-5 0 15-2

-1.5

-1

0.5

0

0.5

1

1.5

2

α [°]

c L

Sec. 1 (wing root)Sec. 2Sec. 3Sec. 4Sec. 5Sec. 6Sec. 7Sec. 8Sec. 9 (wing tip)

Actuatedupwards

Not actuated

Actuateddownwards

105

Front segment Rear segmentz/xx,UP

tM/2rLE

zLE zTE

xUP

αTEβTE tTExDN

z/xx,DN

tM/2

0 0.1 0.2 0.3−0.05

0

0.05

0.1

0.15

S1 S2

S3 S4

S5

S6 v1

v2 v3

v5 E1 E8

E10

x

y

0 0.2 0.4 0.6 0.8 1

−0.2

−0.1

0

0.1

0.2

x

y

0

0.2

0.4

0.6

0.8

1

−0.1

0

0.1−0.05

00.05

x

y

z

Polar curves for the wing sections in various actuation configurations

3-D Airfoil MorphingobtAin optiMAl efficiency in every flight conDitionThe wing is traditionally designed as a compromise for different flight conditions.

increAse MAxiMuM wing lift coefficientAirfoil shape changes can lead to a higher maximum lift: maximum lift coefficient can be maintained along the whole span, making possible to avoid having geometrical twist.

replAce conventionAl control surfAcesLift distribution can be asymmetric, inducing rolling moments;removing control surfaces potentially allows for a laminar profile.

iMpleMenting structurAl loADs AlleviAtion techniquesLift distributions reducing loads – e.g. wing root bending mo-ment – can be obtained.

coMpliAnt structuresCompliant structures achieve airfoil shape changes by deforming structural elements, leading to smooth, gapless solutions.

eMbeDDeD “sMArt” ActuAtorsSmart materials embedded in the compliant structure produce actuation with minimum bulk, complexity and mass.

Aero-structurAl interActionsStructure is rigid to withstand aerodynamic loads, yet compliant to deform as required.

Aero-StructurAl optimizAtionof 3-D ADAptive WingS

With embeDDeD SmArt ActuAtorS

Giulio MolinariAndrés F. Arrieta

Paolo ErmanniCentre of Structure Technologies

ETH Zurich, CH-8092 Zurichwww.structures.ethz.chMotivAtions

ChallengeDetermine an optimal wing planform, an outer aerodynamic shape and an inner compliant structure for a given mission (defined by the trajectory) that maximizes the vehicle efficiency.

integratedMultidisciplinary

Approach

optiMizAtion technique

3-D Morphing wing concept

publicAtions

Piezoelectric bi-morph tab

Honeycomb structural supports

Extensible skin(Dielectric Elastomer)

Flexible skin

Stringers

Piezoelectricbi-morph layup

Rigid skin

Main spar

Compliant ribsRigid wingbox

Structural Parametersribs structure nribs × 18: six Voronoi sites per rib

ribs outer shApe nribs × 10: each section independently defined

3-D structure 3 + nribs × 2: • honeycomb structural supports dimensions • length ratios (rigid wingbox vs. compliant parts)

optimization goalsMAxiMize rolling MoMent (cℓ)Achieve controllability around roll axis by means of morphing.

MiniMize cruise DrAgOptimize un-actuated wing profile for maximum efficiency.

Molinari, G., Quack, M., Dmitriev, V., Morari, M., Jenny, P., and Ermanni, P., “Aero-structural optimization of Morphing Airfoils for Adaptive wings,” Journal of Intelligent Material Systems and Structures, Vol. 22, No. 10, Sept. 2011, pp. 1075-1089.Molinari, G., Quack, M., Dmitriev, V., Morari, M., Jenny, P., and Ermanni, P., “A Multidisciplinary Approach for wing Morphing,” in 21st International Conference on Adaptive Structures and Technologies (ICAST), State College, PA, USA, Oct. 4-6, 2010.

optimization resultsMorphing Abilities• cℓ = 0.091 (conventional airplanes: 0.006 < cℓ < 0.04)• ΔcL up to ±1.2 from undeformed state

Wing dimensions: 3 m × 0.3 mFlight speed: 20 m/s

concurrent Approachchirpfoil 11 geometrical parameters define the shape

of the undeformed airfoil.• based on four 4th order polynomials• more general than NACA 4- and 5- digits

parametrizations

voronoi DiAgrAM-bAseD pArAMetrizAtion

“The Voronoi cell Rk associated with the site Sk is the set of all points whose distance to Sk is not greater than their distance to the other sites Sj , where j is any index different from k.”Parameters: two coordinates per site and thickness of the associated edges.Advantages:• compact representation (limited number of variables required to describe the structure)• real-valued parameters (suitable for mathematical optimization techniques)• continuity properties (small changes in the parameters lead to small changes in the shape)• no unconnected nodes (no need to define connectivity matrices)• genotype easily extendable (enables variable length genotype optimizations)

Aerodynamic Shape Parametrization

Compliant Structure Parametrization

Static Aeroelastic Analysis

Optimizeraerodyn. params.

candidate

actuation levels

static aeroelastic analysis

performance evaluation

performance weighting

flight condition 1

structural params.

displacementspressuredistribution

structural analysis(linear/nonlinear)

aerodynamic analysis(extended lifting line)

numerical model

flight condition 2

actuation level

…

flight condition

(from traj. opt.)

aer. resultantsl, mR, mP, mY

structural params.

extenDeD lifting line captures 3-D potential flow and 2-D viscous effects on the various sections of the profile.

concurrent MultiDisciplinAry optiMizAtion

“The multidisciplinary-determined optimum is superior to the one identified by multiple single-disciplinary optimizations.”• “Morphed” deformed shape is not prescribed, but calculated.• Figure of merit depends directly upon aerodynamic performance.• The multidisciplinary optimizer can exploit interactions between

the different disciplines.

Honeycomb filling