Aeroelastic Tailoring. In 2016 Applied Aerodynamics Conference . - CORE
View metadata, citation and similar papers at core.ac.ukbrought to you byCOREprovided by Explore Bristol ResearchKrupa, E., Cooper, J., Pirrera, A., & Nangia, R. (2016). ImprovedAerodynamic Performance Combining Control Surface Deflections andAeroelastic Tailoring. In 2016 Applied Aerodynamics Conference: Evolution& Innovation Continues - The Next 150 years of Concepts, Design andOperations (pp. 12). Royal Aeronautical Society.Peer reviewed versionLink to publication record in Explore Bristol ResearchPDF-documentThis is the accepted author manuscript (AAM). The final published version (version of record) is available onlinevia Royal Aeronautical Society at http://www.aerosociety.com/News/Proceedings. Please refer to any applicableterms of use of the publisher.University of Bristol - Explore Bristol ResearchGeneral rightsThis document is made available in accordance with publisher policies. Please cite only the publishedversion using the reference above. Full terms of use are terms
Improved Aerodynamic Performance Combining Control SurfaceDeflections and Aeroelastic TailoringEduardo P. Krupa1, Jonathan E. Cooper2, Alberto Pirrera3 and Raj Nangia4Department of Aerospace Engineering, University of Bristol, Queen's Building, University Walk,Bristol BS8 1TR, UK.The interplay between passive and active wing shape adaptation for improved aerostructural performance is analysed in this paper. Shapeadaptation is sought as a means for load redistribution, alleviation and, in turn, weight saving. Passive aeroelastic responses are obtained bydesigning bend-twist coupling into a hybrid wing-box with composite skins. Active shape variations are realised via trailing edge controlsurfaces (similar to ailerons), distributed along the full wingspan. A bi-level design framework, incorporating gradient-based and particleswarm optimisations, is utilised to search the wing’s design space for beneficial aerostructural properties and control surface deflectionscheduling. Optimisation design variables include structural dimensions, composite lamination parameters, stringer position, rib orientationand spacing, and the deflections of individual control surfaces. Design constraints consist of allowable stresses and deformations, structuralstability (i.e. buckling) and composites manufacturing guidelines. The design approach is shown to produce weight reductions and improvedaerodynamic performance.Keywords: aeroelastic tailoring, load alleviation, composite optimisation, active trailing edge devices.1. IntroductionAeroelastic tailoring is the branch of aircraft designthat considers the interactions between aerodynamic loadsand deformable airframes. It involves fine-tuning of wingmass distribution and stiffness properties, so thataerostructural design metrics are met, to achieve a desiredperformance. A more general definition is found in Shirket al. [1] that describe aeroelastic tailoring as: “theembodiment of directional stiffness into an aircraftstructural design to control aeroelastic deformation,static or dynamic, in such a fashion as to affect theaerodynamic and structural performance of that aircraftin a beneficial way”.Composite materials offer significant tailoringcapabilities, because one can design a structure and itsconstituent material concurrently. Composites aretherefore increasingly common in aerospace structures(e.g. 787 and A350).Although passive aeroelastic tailoring has beenpossible since the 1980s, using both metallic andcomposite materials, it is expected that greaterimprovements in aircraft performance may be achievedvia servo-aeroelastic tailoring. A discipline that aims toexploit the synergies between passive aeroelasticstructural adaptation and active control of aerodynamicsurfaces. The expected outcome is the creation of designsthat outperform those conceived by following solelypassive aeroelastic tailoring paradigms. Potential benefitsinclude: load alleviation and management, airframelightweighting, drag reduction, extended range andaugmented control capabilities and authority.A number of recent studies has explored eitherpassive or active aeroelastic adaptations as a means tominimise wing weight under a variety of designconstraints [2–8]. The use of active devices to controlspanwise lift distribution on a composite wing structure isexplored in [9], with drag reduction over a range of flightspeeds as the main objective. The study demonstrates that,by combining passive stiffness tailoring with small controlvariations, induced drag can be reduced. For further1relevant literature, the reader is referred to [10–14], thatshow improvements in aerodynamic performanceadopting trailing edge devices, and to [15,16] thatdemonstrate the applicability of passive/active tailoringusing anisotropic piezoelectric actuators for roll controland flutter suppression.As regards design optimisation studies, [17,18]address the static aeroelasticity and flutter suppression forthe metallic wingbox of NASA’s Common Researchmodel [19]. These optimisations consider detailedthickness variations of ribs, spars and skin patches alongthe wing’s semispan and show that a significant massreduction is achievable for a given flutter margin.Despite the growing interest in passive-adaptive andactive servo-aeroelastic concepts, most of the workundertaken by the technical community has focused onmetallic airframes and on the optimisation of their dragand weight. In this paper, a hybrid metal-compositewingbox is tailored for load alleviation and mass savingvia passive and active shape adaptation. In particular, wepresent a bi-level optimisation framework for the servoaeroelastic tailoring of composite wing structures withdistributed trailing edge ailerons. A total of 20 trailingedge aerodynamic control surfaces are incorporated alongthe wingspan in the models herein. The objective is tominimise wingbox mass, whilst attaining a specific liftdistribution via passive elastic deformations and activedeflections of the aerodynamic control surfaces.The proposed design and optimisation strategy isshown to be able to produce a considerable change in thespanwise loading by shifting the wing centre of pressureinboard. An approximatively linear lift distribution,particularly suited for structural efficiency and stallrecovery, is achieved. In addition, the optimisationproduces aerostructural designs dominated by torsionalloads, therefore leading to higher bend-twist coupling andmore stringent shear strength requirements.The remainder of the paper is structured as follows:Section 2 describes the reference wing model adopted forthis study. Section 3 presents the aeroelastic methodologyPh.D. Research Student.Royal Academy of Engineering Airbus Sir George White Professor of Aerospace Engineering, AFAIAA.3 Lecturer in Composite Structures, Advanced Composites Centre for Innovation & Science (ACCIS).4 Honorary Research Fellow2
used to calculate aerodynamic loads and elasticdeformations. Relevant models for composite laminatesand composite design guidelines are introduced in section4. The optimisation problem, its design variables,constraints and the objective function are described insection 5. Finally, results are discussed and conclusionsare drawn in sections 6 and 7, respectively.The wingbox is modelled in NASTRAN withCQUAD4 elements for skins, spars and ribs and CBARelements for stiffeners. NASTRAN’s doublet latticemodel is used for computing steady aerodynamic loads.Similarly to [18], 20 discrete trailing edge ailerons aredistributed along the wingspan. These devices occupyapproximately 15% of the local wing chord. Theircontribution to the wing inertia is represented with lumpedmasses placed at the mid-position of the hinge line. Themasses are assumed to be proportional to the flaps’ area.The aerodynamic panelling consists of 2820 boxes.The panels are distributed evenly spanwise and followinga cosine mesh chordwise. The aerodynamic mesh for thecontrol surfaces is finer (see Figure 1) in order to capturerapid changes of pressure due to flap deflections.The interpolation between the structural andaerodynamic degrees of freedom is based on the finiteplate 3D spline method as implemented in NASTRAN’sSPLINE6 card.Further details of the geometrical arrangement,thicknesses distributions and the aeroelastic FE model areshown in Figures 1 to 3.2. Baseline Aeroelastic Wing ModelThe model is representative of a state-of-the-artregional commercial jet—more specifically, of a short-tomedium-range aircraft designed for transonic speeds.The structural finite element (FE) model is a rightcantilevered half-wing with conventional architecture, i.e.a wingbox with front and rear spars along the entire span.The wing skins have stiffeners regularly spaced in thechordwise direction, represented by the dashed lines onthe left-hand-side of Figure 1. Ribs, spars and stiffenersare made of Aluminium 7050–T7651. The wing skins aremade of symmetric and balanced composite laminates.Upper and lower wing skins are divided into fivepartitions. The wingbox has straight ribs, aligned with thefree stream and distributed uniformly within each of thefive partitions. The laminates’ stacking sequence iscomprised of blocked stacks of [ 45 /0 /90 ]s for anormalised ply distribution as shown in Figure 2. Thesevalues are found allowing the maximum Tsai-Wu plyfailure index for a 2.5g symmetrical pull-up manoeuvre tobe 0.75 (1 meaning damage). Material properties areshown in Table 1.Inertial effects due to leading and trailing edge substructures and fuel weight are approximated by means oflumped masses connected to the spars via interpolationrigid elements. An additional lumped mass is placed at theaircraft centre of gravity (CG) to represent fuselage,payload, empennage and reserve fuel.Table 1: Composite and metallic material properties.Composite material (Hexcel 8552 NMS 128/2)PropertyValuePropertyValue148 GPa2439 MPaE11X1t10.3 GPa66 MPaE22X2t0.272013 MPaν12X1t5.9 GPa381 MPaG12X2c5.9 GPa78 MPaG23S12SBonding5.9 GPa34.7 MPaG131577 kg/m³ρt*Temperature condition: -54 CAluminium material (7050-T651)PropertyValuePropertyValue71.7 GPa490 MPaEσY0.332830 kg/m³νρFigure 1: Details of the baseline wingbox arrangement and the aerodynamic panelling.2
Figure 2: Thicknesses spanwise variations of the main wing structure components.Figure 3: Structural FE model and aerodynamic mesh.Figure 4: Spanwise loads at cruise condition.Figure 5: Local twist distribution of the Jig-Shape and cruise condition.3
3. Static Aeroelasticity and Buckling Calculations4. Background Laminate EquationsTwo symmetric load cases are considered throughoutthis study: a 2.5g pull-up manoeuvre and a -1g manoeuvre,at Mach 0.82 and altitude h 35000 ft. In both cases, fullfuel mass is assumed (reserve fuel included. Note this isthe value for the whole aircraft. Only one half is includedin the FE semi-span model.).Static aeroelastic loads and structural stresses arecomputed using NASTRAN solution 144. NASTRANimplements the Doublet-Lattice subsonic lifting surfacetheory (DLM) to calculate the aerodynamic loads. SinceDLM uses a linear aerodynamic potential theory, effectsof viscosity and aerofoil thickness are ignored. Structuralnonlinearity and non-planar aerodynamic effects are alsoneglected. Consequently, constraints on maximum tipvertical displacement and maximum tip twist angle areapplied to limit the structure to elastically lineardeformations. The aerodynamic loads are transferred tothe structural mesh via a finite surface spline (SPLINE6).Specifically, aerodynamic and structural degrees offreedom are interpolated using a surface spline connectedto the FE nodes on the upper profile of spars and ribs.A longitudinal trim analysis is performed todetermine the loads acting over the wingbox. The trimvariables used in this work are: angle of attack, pitchacceleration, normal load factor, pitch rate, and thedeflections of the 20 control surfaces. Angle of attack andpitch acceleration are unknowns in the system ofequations for trim equilibrium. The deflections of thecontrol surfaces are fed to the system as know variables asfound by the optimisation framework. The pitch rate is setto zero. Since the aircraft tail is not included in theanalysis, an equivalent lumped mass is positioned at theCG of the aircraft to emulate airframe and payload inertialeffects. This approach in turn causes a negligible, but nonzero, pitching acceleration.The spanwise lift loading is obtained from the locallift coefficient distribution, which, in turn, is calculatedintegrating the aerodynamic pressure coefficients chordwise over the aerodynamic mesh.Lastly, the aerodynamic loads are fed to NASTRANsolution 105 for a linear buckling analysis to examinestructural stability. Five buckling eigenvalues andeigenmodes are computed and aggregated as a designconstraint as explained in §5.1.2.For design purposes, wing structures are usuallydivided into many stiffened panels corresponding toindividual, or clusters of, rib/stringer-bays. Consequently,an often impractical number of design variables isrequired to optimise the ply book (ply orientations in useand stacking sequence) for the whole airframe. Thisproblem can be tackled using lamination parameters, analternative way of modelling laminate stiffness thatreduces the total number of design variables.Typically, the in-plane stretching, [A], coupling, [B],and bending, [D], stiffness matrices that govern laminatebehaviour can be found from classical laminate theory(CLT) [20,21], where they are functions of the stackingsequence and material properties.According to CLT, elastic stresses induce a state ofdeformation described in terms of resultant forces, 𝑁 {𝑁𝑥 , 𝑁𝑦 , 𝑁𝑥𝑦 }𝑇 , and moments, 𝑀 {𝑀𝑥 , 𝑀𝑦 , 𝑀𝑥𝑦 }𝑇 , andrelated strains, 𝜀 0 {εox , εoy , γoxy }𝑇 , and curvatures, 𝜅 {κx , κy , κxy }𝑇 such that𝑁𝐴 𝐵 𝜀0[ ] [][ ]𝑀𝐵 𝐷 𝜅𝑁𝑥𝐴11 𝐴12 𝐴16 𝐵11 𝐵12𝑁𝑦𝐴22 𝐴26𝐵22𝑁𝑥𝑦sym𝐴66 sym 𝑀𝑥𝐵11 𝐵12 𝐵16 𝐷11 𝐷12𝑀𝑦𝐵22 𝐵26𝐷22𝐵66 sym{𝑀𝑥𝑦 } [sym(1)𝐵16εo𝑥𝐵26εo𝑦𝐵66 γo𝑥𝑦𝐷16 κ𝑥𝐷26 κ𝑦𝐷66 ] {κ𝑥𝑦 }(2)For balanced, symmetrical and orthotropic laminates𝐴16 𝐴26 0, and 𝐵𝑖𝑗 0.Tsai et al. [20] and Tsai and Hahn [22] introduced analternative representation for the stiffness characteristicsof a laminate. This representation is based on twelve (eight𝑗when [B] 0) lamination parameters, ξ𝑖 , and five materialinvariants, 𝑈𝑘 , with 𝑖 1, 4, 𝑗 𝐴, 𝐵, 𝐷, and 𝑘 1, 5. The use of lamination parameters can be beneficialfor optimisation purposes, because it reduces the numberof design variables. In particular, [A] and [D] can bewritten asξA31ξ1𝐴𝐴ξA31 ξ100 ξA3 ξA3000 ξ2𝐴 2 ξA4𝐴[ 0 ξ2 2 – ξA400100000 𝑈1𝑈0 2𝑈31 𝑈40 [𝑈5 ]0](3)ξ𝐷31ξ1𝐷𝐷11ξ𝐷3𝐷221 ξ1𝐷3ℎ 0𝐷12 ξ𝐷30 𝐷6612 0 ξ𝐷30𝐷260 ξ𝐷2 2 ξ𝐷4𝐷[𝐷26 ][ 0 ξ2 2 – ξ𝐷400100000 𝑈1𝑈0 2𝑈31 𝑈40 [𝑈 ]50](4)𝐴11𝐴22𝐴12 ℎ𝐴66𝐴26[𝐴26 ]3.1 Static Aeroelastic Analysis of a Nominal CruiseConditionFigure 4 shows sectional lift coefficient, 𝐶𝑙𝑙 , and spanload coefficient, 𝐶𝑙𝑙 𝑐/𝑐avg , for the baseline configurationflying at Mach 0.78 and altitude h 33000 ft, with allcontrol deflections set to zero. The rigid wing liftcoefficient is 𝐶𝐿 0.4778. When the flexibility of thestructure is taken into account 𝐶𝐿 0.4504.From Figure 4 one can observe that, in the portion ofthe wing between 40% to 90% of the semispan, the loaddistribution is approximatively linear. Figure 5 shows thewing twist deformation at cruise, in comparison to the jigshape. It is then inferred that the load distribution is due togeometric bend-twist coupling, because the baselinestacking sequence gives marginal material coupling andan overall negligible contribution to the aeroelasticdeformation of the wing (this is shown in detail in §6.3).where ℎ is the laminate thickness andℎ 2𝐴ξ[1,2,3,4]1 [cos2𝜃, sin2𝜃, cos4𝜃, sin4𝜃]d𝑧ℎ(5) ℎ 2ℎ 2ξ𝐷[1,2,3,4] 12 [cos2𝜃, sin2𝜃, cos4𝜃, sin4𝜃]𝑧 3 d𝑧ℎ3(6) ℎ 2with 𝜃(𝑧) corresponding to the ply angle along thethrough-thickness coordinate z.4
To conclude, based on eqs. (5) and (6), ξ2𝐴 ξ4𝐴 ξ𝐷 0 for balanced and symmetric laminates with ply4orientations limited to 45 , 0 , 90.4.1 Laminate Design GuidelinesTo ensure that the laminates output by theoptimisation satisfy engineering and manufacturabilitystandards, guidelines and design practice as per [23] areapplied as design constraints. Specifically:- Only four ply directions are allowed, i.e., 45 , 0 , 90 .- Laminates should be symmetric to eliminatemembrane-bending coupling (𝐵𝑖𝑗 0).- A minimum of 10% of each ply direction must bepresent in the laminate.- The laminate must be balanced (𝐴16 𝐴26 0) toavoid extension-shear coupling, i.e. the number of -45 and 45 plies must be the same.- At most four plies of the same thickness and orientationcan be stacked together. This is to prevent matrixcracking between layers.Figure 6: Bi-level optimisation framework combiningGradient-based and Particle-Swarm optimisations.NASTRAN solution 144 is used to evaluate theperformance metrics of the 𝑛𝑡ℎ set of design variables.MATLAB checks the constraints and computes theobjective function. The process ends when one of thestopping criteria is met (i.e. thresholds for the optimisationstep-size and first-order optimality measure).5. Optimisation Problem FormulationThis paper investigates the trade-offs and synergiesbetween passive and active aeroelastic adaptation for loadalleviation and lightweighing. This is done by setting uptwo optimisations studies. In the first study, mass isminimised by only optimising the passive aeroelasticperformance of the wingbox (the control surfaces are heldat zero deflection). The second study includes activecontrols. The control surfaces are employed to reshape thelift distribution over the wing to reduce induced stresses.An aggregate objective function is used, where the firstobjective is minimum mass and the second objective is tominimise the distance between a target triangular-likespanwise loading and the spanwise loading of the 𝑗𝑡ℎoptimisation iteration at a fixed lift coefficient.The aeroelastic problem is solved in terms oflamination parameters. The laminate ply-book isdetermined contextually, but within a separateoptimisation. Recent work by [24-26] has demonstratedthat this ‘bi-level’ approach provides an efficient way ofsolving the optimisation of laminated compositestructures. Their design strategies typically combinegradient-based methods or integer linear programming,for the first level, and a permutation Genetic Algorithm(GA) or Particle-swarm Optimisation (PSO), for thesecond level.We adopt a similar approach. The problem is brokendown in an outer level gradient-based optimisation, wherelamination parameters and thicknesses are used as designvariables for mass minimisation, and an inner particleswarm optimisation level, where stacking sequences arefound that meet manufacturing guidelines, whilstmatching the lamination parameters obtained from theouter level. Constraints such as buckling, stress, strengthand feasible regions for the lamination parameters [27] areapplied at the outer level.The optimisation scheme adopted here is representedin the flow chart of Figure 6. Starting with the baselinedesign of §2, aeroelastic sensitivities are calculated viafinite differences by the gradient-based optimiser in theouter level (delimited by the solid black line). The designvariables that define the stiffness properties of thecomposite skins are passed to the inner level optimisation(within the dashed line), where a particle-swarm algorithmis used to retrieve detailed stacking sequences.5.1 Outer Level Optimisation Using Gradient-basedAlgorithmGradients of the objective function and gradients ofthe design constraints with respect to the design variablesare estimated using MATLAB fmincon via central finitedifferences. Central finite differences have shown to becomputationally more expensive, but more accurate incomparison to alternative methods. A standard interiorpoint algorithm is employed to solve the constrainedoptimisation problem.5.1.1Design VariablesThe outer optimisation design variables consists ofthicknesses of the metallic and composite panels (𝑥t ),composite lamination parameters (𝑥comp ), orientation andspacing of stringers and ribs (𝑥sa ), and control surfacedeflections (𝑥ctrl ). Each wing skin is divided into fivepatches, each with different thickness and laminationparameters. Spars and ribs thicknesses and the deflectionpattern of the control surfaces, 𝛿, are parameterized usingan average sum of sine and cosine series. For a genericfunction 𝑓, discretised in 𝑖 1, , 𝑛 points, these seriesare defined as1𝑖𝑖𝑓𝑖 (𝑓cos 𝑓sin),(7)2with(𝑓 𝑓min)𝑖̅𝑓[cos,sin] (1 𝜌)𝑓[cos,sin] 𝜌 max𝑖,(𝑛 1)̅𝑓[cos,sin] 𝑓min (𝑓max 𝑓min )[cos, sin] (𝜋(8)),𝑖(𝑛 1)(9)where 𝜌 represents the clustering factor of the series, 𝑓maxand 𝑓min denote the bounds to 𝑓. By changing theclustering factors, a wide range of curves can be achieved.To ensure that all variables are of the same order and avoidthat the problem is indifferent to optimisation step-sizevariations, all unknowns are nondimensionalised andscaled to vary between 0 and 1.5
2Structural arrangementvariables (xsa )Rib pitch1Rib orientation1Stringer pitch1Control variables (xctrl )4(𝜉𝑗𝐴Max deflection2Min deflection2Clustering factor 12Clustering factor 22Total8Thickness variables (xt )4(𝜉𝑗𝐴Total3Composite variables (xcomp t sparlamination30Rear SparparameterWing skinsTotal50TotalMaximum number of variables: 8344410225.1.3(10)𝐶bending 1,𝑧tip𝑧allowed 1,𝑁𝐿𝑚𝑖𝑗𝐶𝑙𝑙 𝑐𝑆𝐿 [()𝑐avg𝑖 1𝜃allowedObjective Function(15)Here, 𝑊 is the wing weight, 𝛼 is a weighting factor andwhere 𝐶max is the maximum allowable constraint metricand 𝐶𝑖 represents the value of the constraint metric for the𝑖𝑡ℎ finite element/buckling load factor. The parameter 𝜌𝐾𝑆represents the aggregation factor. Its value is set to 50 inorder to avoid machine-zero errors. The advantage of the𝐾𝑆 function lies in the fact that a large number ofconstraints can be combined into only one parameter.Three different 𝐾𝑆 parameters are used to aggregate:(a) the Tsai-Wu composite failure index, where 𝐶max 1,that is the maximum Tsai-Wu allowable value; (b) von–Mises stresses for the metallic sub-structures, where 𝐶maxequals the material maximum allowable stress, and (c)linear buckling load factors of different modes. 𝐾𝑆 valuesgreater than one represents constraint violations.Structural deformations such as tip twist angle andtip vertical displacement are also constrained. Theseconstraints are expressed as𝐶twist (13)(14)𝑓obj1 (𝑥) 𝛼𝑊 (1 𝛼)𝑆𝐿.𝑛𝜃tip 0,The objective function is the weighted sum of theaircraft wing weight and a lift spanwise loadingparameter, SL. The loading parameter is expressed as afunction of the square differences between a targetspanwise loading and the calculated spanwise loading atthe 𝑛𝑡ℎ gradient-based iteration:A number of constraints is applied in the optimisationroutines to obtain realistic designs.Structural stresses and buckling load factors areconstrained using the Kreisselmeier–Steinhauser (KS)[28,29] aggregation method. The aggregation formula isgiven by𝐾𝑆metric 0,𝐶lift 𝑊Design Constraints1 𝐶max ln [ 𝑒 𝜌𝐾𝑆 (𝐶𝑖 𝐶max) ],𝜌𝐾𝑆222(𝜉1𝑖 ) (𝜉2𝑖 ) 1,4 1)(𝜉𝑗𝐷 1) (𝜉𝑗𝐴 1)4 1)(𝜉𝑗𝐷 1) (𝜉𝑗𝐴 1)𝑖 1 𝜉𝑗 1,where 𝑖 𝐴, 𝐷 and 𝑗 1, ,4. These inequalities areincluded in the optimisation as nonlinear constraints. Theyensure convexity of the design space, a property thatguaranties retrieval of global, rather than local, optima.Table 3 summarises the type and number of constraintsused in the first level optimisation.Finally, to guarantee that the aerodynamic loads areconsistent, a redundant constraint is imposed on the totallift to make it equal to the aircraft weight. This is done toprevent sudden drops in aerodynamic loads that may arisedue to poor aero-structural spline interpolations, whichtend to occur because of architectural changes that canmodify the spline configuration. This constraint isexpressed asTable 2 summarises the type and number of designvariables used in this work. All thicknesses are boundbetween 2 mm and 16 mm. Control surfaces are allowedto move between –5 deg and 5 deg. Laminationparameters lie in the interval [-1,1], with additionalrestrictions discussed in §5.1.2. Rib orientation can varyfrom parallel to the free stream to perpendicular to thefront spar.5.1.222(1 𝜉3𝑖 )(𝜉2𝑖 ) 4𝜉1𝑖 𝜉2𝑖 𝜉4𝑖 (𝜉4𝑖 ) (𝜉3𝑖 2(𝜉1𝑖 ) 1) (1 𝜉3𝑖 ),Table 2: Type and number of the first level designvariables.𝑖,𝑗2̆𝐶𝑙𝑙 𝑐 () ]𝑐avg(16)𝑖,𝑗where, 𝑐avg is the average chord length, 𝑐(𝜂) and 𝐶𝑙𝑙 (𝜂)are the local chord and lift coefficient. The parameter 𝜂 isthe normalized semi-span position, whilst 𝑖 and 𝑗 areindexes referring to load cases and the number ofdiscretisation points along the semispan. Here, the target̆𝐶 𝑐spanwise loading ( 𝑙𝑙 ) has triangular-like shape given by𝑐avg𝑃(𝜂) 𝑎 1 𝜂2 (1 𝜂2 0.25𝜂4 ),(17)where the coefficient a is calculated within theoptimisation so to keep the integral of the lift distributionconstant. In summary, the outer level optimisationproblem can be stated asminimise 𝑓obj1 (𝑥)𝑥𝑇𝑤𝑖𝑡ℎ 𝑟𝑒𝑠𝑝𝑒𝑐𝑡 𝑡𝑜: 𝑥 {𝑥t , 𝑥comp , 𝑥ctrl , 𝑥sa}𝑖𝐾𝑆Mises 1𝑖𝐾𝑆Tsai Wu 1𝐾𝑆Buckling 1(11)(12)where 𝜃allowed is the maximum allowed tip twist angleand 𝑧allowed denotes the maximum tip verticaldisplacement, which is limited to 20% of the semi-span.These limits ensure linear elastic behaviour.As regards lamination parameters, one can retrievefeasible stacking sequences when the design space isbounded by the following equations [27]𝑠𝑢𝑐ℎ 𝑡ℎ𝑎𝑡 𝐶(𝑥) 𝑖𝐶twist 1𝑖𝐶bending 1𝑖𝐶lift(18)𝑖 1, , 𝑁𝐿 𝑊MTOW𝐶(𝑥comp ) 0{ 0 𝑥 1where 𝑥 {𝑥t , 𝑥comp , 𝑥ctrl , 𝑥sa }𝑇 is the vector of designvariables, 𝐶(𝑥) are the design constraints as a function of𝑥 and 𝑁𝐿 is the number of static aeroelastic load cases.6
“OPT2” to indicate the passive adaptive and servoaeroelastic designs, respectively.Figure 7(a) shows the spanwise variation of thesectional lift coefficient for all of the design cases. Thebaseline and OPT1 designs, have similar local liftdistribution. This effect reveals a limited exploitation ofthe tailoring capabilities offered by composite materials.This is because the wing skin are divided into largepartitions so, when active, the optimisation constraintsinfluence the sizing of large portions of the structure,leading to a conservative design. Future developmentswill address this limitation by taking a more “local”tailoring approach, where the skins are optimised atrib/stringer-bay level.The peak local lift coefficient occurs atapproximately 75% of the semispan for the baseline andOPT1 designs. This indicates that the wing tip stalls first,producing an undesirable disruption in roll control andaileron effectiveness. For the OPT2 design, the peak 𝐶𝑙𝑙 isshifted considerably inboard, occurring at 27% of thesemispan, showing improvements not only in the stallbehaviour but also in structural efficiency (the wing rootcarries more load than the wing tip, therefore producing asmaller root bending moment).The dimensionless span loads, 𝐶𝑙𝑙 𝑐/𝑐avg , inFigure 7(b) shows that both initial and OPT1 designs havean approximatively triangular load distribution past the40% of the semispan. This distribution results from achange in geometrical stiffness due to reductions in crosssectional area. The span load distribution for OPT2 isclearly more triangular, with greater loads inboard.Intuitively, this loading shape is preferable from astructural standpoint, because the centre of pressure isshifted towards the inner wing, therefore reducing the rootbending moment. Nevertheless, the load distribution inOPT2 does not match the target shape exactly. AnalysingFigure 8(a), where a negative sign represents a downwardsurface deflection, and comparing the deflection patternwith the span loads in Figure 7(b), one can note that theoptimised lift distribution is limited by the controldeflections at the wing root. This limitation is associatedwith the parameterisation chosen for the control deflectionscheduling. If the controls surfaces were allowed to moveindependently from each other, further improvementscould be achieved. Similarly, a different target shape,where greater negative tip control deflections createnegative lift (thus decreasing the bending moment evenmore), could lead to further weight reductions.Table 3: Type and number of constraints used in thefirst level optimisation eters2Ctwist80 KSTsai-Wu 2feasibilityKSBuckling 1 Cbending2criteriaTotal80 Total5 Total6Maximum number of constraints: 915.2 Optimisation Scheme for Optimum StackingSequence (Inner level)The goal of the inner level optimisation is to find afeasible stacking sequence that matches the in-plane andout-of-plane mechanical properties found in terms oflamination parameters in the first level optimisation.For this optimisation problem, the design variables,𝑥̅ , are the ply angles of each composite panel, constrainedby the design guidelines of §4.1. The number of plies, andconsequently the number variables is based upon thelaminate thickness from the outer level.The objective function is a weighted sum of squaredifferences between the lamination parameters from theouter level, 𝜉̌𝑗𝐴,𝐷 , and the lamination parameters calculatedat the 𝑛𝑡ℎ PSO iteration so that4422𝑓obj2 (𝑥̅ ) 𝛼 (𝜉𝑗𝐴 𝜉̌𝑗𝐴 ) (1 𝛼) (𝜉𝑗𝐷 𝜉̌𝑗𝐷 )𝑗 1(19)𝑗 1where the weighting factor 𝛼 is set to 0.5.6. Results DiscussionResults are presented for two different optimisationcase studies: (i) a passive aeroelastic design, where thecontrol surfaces are held at 0 deg, and (ii) a servoaeroelastic wing, where a triangular spanwise distributionof load is set to be one of the objectives for the optimiser.For reasons of brevity, results are presented for themost critical load case only, i.e. the 2.5g symmetric pullup manoeuvre; Not
Aerodynamic Performance Combining Control Surface Deflections and Aeroelastic Tailoring. In 2016 Applied Aerodynamics Conference: Evolution & Innovation Continues - The Next 150 years of Concepts, Design and Operations (pp. 12). Royal Aeronautical Society. Peer reviewed version Link to publication record in Explore Bristol Research PDF-document
The Aerodynamic Analysis and Aeroelastic Tailoring of a Forward-Swept Wing. (Under the direction of Dr. Charles E. Hall, Jr.) The use of forward-swept wings has aerodynamic benefits at high angles of attack and in supersonic regimes. These consist of reduction in wave drag, profile drag, and increased high angle of attack handling qualities.
PROJECT PROPOSAL 2013: EMPOWERING THE VULNERABLE AFFECTED REFUGEE WOMEN WITH SEWING AND TAILORING TRAINING SKILLS PROJECT SUMMARY PROJECT TITLE Empowering Vulnerable affected refugee women in Kampala with Sewing and Tailoring training skills PROJECT DURATION Six months. ( Starting when we get the funds) PROJECT AREAS
manual (chapter 19). It is now introduced in chapter 4 and is a constant throughout the manual: Tailoring and Adopting PRINCE2 (Chapter 4) I. Tailoring PRINCE2 –General considerations. II. Adopting PRINCE2 . III. Tailoring PRINCE2 to suit different projects. IV. Adopting PRINCE2
Optimization Dean E. Bryson and Markus P. Rumpfkeily University of Dayton, Dayton, Ohio, 45469, USA and Ryan J. Durscherz Air Force Research Laboratory, Aerospace Systems Directorate, Wright-Patterson AFB, Ohio, 45433, USA A multi delity aeroelastic analysis has been implemented for design optimization of a lambda wing vehicle.
Figure 1: Coupling of linear structural model and nonlinear unsteady aerodynamics within an aeroelastic CFD code such as FUN3D. A CFD-based aeroelastic system (such as the FUN3D code) consists of the coupling of a nonlinear unsteady aerodynamic system (ow solver)
Keywords: Unsteady Aerodynamics, Aeroelasticity, Computational Fluid Dynamics, Transonic Flow, Separated Flow. 1 Introduction The Aeroelastic Prediction Workshop (AePW) has been patterned after two very successful workshops conducted over the past decade: the Drag Predict
calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear
Abrasive water jet machining Ultrasonic machining. Difference between grinding and milling The abrasive grains in the wheel are much smaller and more numerous than the teeth on a milling cutter. Cutting speeds in grinding are much higher than in milling. The abrasive grits in a grinding wheel are randomly oriented . A grinding wheel is self-sharpening. Particles on becoming dull either .
