1

Aeroelastic Optimisation of an Alternative HighAltitude Long Endurance Wing Stiffening StructureNicholas F. Giannelis and Gareth A. Vio

Abstract: This paper considers an alternative internal wing stiffening structure to improve the volumetric efficiencyof a generic High Altitude Long Endurance aircraft wing. Finite element models for this structure and an equivalentconventional configuration are developed in NASTRAN. A Binary Genetic Algorithm optimisation routine is employedunder transient and dynamic aeroelastic constraints to determine the optimum weight for each model. A quasi-staticdiscrete gust model and linear flutter analysis is used for the transient and dynamic aeroelastic formulation respectively.Results find that although qualitatively similar aeroelastic behaviour is observed in both configurations, the alternativetopology is structurally inefficient in high aspect ratio applications.

IntroductionThe past decade has seen a substantial increase in research

and development for High Altitude Long Endurance (HALE)unmanned aerial systems [1]. The obvious driving force forsuch systems has been the defence sector, where intelligenceand reconnaissance operations may be implemented economi-cally and without the risk of human casualty [2]. Nonetheless,commercial and scientific applications, including communica-tion network modules, earth and atmospheric remote sensingand long endurance flight research, are becoming common-place [3–5].

With highly complex, multiobjective mission profiles, thevolumetric efficiency of HALE structures is of pivotal concern.An effective topology is necessary to house the plethora of sub-systems required by military or science specifications. [6] hasexplored the improvement of high aspect ratio wing structuralefficiency through the redistribution of wing stiffening mem-bers of a conventional wing box configuration, with advantagesobserved in both weight and flutter stability of the platform. In[7], the issue of volumetric efficiency of a stored HALE wing isaddressed, with a skin integrated stiffening structure permittinga 25-35% wing weight reduction compared to a baseline. Anintegrated multi-lobe wing stiffening structure is proposed in[8], with a reduction of 22% wing weight relative to correlatedweights of advanced transportation systems. This analysis isfurthered in [9], where the flutter stability of the multi-lobestiffening structure exceeded an equivalent rib and spar wingby 13.9%. In performing structural optimisation with the largeparameter sets required by HALE aircraft, global heuristic op-timisation methods, such as the Genetic Algorithms used in[10] and [11], have proven effective in locating globally opti-mum solutions.

The long endurance aspect of HALE missions necessitatesa high aspect ratio planform to achieve the required aerody-namic performance [12]. Consequently, such vehicles typ-ically exhibit low structural weight with highly flexible lift-

Nicholas F. Giannelis. School of AMME, Building J11, The Uni-versity of Sydney, NSW, 2006, AustraliaGareth A. Vio. School of AMME, Building J11, The Universityof Sydney, NSW, 2006, Australia

ing surfaces, making them susceptible to significant transientaeroelastic loads from atmospheric gusts and turbulence [13].Substantial research efforts have thus been devoted to the mod-eling of aeroelastic phenomena in high aspect ratio wings [14,15]. Traditionally, a quasi-static, discrete gust formulation,based on a worst case one-minus-cosine waveform has beenapplied to model transient aeroelastic loads [16]. Statisticalmodeling techniques, including a Statistical Discrete Gust andcontinuous Power Spectral Density functions have since beendeveloped [17], however evidence suggests that the worst casegust is an application of an extreme excursion under the statis-tical methods [18, 19]. More recently, high fidelity, transientComputational Fluid Dynamics (CFD) simulations have beenemployed in the aeroelastic analysis of HALE vehicles [20].Although the computational overhead of such methods maybe mitigated through Reduced Order Modeling, as in [21], thecomputational effort remains significant compared to a discreteformulation. A number of recent studies have also focused onthe significance of nonlinearities in the aeroelastic response ofhigh aspect ratio wings [5, 15, 22], with [22] observing a 50%reduction in flutter stability when accounting for nonlinear ef-fects. Nonetheless, [23] concluded that although nonlinearitiesare significant for HALE aircraft, quasi-static linear analysisremains a primary tool in the preliminary design phase.

In this paper, an alternative internal wing stiffening structurewith improved volumetric efficiency will be developed for ageneric HALE wing. An equivalent conventional rib and sparmodel is also presented as a baseline. The structures will beoptimised for weight under dynamic and transient aeroelasticconstraints through use of a Binary Genetic Algorim (BGA).The formulation of the optimisation routine, along with linearaeroelastic system and discrete gust model will be described.The optimal structures for each configuration will then be com-pared in terms of structural sizing and aeroelastic performance.

MethodThe method is broadly divided into three sections. The first

details the development of the two structural models under aFinite Element scheme. The aeroelastic formulation applied inthis paper is then presented, with definitions of both the dy-namic and transient phenomena to be analysed. The structuraloptimisation routine is then described, with focus given to the

Fourth Australasian Unmanned Systems Conference : 1–8 (2014)

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optimisation constraints, fitness function and the Binary Ge-netic Algorithm used.

Structural ModelThe wing planform has been developed to reflect a generic

HALE vehicle structure. A rectangular section of aspect ratio7 (2.5 m chord and 17.5 m span) represents the base wing plan-form for both conventional and multi-lobe stiffening configu-rations. A typical high lift-to-drag aerofoil profile for HALEapplications [7], the NASA LRN1015 shown in Figure 1, givesthe aerodynamic section in both structures.

0 0.2 0.4 0.6 0.8 1−0.1

0

0.1

x/c

y/c

Fig. 1. LRN1015 Aerofoil Profile

The finite element models for analysis are realised in NAS-TRAN. The external wing skin is identical for both stiffenedconfigurations, and is represented by quadrilateral shell ele-ments. The conventional model internal structure, given inFigure 2, employs a rib and spar configuration. Four sparsextend from wing root to tip, with eight equally spaced ribsstationed along the span, a representation of the Global Hawkinternal wing structure [24]. Both ribs and spars are comprisedprimarily of quadrilateral shell elements, with triangular ele-ments used to close the rib sections at the leading edge. Thiswork does not attempt to optimise the topology of either theconventional or alternative structure, but rather seeks to ascer-tain the efficacy of the multi-lobe stiffening structure for highaspect ratio application. Each spar and rib is grouped individ-ually for sizing of the shell thickness, with the wing skin alsogrouped separately.

Fig. 2. Conventional Internal Structure

An equivalent alternative wing stiffening structure is givenin Figure 3. The vertical webs are stationed at equivalent chord-wise positions as the conventional model and consist entirelyof quadrilateral shell elements. Rigid bar elements provide

continuity between the vertical webs and external skin. Theupper and lower surface lobe arcs are also comprised of quadri-lateral shell elements and provide the improved volumetric ef-ficiency for the multi-lobe structure. The minimum internalvolume in the alternative configuration is 1.12 m3, a 65% in-crease from the 0.68 m3 maximum internal volume of the con-ventional structure. Each of the lobe arcs, webs and the skinis again grouped independently for sizing, where the lobe arcgroups are not segmented in the spanwise direction and a sin-gle group runs along the entirety of the span.

Fig. 3. Multi-Lobe Internal Structure

In both configurations cantilever boundary conditions areapplied at the wing root to the internal stiffening structure.Nodes at the wing root are constrained in six degrees of free-dom to represent attachment to the fuselage. Aluminium 6061is used throughout each model, with material properties rele-vant to the analysis given in Table 1. The base models devel-oped are seeded with a uniform shell thickness of 5 cm for eachstructural member, representing the heaviest possible structurein each case.

Table 1. Al-6061 Material PropertiesProperty Value

Elastic Modulus (GPa) 68.9Shear Modulus (GPa) 26.0

Poisson’s Ratio 0.33Density (kg/m3) 2700

Aeroelastic FormulationOptimisation of the two wing configurations is performed

under dynamic aeroelastic constraints. Specifically, this paperconsiders the flutter instability and the transient wing responseto a quasi-static discrete gust load under quasi-static aerody-namics.

Dynamic AeroelasticityUnder the assumption of linearity, the dynamic aeroelastic

problem is governed by the system described by:

Aq +(1

2ρUB + D

)q +

(1

2ρU2C + E

)q = Q [1]

where A is the inertial matrix, B and C are the aerodynamic

and structural damping matrices respectively, D and E are theaerodynamic and structural stiffness matrices respectively, ρ isthe air density, U is the free stream velocity, q are the gener-alised displacements, q is the first time derivative, q is the sec-ond time derivative, and Q are the generalised external forcesapplied to the system. For a given structure, the inertial, damp-ing and stiffness matrices are constant, reducing the stabilityof the system to a function of dynamic pressure.

The flutter instability is a product of the interaction of or-thogonal modes of vibration. The coupling of elastic modes ina linear system produces self-excited oscillations of the struc-ture, typically resulting in catastrophic failure. As identifica-tion of the flutter condition is concerned with the underlyingstability of Equation 1, the generalised excitation force, Q, istaken to be zero. The flutter analysis then proceeds throughNASTRANs 145 Solution, with the inertial, damping and stiff-ness matrices of the system derived from the FE solution. Lanc-zos eigenvalue extraction is used to determine the first ten massnormalised eigenvectors and eigenfrequencies for flutter anal-ysis. Subsonic Doublet-Lattice theory is employed to deter-mine the aerodynamic damping and stiffness matrices, with 25spanwise and 10 chordwise panels across the wing planform.The aerodynamics are determined at a nominal flight condi-tion of 160 m/s TAS at 20 km altitude, representing the cruisecondition of the popularised HALE vehicle Global Hawk [25].Further, matched frequencies are used to calculate the fluttervelocity.

Transient AeroelasticityConverse to the intrinsic flutter instability, the transient aeroe-

lastic response is concerned with the time domain solution dueto non-zero external excitation, namely, a gust load. A discretegust disturbance is modeled as the generalised excitation forcein Equation 1 to characterise the transient aeroelastic responseof the linear system. The gust load is deterministic and as-sumes a vertical disturbance, constant along the wing span witha small magnitude relative to the freestream velocity. Conse-quently, the discrete gust velocity acts to increase the effectiveangle of attack, and hence the aerodynamic forces experiencedby the wing.

A one-minus-cosine waveform is used to model the magni-tude of the gust velocity in this analysis. In the time domain,the gust amplitude is given by:

Wg(t) =1

2

(Wref

(H

12.5

)1/7)(

1− cos2πt

tg

)for ti ≤ t < tf [2]

where Wg(t) is the gust amplitude at time t, ti is the gust starttime with a gust duration of tg and end time of tf . Wref is thereference gust velocity for the flight condition andH is the gustgradient, which defines the time taken for the gust to achievemaximum amplitude. FAA regulations FAR 25 recommend agust gradient of 12.5c for certification, where c represents thechord length [20].

In the present analysis, a discrete gust loading at the cruisecondition is considered. For this flight conditionWref = 15.24

m/s, tg = 0.286 s and H = 31.25 m. The resulting gust inputwaveform, beginning at time 1 s, is given in Figure 4.

The transient aeroelastic analysis is performed under NAS-TRANs 146 Solution, with analogous aerodynamics and flightconditions to the flutter solution. A time step of 0.01 s isused for a simulation time of 2.5 s, allowing sufficient time toobserve decay in the wings displacement amplitude. Controlpoints at the wing tip leading and trailing edges are monitoredfor displacement. The FAR 25 regulations specify that underdiscrete gust loading, the aircraft be constrained to plunge mo-tion only [26]. As such, the critical parameter categorisingthe the transient aeroelastic response of the models is the rootbending moment about the aircraft longitudinal axis. Rigidbody elements are used to connect the constrained wing rootnodes to the centroid of the root aerofoil section, where thetotal root bending moment is computed.

0 0.5 1 1.5 2

0

5

10

15

Time (sec)

Gus

t vel

ocity

(m

/s)

Fig. 4. Discrete Gust Disturbance Velocity Profile

Optimisation RoutineThe objective of this work is to determine the minimum

weight wing configuration that conforms to both a minimumflutter speed and maximum bending moment constraints. Assuch, the problem is formulated as a constrained optimisa-tion, looking to determine the vector of design variables x =

(x1, x2, ...xn)T that minimises the fitness function f(x) sub-

ject to the inequality constraints contained in g(x):

g(x) ={gi(x) ≤ 0, for i = 1, 2, ...,m

with, l ≤ x ≤ u[3]

where l and u are the vectors of lower and upper limits of thedesign variables respectively. The design variables specify thepanel thickness of each structural member, with a search spacebounded by li = 0.001 m and ui = 0.05 m for the ith panelthickness.

Although the objective of the optimisation routine is to de-termine the minimum weight structure for each configuration,the aeroelastic stability and the severity of the transient re-sponse impose significant constraints to the optimal solution.These conditions are imposed as inequality constraints g1(x)and g2(x), where g1(x) represents the flutter mechanism andg2(x) the root bending moment of the respective structures.

4 Fourth Australasian Unmanned Systems Conference , 2014

Mathematically, the constraints are represented by:

g(x) ={FSV − g1(x) ≤ 0, for flutter speedBMV − g2(x) ≤ 0, for bending moment

[4]

where the values of FSV and BMV represent the minimumallowable flutter speed and maximum bending moment respec-tively. The optimal solution thus aims to satisfy simultaneouslya minimum bending stiffness to resist large root bending mo-ments, as well as a torsional stiffness requirement to delay theonset of orthogonal mode coupling, and hence, the flutter in-stability.

In this implementation of the optimisation, the flutter speedconstraint FSV is chosen to be 200 m/s, equivalent to the divespeed of typical HALE aircraft. Solutions producing a flutterspeed above this value are deemed to exhibit exhibit the bestpossible flutter performance as the instability occurs outside ofthe flight envelope. The bending moment constraint, BMV ,due to the gust load is taken to be -180000 N·m, the equivalentbending moment of that generated by an elliptical lift distribu-tion in steady level flight.

Fitness FunctionThe fitness function, f(x), for minimisation is the weight of

the respective wing structures. The constrained optimisationis converted to an unconstrained problem by augmenting thefitness function to include penalty terms for each of the aeroe-lastic constraints. The cost function for minimisation, φ, isthus given by:

φ = φ(x, r) = f(x) +m∑j=1

rjGj

[gj(x)

]︸ ︷︷ ︸

penalty term

[5]

where the term rj represents an arbitrarily large positive con-stant penalty parameter for the jth constraint and Gj is thepenalty function for each of the constraints, as given by:

G(x) ={|FSV − g1(x)|, for j = 1|BMV − g2(x)|, for j = 2

[6]

The penalty term only contributes to the cost function if theconstraints have not been satisfied. The penalty constants arechosen to impart similar magnitudes for both the flutter mecha-nism and bending moment. The large magnitudes of these con-stants are intended to severely penalise solutions that do notsatisfy the aeroelastic criteria, ensuring the optimal structureexhibits satisfactory aeroelastic performance. The modulus ofeach constraint is included to ensure penalty functions increasethe cost of solutions not meeting minimum flutter speed ormaximum bending moment. The cost function of the optimalsolution should thus represent the weight of the structure.

Binary Genetic AlgorithmIn order to determine the most efficient structure for each

configuration a Binary Genetic Optimisation (BGA) routine isapplied in the present work. As a whole, genetic algorithms arefounded upon Darwin’s principal of natural selection, survivalof the fittest. Design variables are expressed as genes, with

various permutations of the design variables examined. Theoptimal gene from a particular set is carried forward to the nextiteration, where it may seed a new set of solution genes for thenext generation. The process proceeds until an optimal gene isobtained.

BGAs represent the design variables as a discrete set throughchromosomes, essentially strings of binary digits. The creationof new solutions from a particular gene set is governed by theprincipals of:

• Crossover. A section of a pair of genes is swapped0 1 1 0 1 0 0 0 0 10 0 1 1 0 1 0 0 0 0

=⇒ 0 1 1 0 0 1 0 0 0 00 0 1 1 1 0 0 0 0 1

• Mutation. The value of a cell within a gene is randomlyswapped0 1 1 0 0 1 0 0 0 0 =⇒ 0 1 1 0 1 1 0 0 0 0

• Translation. The order within the gene is randomlyswapped0 1 1 0 0 1 0 0 | 0 0 =⇒ 0 0 | 0 1 1 0 0 1 0 0

• New Blood. Introduction of new genetic characteristics,independent of the current genes.

The length of each gene is determined by the range of val-ues in the design variable bounds, with each chromosome aconcatenation of each of structural groups panel thicknesses,represented in binary form. In this paper the optimisation al-gorithm follows the process given in Figure 5.

Fig. 5. BGA Solution Process

ResultsResults are given with respect to the structural weight opti-

misation for each structure. A discussion of the optimal mem-ber sizing is provided with regards to the aeroelastic constraints.The dynamic behaviour and aeroelastic performance of the op-timal structures is then presented.

Structural WeightThe BGA optimisation routine progresses through 100 gen-

erations for each of the structural configurations. Figure 6gives the convergence history of the three superior genes of theconventional model. An optimal solution is achieved within56 generations. The multi-lobe structure exhibits an analogoushistory, with the optimal parameter set realised in 59 genera-tions. For each structure the optimal gene results in a cost func-tion equivalent to the structural weight, indicating that bothaeroelastic constraints are satisfied.

0 20 40 60 80 1000

1

2

3

4

5x 10

5

Generation

Cos

t

Fig. 6. Conventional Model Convergence Plot

Given the optimal panel thicknesses from the BGA routine,the conventional structure sees an 83% weight reduction fromthe original model, whereas the multi-lobe configuration expe-riences an 86% decrease. The rib and spar model sizes signif-icantly lighter than the alternative structure, with final weightsof 495 kg and 1920 kg respectively. Although the multi-lobestructure provides a minimum 65% improved volumetric ef-ficiency, the weight penalty is substantial. The heavy sizingof the multi-lobe model is attributed to the single grouping ofthe lobe arcs along the span, where the greater thickness re-quired at the root is carried throughout the entirety of the span.With the alternative structure sizing to 288% that of the con-ventional model, the application of this stiffening structure tothe generic HALE wing is not warranted. Although [9] alsoapplied a multi-lobe topology that sized heavier than an equiv-alent conventional model, the 14% weight increase for a lowaspect ratio wing was a justifiable trade-off for the improvedvolumetric efficiency. Further, the conventional configurationresults in a structural wing weight of 11.3 kg/m2. This is 15%above the maximum HALE structural wing weight proposedin [27], and indicates the need for further design iteration witha possible application of composite members.

Considering the sizing of individual stiffening members, itcan be deduced that the topology of each configuration is not

optimised for the aeroelastic constraints considered. In theconventional model, the front two spars and third rib from theroot size to the minimum thickness bounds. This is also ob-served in the second and third webs (from the leading edge),as well as the front upper and lower lobe arcs in the multi-lobe structure. As such, further progression of this project willrequire a topology optimisation prior to sizing, such as thatimplemented in [28] and [29].

Although no structural members size to the upper bound ofthe search space, considering the heaviest sized componentsgives insight into the critical constraint for this particular ge-ometry. For the conventional model, the two outermost ribsections yield a plate thickness of 200% that of the thickestinboard section. Despite [30] finding a concentrated mass to-wards a wing tip is detrimental to flutter stability, the gust re-sponse is deemed the critical aeroelastic consideration in thisstudy. The increased mass at the wing tip is thus an expectedoutcome, as it acts to provide the greatest restoring bendingmoment to oppose the vertical gust. Under both configurationsthe spanwise stiffening members (spars, webs and lobe arcs)at the trailing edge size significantly thicker than those at themiddle and leading edge stations. This is a likely result of thecritical bending moment constraint, with the routine generat-ing a mass distribution offset furthest from the flexural axis toprovide the largest restoring moment.

Natural FrequenciesAlthough the flutter analysis considers the first ten natural

modes, only the first five are presented here for ease of illus-tration. Table 2 gives the natural frequencies and mode shapecharacteristic for the conventional configuration. Typical ofhigh aspect ratio wings [31–33], first wing bending is excited atlow frequencies (< 5 Hz), with the presence of in-plane bend-ing in the first five modes.

Table 2. Natural Frequencies of Optimal Conventional StructureMode Frequency (Hz) Character

1 1.04 1st Out-of-Plane Bending2 5.50 1st In-Plane Bending3 6.60 2nd Out-of-Plane Bending4 13.36 1st Torsion5 18.25 3rd Out-of-Plane Bending

The natural frequencies of the multi-lobe structure are givenin Table 3. Again, the low frequency in-plane bending modeis present. The dynamic behaviour of the two configurations isqualitatively similar, however the first in-plane bending modeof this structure occurs at higher frequency than the secondout-of-plane bending mode. In both models the observed lowfrequency mode shapes exhibit either pure bending or pure tor-sion characteristics, with no cross-coupling throughout the firstten natural frequencies.

Table 3. Natural Frequencies of Optimal Multi-Lobe StructureMode Frequency (Hz) Character

1 0.95 1st Out-of-Plane Bending2 5.87 2nd Out-of-Plane Bending3 6.58 1st In-Plane Bending4 10.45 1st Torsion5 15.96 3rd Out-of-Plane Bending

6 Fourth Australasian Unmanned Systems Conference , 2014

FlutterThe linear flutter boundary of both configurations lies well

outside the flight envelope of a HALE mission profile. In Fig-ure 7 the V -g and V -ω plots for the conventional model aregiven. Across the velocity range considered, little change isobserved in the natural frequencies and the flutter instabilityis not present. The first torsion frequency begins to approachthe third out-of-plane bending at higher velocities, with thesemodes likely to coalesce at supersonic speeds to produce flut-ter.

0 50 100 150 200 2500

5

10

15

Velocity (m/s)

Fre

quen

cy (

Hz)

0 50 100 150 200 250−0.15

−0.1

−0.05

0

Velocity (m/s)

Dam

ping

Rat

io

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5

Fig. 7. Conventional Model V -g and V -ω Plots

Similar dynamic behaviour is observed for multi-lobe struc-ture in Figure 8. The natural frequencies of each mode remainrelatively constant throughout the velocity range, with a smallexception again in the first torsion mode, which begins to ap-proach the third out-of-plane bending frequency. This resultsin the damping of mode 4 reverting to approach the zero damp-ing condition, however this exists well outside the flight enve-lope of subsonic HALE vehicles.

0 50 100 150 200 2500

5

10

15

Velocity (m/s)

Fre

quen

cy (

Hz)

0 50 100 150 200 250

−0.1

−0.05

0

Velocity (m/s)

Dam

ping

Rat

io

Mode 1 Mode 2 Mode 3 Mode 4 Mode 5

Fig. 8. Multi-Lobe Model V -g and V -ω Plots

A small wind-off frequency spacing is evident between thefirst in-plane bending and second out-of-plane bending modesin both models. Although a narrow frequency spacing betweenorthogonal modes is indicative of a structure prone to the flutterinstability, [34] found that in-plane bending modes have a neg-ligible effect on free flight flutter. This is evident in this studyfor both configurations, with no apparent interactions with thein-plane bending modes.

The high flutter stability of the wings can, in part, be at-tributed to the geometry. The rectangular planform producespure low frequency mode shapes. In the absence of orthogonalcharacteristics within each mode, cross-coupling is delayed toa higher energy state. The addition of sweep or taper to thegeneric planform is likely to increase the significance of theflutter speed to the structural optimisation. Moreover, linear-ity within the aeroelastic system may be a source of overesti-mation of the stability boundary. If, in an extreme case, the50% reduction in flutter velocity observed through the inclu-sion of structural nonlinearities in [22] pertains to the mod-els considered in this paper, instability at operational velocitiesmay emerge. A nonlinear aeroelastic analysis of these config-urations is proposed for future work.

Transient AeroelasticityThe transient root bending moment response for each con-

figuration is given in Figure 9. In line with the results of themember sizing, the bending moment constraint appears criti-cal for both configurations. The maximum root bending mo-ment is marginally achieved in each case with -179.6 kN.mand -173.4 kN.m for the conventional and multi-lobe modelsrespectively. There is little difference between the two as oncethe constraint is satisfied it no longer contributes to the fitnessfunction, at which point the structural weight drives the opti-misation routine.

0 0.5 1 1.5 2 2.5−200

−150

−100

−50

0

50

100

150

200

Time (s)

Roo

t Ben

ding

Mom

ent (

kN.m

)

ConventionalMulti−Lobe

Fig. 9. Transient Root Bending Moment Response

The maximum tip deflection experienced during the gustloading is on the order of 20 cm for each structure. This iswell within the 30% span tip deflection proposed as a max-imum bounds by [5]. This is an indication that the bendingmoment constraint applied is too conservative and the resul-tant wing is overdesigned. As an area for further work, a tipdisplacement constraint of 30% span is to be implemented and

the impact on root bending moment and structural weight willbe analysed.

ConclusionsIn the present paper, an alternative internal wing stiffening

structure for HALE applications has been investigated. Thisstructure was sized using a Binary Genetic Algorithm undertransient and dynamic aeroelastic constraints, along with anequivalent conventional wing model. The numerical results in-dicate the multi-lobe structure is inefficient in a high aspectratio wing. Although the intrinsic dynamic behaviour, flutterstability and maximum root bending moment of the optimalstructures are qualitatively similar, the 288% increase in struc-tural weight of the alternative configuration does not justifythe 65% improvement in volumetric capacity. The results havehowever shown the topology of the two configurations is notoptimal. Further investigation will be necessary to develop anoptimal topology governed by nonlinear aeroelastic analysis.

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