuvre constraintlevel.

Forall usedknockdownfactors,tailoringisincreasing the ma-noeuvrecriticalitywhichexplainsthat nointeractionwithGLAis observedinthe absenceofMLA. Itis interesting tonote that for allknock factors,GLA onlyhasadded value ifMLAisactive. The interplayofMLA andGLA observed inthe MGandTMG optimi-sations is improved for lower knockdown factors, which can be linkedtothehighercontrolsurfaceeffectivenessthatcomes with stifferwings.

Intotal,a substantial shiftofeffectivenessfromactive GLA to passive structuraltailoring is observed withincreasing structural flexibility.Foraknockdownfactorof0.35,thecombinationofMLA andGLA can lead to 94% of the possible mass reduction reduc-ing the added value of structural tailoring to six per cent. For knockdownfactorshigherthan0.65,theaddedvalueofactiveGLA shrinks down to less than five per cent of the achievable mass reduction. That means that with the trend of increasing mate-rialallowablesandtheindustrialisationofstructuraltailoring,the masssavingpotentialofGLAisreduced.However,theaddedvalue ofMLAisstillsignificant.

5. Conclusions

The interaction between the three technologies of active ma-noeuvreloadalleviation,gustloadalleviationandstructural tailor-ing has been investigated. The simultaneous design optimisation ofawingstructure together withthe controlsystemwas carried out onthe example ofa typical long-haultransport aircraft con-ﬁguration.Theoptimisationswiththeindividualtechnologiesand their combinations reveal, that, asalready found by previous re-search, themaximum reduction inprimary wingstructuralmass isachievedbyaconcurrent useofallthreetechnologies.The dis-cusseddesign differencesthat are observedinthe individualand combinedoptimisationsindicatethatcombinedoptimisationis re-quiredto(i) exploitthesynergies ofactivecontrol andstructural tailoringtothefull extentand(ii)toassessthepotential ofeach ofthetechnologiescorrectly.

Aninvestigation ofthe sensitivityof theresults regardingthe knockdownfactorapplied tothematerial propertiesshowedthat withincreasingstructuralflexibility asignificantshiftin effective-ness from active gust load control to passive structuraltailoring isobserved.Whiletheincreasing materialallowables andthe ex-ploitationoftheanisotropicmaterialpropertiespromisesignificant masssavings,therelativepotentialoftheactivegustloadcontrol is reduced. The net benefitof new material technologiesshould, therefore,beassessedbytakingintoaccountactivecontrol.

Asthepresentworkinvolvesagenerallyidealisedapproachfor activeloadalleviationandstructuraltailoring,futurestudieswould benefitfrommore refined implementations.These enhancements couldincludestackingsequenceoptimisation,manufacturing con-straints, chordwise thickness variation or stringer shape and ge-ometryoptimisationaswellasfailurescenariosandmoredetailed constraints, e.g. including continuous turbulence loadconditions. Especiallytheconsiderationoflowspeedhandlingqualitiesis es-sentialasthey aredefining therequiredcontrolsurface effective-nessoftheoutboardaileron.Theaerodynamicmodellingapproach would benefit from the consideration of compressible and tran-soniceffectsenablingtheinclusionofstabilityconstraintsthatare importantforhighaspect ratio wingdesigns.With the introduc-tionofflutterconstraints,fluttersuppression methodsneedtobe considered alongside. Further studies are also required tpassess thetransferabilityofthemainresultsofthisworktootheraircraft configurationsandsizes.

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Declarationofcompetinginterest

Theauthorsdeclarethattheyhavenoknowncompeting ﬁnan-cialinterestsorpersonalrelationshipsthatcouldhaveappearedto inﬂuencetheworkreportedinthispaper.

Acknowledgements

Theauthors wanttothankPaulLancelotfromDelftUniversity ofTechnology forprovidingthe CFDdataused forthe derivation ofthecorrectionlawofthedownwashdistributionusedfor mod-ellingspoilerdeﬂectionswithpanelbasedaerodynamicmodels.

This research didnot receive any speciﬁc grant from funding agenciesinthepublic,commercial,ornot-for-proﬁtsectors. References

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