Feasible Conceptual Design of Morphing Structures

Feasible Conceptual Design of Morphing Structures

Noud P.M. Werter∗ and Roeland De Breuker †

Delft University of Technology, 2629 HS Delft, The Netherlands

Chris S. Beaverstock ‡ and Michael I. Friswell§

Swansea University, Swansea, Wales SA2 8PP, United Kingdom

Werter et al.1 introduced a novel approach to the conceptual design of morphing aircraftby means of a two-level design approach. This paper presents the extension of this modelwith camber and span morphing. The first level consists of a morphing wing model specificto the concept that is investigated. This is used to identify the types of morphing inthe concept and generate the corresponding morphing constraints for the second level.The second level is a generic morphing aeroelastic optimisation framework that is usedto optimise the morphing parameters and find the optimal morphing configuration forthe flight cases under consideration. The second level also returns the morphing energyrequirements to overcome the forces induced by the external loads, which can be used toassess the feasibility of the concept and potentially identify new constraints for a secondoptimisation run. The design approach has been applied to the optimisation of a wingwith twist, camber, shear, and span morphing to illustrate the potential of the designapproach. The results clearly show the potential of the morphing technologies and theadded information this design approach can give in the conceptual design stage.

I. Introduction

The main advantage of morphing wings is that the wing can be optimised for several different flightphases with conflicting requirements, by changing its shape when transitioning from one phase to another.The concept of morphing wings is not new and has been applied since the early ages of aviation. The WrightFlyer, the first heavier than air aircraft with an engine, enabled roll control by changing the twist of its wingusing cables actuated directly by the pilot.2 The increasing demand for extra payload and higher cruisespeeds led to a demand for a stiffer wing structure, making it difficult to morph the wing depending onthe mission profile. Current aircraft wings are therefore designed as a compromise for the missions they fly,performing sub-optimal at each individual flight state. Extensive research has been performed on methodsto incorporate the ability to morph as the flight state requires, into wings with are sufficiently stiff to copewith the requirements of increased payload and flight speed. Barbarino et al.2 give a detailed overview ofthe current state of the art in morphing research and the concepts that have been developed over the years.An overview of morphing aircraft throughout history, including various morphing mechanisms, is given inFigure 1.

In the 1980s, NASA launched two research programs dedicated to morphing structures with the ActiveFlexible Wing program3 and its Mission Adaptive Wing program.4 This research effort was followed by sev-eral research programs in the 1990s and 2000s in the USA, the Smart Materials and Structures Demonstrationprogram,5 the Aircraft Morphing program,6,7 the Active Aeroelastic Wing program,8 and the Morphing Air-craft Structures program.9 Parallel to the research done in the USA, the European Union has also fundedseveral research programs since 2002, including the Active Aeroelastic Aircraft Structures (3AS) project, the

∗Ph.D. Student, Faculty of Aerospace Engineering, Aerospace Structures and Computational Mechanics, Kluyverweg 1;[email protected].†Assistant Professor, Faculty of Aerospace Engineering, Aerospace Structures and Computational Mechanics, Kluyverweg

1; [email protected].‡Researcher, School of Engineering, Singleton Park; [email protected].§Professor, School of Engineering, Singleton Park; [email protected].

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American Institute of Aeronautics and Astronautics

22nd AIAA/ASME/AHS Adaptive Structures Conference

13-17 January 2014, National Harbor, Maryland

AIAA 2014-1260

Aircraft Wing Advanced Technology Operations (AWIATOR) project, the New Aircraft Concepts Research(NACRE) project, the Smart Fixed Wing Aircraft (SFWA) project, the Smart Intelligent Aircraft Structures(SARISTU) project, the Novel Air Vehicle Configurations (NOVEMOR) project and the CHANGE project.

These examples illustrate the complexity of integrating morphing mechanisms onto an aircraft wing andthus also the complexity in the analysis of morphing wings and their potential benefits. Substantial researchin past decades has focused on the aeroelastic modelling of these morphing aircraft using models of differentlevel of complexity11–13 and the optimisation of morphing aircraft by changing the wing sweep, span, chorddistribution, and many other wing parameters14 and by optimising the internal structure of the wing usingtopology optimisation.15,16 However there seems to be a lack of a transparent way to discretise a morphingaircraft for optimisation in a way that results in a sufficiently low number of design variables for quick sizing,while not constraining the design space a priori. It was stated by Dr. Anna-Maria Rivas McGowan during ashort course on morphing aircraft in Lisbon, Portugal, 200817 that there is a need for a set of generic designtools for the conceptual design of morphing aircraft that are at the right level of fidelity, so that the designspace can be explored efficiently even with a large number of design variables.

Most of the current models limit the design space a priori based on the specific concept they are designingor they don’t limit the design space at all, leaving the question whether a feasible design can be obtained.Werter et al.1 introduced a novel two-step approach in the aeroelastic modelling and conceptual designof morphing wings. Section II gives a brief overview of the two-step approach proposed by Werter et al.,followed by a description of the extension of this model to incorporate camber morphing and span morphingsuch that the model includes all commonly used morphing mechanisms. Some results of the application ofthis approach to a UAV are given in section III, followed by conclusions and recommendations for futurework in section IV.

II. Approach

As explained in the introduction, the morphing conceptual design tool consists of two levels. The firstlevel is interchangeable depending on the morphing concept(s) to be analysed and is used to limit the designspace of the generic morphing optimiser based on the limits of the morphing concept(s) that need to beanalysed. The second level is the generic morphing analyser and optimiser that, based on the constraintsgiven by the first level, will optimise the morphing wing parameters and return the required morphing energy.Based on the results of the optimisation, the validity of the initial feasibility constraints can be assessed andeither an additional optimisation can be started with updated constraints or a feasible design has been found.A schematic overview of the design approach is shown in Figure 2.

Both levels of the approach will be discussed in more detail in the following subsections.

II.A. Morphing concepts and feasibility constraints

When considering morphing, in general several different types of morphing are distinguished. First of all adistinction can be made between what, as defined by Werter et al.,1 is called global and local morphing. Localmorphing is defined as the morphing of the wing cross-section perpendicular to the wing span direction, thusaffecting mainly the local aerodynamic flow around the wing, while global morphing is defined as morphingalong the span of the wing thus affecting the overall aerodynamic flow around the wing.

For the morphing analysis, the wing is discretized into several spanwise segments, which can morph in-dependently. Based on this spanwise discretisation, a further distinction can be made in global morphingbetween inter-segment morphing and intra-segment morphing. Inter-segment morphing is defined as morph-ing where the actuators are located at the ribs of two adjacent wing segments, such that morphing occurs bymoving both segments, with respect to one another. For intra-segment morphing, the actuators are locatedin a specific wing segment such that both end ribs of the segment can morph with respect to one another,resulting in a morphing motion where a single wing segment changes its shape. A schematic overview ofthese distinctions in morphing is given in Figure 3.

Within these categories several types of morphing can be distinguished. Examples of local morphingmainly involve camber morphing, where the shape of the airfoil is adjusted by changing the camber line ofthe airfoil, and chord extension, where the shape of the airfoil is adjusted by extending the chord of theairfoil. Conventional discrete flaps and slats can be seen as a form of local morphing where in general boththe camber of the airfoil as well as the chord of the airfoil are adjusted.

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(a) A history of morphing aircraft.2

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(b) A history of morphing aircraft.10

Figure 1: An overview of morphing aircraft

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Morphing concepts

Sweep

Fold

Twist

Extension

Camber

Constraints

Feasible concepts

Conceptual Design Optimisation

Morphing displ./rot.

Force requirements

Energy requirements

Static aeroelastic analysis

Figure 2: Two-level approach for morphing wing conceptual design

Figure 3: Global and local morphing and inter-segment and intra-segment morphing.10

Examples of inter-segment global morphing are variable dihedral or fold morphing, where the dihedral ofthe wing is adjusted and variable sweep - depending on the way the variable sweep is implemented - wherethe sweep angle of the wing is adjusted by sweeping one wing segment with respect to another wing segment.

Finally examples of intra-segment global morphing are; variable span, where the span of the wing ischanged, variable twist, where one end of the wing segment is twisted with respect to the other end, spanwisebending, where, instead of a discrete change in dihedral, the wing dihedral is changed continuously in a wingsegment, and wing shear, which is similar to wing sweep.a

These various types of morphing can be implemented in level 1 of the morphing conceptual design tooland, based on the specific morphing concept considered, feasibility constraints are put on the morphingdesign variables in the optimisation. Next to the feasibility constraints, the morphing energy required tomorph the concept under consideration can also be included in the analysis. However, since no specificconcepts are discussed in the current paper, the morphing energy results in section III will only include theenergy required to overcome the aerodynamic forces and not the concept specific morphing energy required.Further input from level 1 to the analysis module includes; geometry, structural, inertial properties andoperational flight envelope information.

II.B. Morphing analysis model and optimiser

The current morphing analysis model is based on the work by De Breuker et al.10 The model is based on thespanwise discretisation of the wing into several segments, as already indicated in Figure 3. The morphingframework considers both global and local morphing, namely shear/sweep, twist, span, and camber morphing.The shear/sweep and twist morphing were already implemented by Werter et al.1 and the implementationwill therefore not be repeated here. A brief outline of the morphing analysis model, the optimiser, and theimplementation of span morphing and camber will be given in the remainder of this section.

aIn this case one end rib of the wing segment is sheared backward or forward with respect to the other end, effectively havingthe same effect as wing sweep.

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II.B.1. Aeroelastic analysis model layout

The aeroelastic analysis module is based on the work of De Breuker et al.10 The structural model is a finiteelement beam model using linear Timoshenko beam elements. The elements are coupled in a co-rotationalframework to obtain a non-linear structural solution. The aerodynamic model is a linear model based onlifting line theory. This model was adapted for the analysis of swept wings by Weissinger.18 The wing isdiscretised in several spanwise elements each containing a horseshoe vortex, as illustrated in Figure 4. Thestructural and aerodynamic model are closely coupled and the geometrically nonlinear solution is obtained bythe Newton-Raphson root finding method. In order to incorporate the effect of camber on the lift generated,the lift is corrected with airfoil data, as is explained in more detail in section II.B.2.

The aerodynamic drag on the wing consists of two components, the profile drag and the induced drag.The profile drag is estimated by means of curve fitting airfoil data of a NACA0012 profile,19 resulting in thefollowing relation for the profile drag as a function of the local lift coefficient:

CD = 0.01 + 0.02C2L (1)

Since the drag of a cambered airfoil is equivalent to the drag of an uncambered airfoil at the same angleof attack (based on airfoil data19), the profile drag was computed based on the flat plate lift coefficient andnot the total wing lift coefficient. The induced drag is computed by means of the Trefftz plane.20 In orderto account for the induced drag generated by the lift resulting from camber, the drag obtained from theTrefftz plane analysis has to be corrected. Therefore, using the fact that induced drag scales with C2

L, thetotal induced drag was obtained by scaling the flat plate induced drag with C2

L/C2Lfp

. The total drag on thewing is then found by adding the profile drag and induced drag. The wing is trimmed by means of its angleof attack to ensure level flight.

Figure 4: Discretisation of the wing into several horseshoe vortices.10

The results of the analysis are the aerodynamic load distribution and structural deformations. Theaeroelastic model is augmented with a morphing module to incorporate the different morphing mechanismsand the energy required to morph from one state into another. Note that the current framework does notincorporate a dynamic aeroelastic module that is required to assess the dynamic aeroelastic stability of thewing design. It should be noted that, since any morphing manoeuvre is dynamic, the required energy for aspecific morphing manoeuvre computed using static snapshots of the manoeuvre can only give an estimate ofthe required energy. However the static results should produce an estimate in the correct order of magnitudeas long as the morphing manoeuvre is assumed to be slow.

II.B.2. Camber morphing

In constrast to the other morphing mechanisms incorporated in the model, camber morphing is a type oflocal morphing. Since the aerodynamic model is based on Weissinger’s method, no information about theairfoil geometry is presented in the current aerodynamic model. Therefore, in order to incorporate cambermorphing, the current aerodynamic model is updated with 2D airfoil data obtained with XFOIL.21 Viscouseffects are not included in the analysis, so a linear approximation of the pressure distribution over the airfoilis obtained.

XFOIL is used to generate a lookup table of the pressure distribution over the airfoil series consideredat various levels of camber for a range of angle of attack between −10 and 10deg. In order to use this datafor arbitrary wing planforms, several assumptions have to be made. First of all, linear interpolation between

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the closest data points is used to obtain the pressure distribution at an arbitrary angle of attack and at anarbitrary level of camber within this range. Secondly, the airfoils are scaled such that the undeformed airfoilhas a chord equal to the chord at the spanwise section considered and the morphed airfoils have a meancamber line equal to the undeformed airfoil. This way the pressure distribution of a 2D airfoil is obtainedfor each spanwise section at the local angle of attack, with the local chord, and the local camber morphing.Finally to account for 3D effects, the pressure distribution is scaled such that the lift curve slope of the 2Dairfoil is equal to the local 3D lift curve slope obtained by Weissinger’s method.

In order to account for the effects of camber on the lift distribution of the wing, the Weissinger aerody-namic model is augmented with a value for Cl0 based on the scaled pressure distribution at the requestedlevel of camber at α = 0. Furthermore, by specifying an initial and final level of camber, the pressuredistributions can be used to compute the energy required for the camber manoeuvre. First, the pressuredistribution data is multiplied with its respective panel area (airfoil panel length times section width) toobtain a force distribution over the airfoil:

Fij = pijsij · nij (2)

where pij is the pressure at for panel i of wing section j, sij is the panel area, and nij is the panel normalvector. Secondly, the morphing displacement of each panel is required to compute the energy required forthe morphing manoeuvre. In order to compute the displacement, first a reference axis about which the airfoilis morphed needs to be specified. Then the displacement of each panel can be computed by the change inairfoil coordinates. An example of such a camber manoeuvre with corresponding displacement vectors isshown in Figure 5. Finally the energy required for the camber manoeuvre is obtained by integrating thework done:

cam1∫cam0

∫saf

F · δ dsdcam (3)

which can be approximated by the trapezoidal rule for both the integral over the airfoil and the integralover the camber manoeuvre to obtain a approximation for the energy required for the camber manoeuvre.Next the morphing energy for the entire wing can be computed by a summation over the spanwise sections.Finally, the total morphing energy is computed by adding the morphing energy required to activate themorphing mechanism.

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−0.2

−0.1

0

0.1

0.2

0.3

Chord direction, x

Out

-of-p

lane

dire

ctio

n, z

Figure 5: Example of a camber manoeuvre of a NACA0012 airfoil to a NACA6512 airfoil about x = 0.5, including thepanel displacement vectors.

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II.B.3. Span morphing

As mentioned before, span morphing is one of the global morphing mechanisms. The morphing wing canchange its length using the span morphing mechanism. The change in length of the wing is defined along thequarter-chord direction of the wing, so for a swept wing, this implies that the change in span is not equal tothe extension or retraction of the wing.

The morphing wing is divided into morphing sections that can individually change with a length δ, asindicated in Figure 6. Since the geometrically nonlinear structural solution of the morphing wing is obtainedusing a corotational framework, the span morphing at the local element level can directly be implementedby adding the morphing change to the local elastic element deformation.

Figure 6: Extension morphing mechanism, note: dashed line is original configuration

Note that for span morphing, no morphing energy is required to overcome the aerodynamic forces,since these forces act perpendicular to the wing and therefore perpendicular to the direction of morphing.Therefore, the only energy required for span morphing is given by the energy required to overcome theinternal friction in the morphing mechanism and the energy required to actually activate the mechanism.

II.B.4. Optimisation approach

The current version of the framework uses a gradient based optimiser based on the method of movingasymptotes.22 The optimisation procedure allows the user to optimise the morphing variables for minimumwing drag. The inputs to the optimisation procedure are the wing geometry and stiffness parameters andthe constraints on the morphing variables that need to be optimised. These come from the first level of theconceptual design, where the types of morphing and their limitations are defined, as schematically representedin Figure 7. Furthermore a constraint is put on the root bending moment of the wing to prevent a significantstructural weight increase for the morphed wing. By selecting an initial configuration, the optimisationprocedure will also return the morphing energy required to morph from this configuration to the optimumconfiguration. A schematic overview of the morphing optimisation procedure is shown in Figure 8.

The morphing wrapper defines the general morphing parameters available,where the relationship between the morphing concept and general parameters issupplied by a model of the actuation concept integrated. This model is generatedby the concept developer, and is integrated along with other concepts as optionsfor the sectional approaches. The types of morphing refer to the categoriesavailable such as span, twist, dihedral, skew and chord. This is presented infigure .

Figure 5: Twist

Along with the mission specification, the analysis framework is used to gen-erate the parameters used to asses the design. These are used in the objectivefunction and constraints, with appropriate weightings, in a multi-objective op-timisation framework.

3

Figure 7: Schematic representation of level 1 of the conceptual design approach.

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Input – Geometry

– Stiffness + Mass distribution

– Flight Cases

– Morphing Concept Constraints

– Morphing Deformations

Analysis – Aerodynamics

– Structures

– Aeroelastics

Outputs – Aeroelastic loads

– Performance

– Drag

Optimisation – Morphing parameters

Figure 8: Overview of the optimisation loop.

III. Preliminary Results

In order to illustrate the morphing optimisation framework, a wing based on the Boeing ScanEagle UAV23

will be optimised, incorporating a twist morphing mechanism, a shearing morphing mechanism, a cambermorphing mechanism, and a span morphing mechanism. Note that in this case no specific morphing conceptis analysed, so all morphing parameters are varied independently. However, in reality feasibility constraintsshould be applied based on the specific morphing concept considered. In order to assess the results obtainedfor the morphed configurations, a reference configuration was selected. The wing properties of the referenceconfiguration are given in Table 1, resulting in the planform as shown in Figure 9. The wing has no twist andthe NACA4512 airfoil was selected as reference airfoil for this wing. The flight speed range of the ScanEaglewas increased slightly in order to illustrate the use of the morphing assessment framework and as such thewing was optimised for a low-speed configuration at 40mph and a high-speed configuration at 80mph. Theresulting performance of the reference configuration at these flight speeds is shown in Table 2.

Table 1: Wing properties

Planform Wing box General

Span 3.1m Skin thickness 0.5mm Weight 18 kg

Root chord 0.3m Height 10% chord

Tip chord 0.2m Width 65% chord

Sweep angle 18◦

0

0.2

0.4

−1.5 −1 −0.5 0 0.5 1 1.5Span direction, y (m)

Cho

rd d

irect

ion,

x (

m)

Figure 9: Wing planform of the reference configuration

In order to ensure feasible results several constraints are applied on the morphing design variables inthe optimisation. A constraint is put on the local angle of attack to limit it to the range of ±15◦ to avoidexcessive angles of attack predicted by an optimisation using linear aerodynamic models. Camber morphingis restricted to the NACA 4-digit, 12-series airfoil between −8% and 8% camber at 50% chord (NACA0012- NACA8512). The relative shear angle between to neighbouring sections is restricted to ±15deg to preventexcessive shear angles differences between two sections. Span morphing is constrained to ±50%. Finally, aconstraint is put on the root bending moment, as can be seen in the discussion of the results.

A discussion of the results at 40mph is given in section III.A, followed by the results at 80mph in section

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Table 2: Aerodynamic performance of the reference configuration

40mph 80mph

Drag (N) 5.27 6.63

Wing root bending moment (Nm) 63.10 63.05

Trim angle (deg) 8.57 −1.62

III.B. The required energy to morph is calculated for the case where morphing takes place between the lowand high speed configuration, or vice versa. The morphing manoeuvre is carried out at the high flight speedbecause morphing at the low flight speed would result in the aircraft flying at the low speed while beingmorphed in the high speed configuration, before speeding up to the high speed. This would result in a lossin lift which can not be compensated by an increase in angle of attack since the low speed configurationtrimmed angle of attack is already close to stall.

III.A. Low-speed configuration

First, as mentioned above, the morphing wing is optimised at 40mph to show the potential use of thedesign tool in the conceptual design of morphing aircraft. The wing was divided in 4 morphing sections,as indicated in Figure 9. Each morphing section was allowed to change its twist, shear, camber, and span.Several optimisations were done to minimize the wing drag, while varying the constraint on the wing rootbending moment between 10% and 120% of the wing root bending moment of the reference wing, resultingin the Pareto front shown in Figure 10.

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.30.2

0.4

0.6

0.8

1

1.2

1.4

1.6

D Dre

f(−)

MM r e f

(−)Figure 10: Pareto front showing the interaction between wing root bending moment and wing drag with respect to thereference configuration at a flight speed of 40mph.

The Pareto front shows two effects. First of all, as expected a reduction in wing root bending momentresults in an increase in drag. Secondly, no solution could be found for a wing root bending moment below50% of the reference wing root bending moment without violating any other constraints. Note that if themorphed configuration is compared to the reference wing, a reduction in drag of 60% is observed at an equalroot bending moment. The kinks in the Pareto front can be explained by the fact that the optimiser onlyfinds a local optimum and only one initial design was optimised. In order to improve the Pareto front, severaloptimisations should be run with different initial designs.

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The optimised morphing parameters for two data points of the Pareto front are shown as an example inTable 4. When comparing the morphing variables for a relatively low root bending moment and a relativelyhigh root bending, two clearly different trends can be observed. When looking at the results for a rootbending moment of 120% of the reference root bending moment, the morphing capabilities are clearly usedto reduce drag. Firstly, maximum camber appears to result in minimum drag. This is probably related tothe assumptions made on the drag caused by camber morphing. This needs further investigation by meansof an improved drag model for camber. Furthermore at high levels of camber, viscous effects might becomesignificant, so these should also be incorporated. Secondly, span extension and shear are used to increasethe aspect ratio of the wing, thus reducing the induced drag. Finally, in order to still meet the root bendingmoment constraint, some minor twist is used to shift some of the lift inboard. Note that when looking atthe trim angle in Table 3, the trim angle is reduced significantly, which adds to the significant reduction indrag.

Table 3: Trim angle of attack results from the optimisation

Flight speed Moment (%Mref ) Trim angle (deg)

40mph 120% 0.60

40mph 60% 8.44

80mph 43% 0.53

80mph 10% 0.03

When the root bending moment constraint is lowered, it is interesting to see that not all morphingcapability can be used to reduce the drag. The lift has to be shifted inboard to reduce the root bendingmoment. This can clearly be observed when looking at the camber levels. However, when looking at thespan extension and shear angles, a significant increase in the wing span can be observed. This might seemcounter-intuitive when a reduction in root bending moment is required. However, when looking at thewing tip section, two effects can be observed. First of all, this section is significantly extended, resultingin a significant increase in length of this specific section, and secondly a very negative level of camber ispresented, resulting in a negative lift. When these two effects are combined, the root bending momentis actually reduced by moving the tip section outboard, while all lift is generated inboard. Note that inconstrast to the case of a relative high root bending moment, in this case the trim angle is no longer reduced,so no extra drag reduction is obtained.

Finally an estimate of the maximum required morphing energy to morph to the optimised configurationor back to the reference configuration is shown in Table 5. As can be seen, most energy is required for cambermorphing. This can be expected, since work is directly against the aerodynamic lift for camber morphing.The second most energy is required by shear, which has to work against the wing drag. Finally, twist costsalmost no energy, since part of the aerodynamic force on the wing is always assisting in twisting. Of course,as explained before, span morphing costs no energy, when looking at the aerodynamic forces.

III.B. High-speed configuration

Similar to the low-speed configuration, the morphing wing is also optimised at 80mph. Once again severaloptimisations were done to minimize the wing drag, while changing the wing twist, shear, camber, and span,and varying the constraint on the wing root bending moment between 10% and 120% of the wing rootbending moment of the reference wing. The results of the optimisation are shown in Figure 11.

First of all, similar to the low-speed configuration, as expected a reduction in wing root bending momentresults in an increase in drag. Secondly, note that setting the constraint on the wing root bending momenthigher than 43% no longer resulted in a drag reduction, since the optimiser found an optimum without theroot bending moment constraint being active. Similar to the low-speed configuration, it can be concludedthat the morphed configuration shows a significant improvement over the reference wing. Once again, inorder to improve the Pareto front, several optimisations should be run with different initial designs.

When comparing the morphing variables for a relatively low root bending moment and a relatively highroot bending, two clearly different trends can be observed, as can be seen from Table 4. If a relatively highroot bending moment is allowed, all morphing capability can be used to reduce drag. So similar to thelow-speed configuration, camber is maximised. However in this case, instead of an increase in span, the span

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Table 4: Optimised morphing parameters

Flight speed Moment (%Mref ) Shear (deg) Twist (deg) Span (m) Camber (%c) Location

40mph 120% −3.6 −0.6 0.04 8.0 tip

−8.0 −0.1 0.08 8.0

−5.3 0.0 0.04 8.0

−9.3 0.4 0.08 8.0 root

40mph 60% −6.2 −1.2 0.10 −8.0 tip

−11.5 −2.3 −0.09 2.5

−22.5 −3.8 0.09 8.0

−18.7 −2.0 0.23 8.0 root

80mph 43% 22.2 0.6 −0.18 6.0 tip

13.6 −0.1 −0.25 8.0

10.6 −0.2 −0.15 8.0

14.3 −0.2 −0.23 8.0 root

80mph 10% 2.4 −1.0 0.04 −3.4 tip

3.0 −0.6 0.08 −1.3

1.0 −0.5 0.03 3.6

0.8 −0.3 0.05 7.9 root

Table 5: Maximum morphing energy required

Flight speed Moment (%Mref ) Shear (Nm) Twist (Nm) Camber (Nm) Location

40mph 120% 0.007 0.001 0.11 tip

0.074 0.002 0.12

0.055 0.004 0.25

0.194 0.027 0.18 root

40mph 60% 0.002 0.000 0.26 tip

0.057 0.022 0.25

0.350 0.106 0.18

1.297 0.138 0.90 root

80mph 43% 0.347 0.006 0.40 tip

0.111 0.005 0.48

0.139 0.001 0.99

0.046 0.004 0.42 root

80mph 10% 0.016 0.014 0.33 tip

0.009 0.006 0.02

0.024 0.000 0.07

0.004 0.001 0.30 root

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0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450.40

0.45

0.50

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

MM r e f

(−)

D Dre

f(−)

Figure 11: Pareto front showing the interaction between wing root bending moment and wing drag with respect to thereference configuration at a flight speed of 80mph.

is reduced significantly to increase the trim angle to almost zero, as can be seen in Table 3, thus reducingthe drag. To compensate for the increase in root bending moment caused by the increase in wing span, thewing is swept back. Overall this results in a significant decrease in drag.

When the root bending moment constraint is lowered, all morphing capability can no longer be used toreduce drag. In this case, twist and camber are used to shift the aerodynamic force inboard, thus reducingthe wing root bending moment. This results in a reduced lift, which is partially compensated by an increasein span and partially compensated by an increase in trim angle. Note that the trim angle is almost zero,once again resulting in a reduction in drag.

Finally, similar to the low-speed configuration, an estimate of the maximum required morphing energy tomorph to the optimised configuration or back to the reference configuration is shown in Table 5. Once again,camber requires most energy, followed by shear and twist. Of course span morphing requires no energy.

IV. Conclusions and recommendations

This paper discussed an aeroelastic framework suitable for the analysis and optimisation of generalmorphing wings. To be more precise, the paper described an extension of the framework which was presentedearlier by the authors. Morphing wings can now be designed for a general distribution of sweep, twist, spanmorphing and camber for minimal drag and root bending moment.

Results were generated for a general UAV which should morph to fly at minimum drag and root bendingmoment at two off-design flight speeds. Given the fact that the objective consisted of two parts, Pareto frontresults were presented. It was demonstrated that the drag could be reduced significantly at the expense ofroot bending moment, or vice versa. It was also demonstrated that the preferred lift gaining or dumpingmechanism was camber rather than twist. Wing sweep and extension were merely used to tune the aircraftangle of attack to obtain optimal lift over drag ratios. It should be noted, however, that even though camberis preferred over twist from an aerodynamic point of view, from an energy point of view, twist morphingcosts significantly less energy than camber morphing.

In conclusion, although some extensions to assess dynamic aeroelastic stability and flight dynamic stabilityare still required, the results of this paper showed that the framework presented can be used successfully forthe design and optimisation of morphing wings.

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V. Acknowledgements

The work presented herein has been partially funded by the European Community’s Seventh FrameworkProgramme (FP7) under the Grant Agreement 314139. The CHANGE project (Combined morphing as-sessment software using flight envelope data and mission based morphing prototype wing development) is aLevel 1 project funded under the topic AAT.2012.1.1-2. involving 9 partners. The project started on August1st 2012.

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Feasible Conceptual Design of Morphing Structures

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