MULTIDISCIPLINARY AIRFRAME DESIGN OPTIMISATION

MULTIDISCIPLINARY AIRFRAME DESIGN OPTIMISATION

Gerd Schuhmacher∗ , Fernaß Daoud∗ , Ögmundur Petersson∗ , Markus Wagner∗∗Cassidian, Rechliner Straße, 85077 Manching, GERMANY

[email protected]; [email protected];[email protected]; [email protected]

Keywords: MDO, LAGRANGE, sizing, loads, sensitivity analysis, design automation

Abstract

Aircraft design is set to become ever more chal-

lenging in future, as development budgets shrink

and time schedules of new projects are com-

pressed. At the same time, the technical com-

plexity of designing a new aircraft is increasing

or remains at least as difficult as before. In other

words, the complex technical tasks of airframe

development must be accomplished with signif-

icantly reduced man-power and within shorter

time frames. Traditional design methods, that

iterate manually between loads calculations and

sizing of structural members may no longer con-

verge quickly enough for shortened development

times or fail to meet the design and performance

requirements. The answer to these challenges

identified at Cassidian is to take advantage of

Multidisciplinary Design Optimisation Methods

in the conceptual and preliminary design phases.

The loads calculation and structural sizing are

tightly integrated and combined with appropri-

ate design criteria models in order to simultane-

ously consider the full set of design driving re-

quirements within the optimization process.

1 Introduction

The complexity of aircraft designs increases witheach subsequent generation. This is often due toincreased interaction between the individual dis-ciplines determining the performance of the air-craft. The most influential from a structural pointof view being aerodynamics, loads, aeroelastics,stress and flight controls. At the same time, de-

velopment times are being shortened whilst theintervals between military aircraft projects in-crease, leading to a loss of valuable experience.Furthermore, aspects as sensor and systems in-tegration become more and more important forfuture military aircraft. In order to developsufficient knowledge about the complex multi-disciplinary interactions in the system promptlyenough to be of value in the early design phases,appropriate methods must be developed and pro-vided in tools suitable for industrial use.

Numerical simulation tools are powerfulmeans to analyse the complex physical phenom-ena influencing the behaviour of the aircraft aswell as the interactions between individual disci-plines at an early design stage. By coupling thesewith mathematical optimisation procedures, asystematic search of the parameter space for im-proved designs is enabled.

Multidisciplinary Design Optimisation(MDO) is based on rigorous mathematicaloptimisation methods that seek the minimum ofa constrained objective function. The objective,in general mass and, in particular, the con-straints e.g. strength and stability, flutter speed,aeroelastic control surface effectiveness etc. areusually highly nonlinear functions of the designvariables – the freely variable parameters of thedesign. The system analysis, based on variousdisciplinary analysis models (usually numericalsimulation models), provide the associationbetween the design variables and the relevantresponses of the system necessary to evaluatethe constraints. Using the system equations as

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G. SCHUHMACHER, F. DAOUD, Ö. PETERSSON &M. WAGNER

well as appropriate coupling methods betweenthe disciplines in combination with optimisationtechniques, the optimum design with respect togiven criteria is determined by the optimisationalgorithm. This leads not only to improvementsof the design with respect to the selected designand performance criteria but also to invaluableinsight into the trade-offs between various designdrivers. This becomes extremely important, inparticular if new design criteria with unknowninfluence on the design have to be considered.

By integrating MDO into the airframe de-sign process from the very beginning, knowledgeof the design in the earlier stages, where designfreedom is the greatest, is thus increased leadingto improved product performance (e.g. by reduc-tions in mass) at a simultaneous drastic reductionin development time and cost as illustrated in fig-ure 1.

(a) Traditional design process

(b) MDO assisted design process

Fig. 1 Increasing knowledge at earlier designphases with greater design freedom and subse-quent reduction in development times thanks tooptimisation methods [2].

Of particular importance when performingoptimisation of the airframe is the integration ofall design driving disciplines in the optimisationprocess in order to ensure the completeness ofthe problem description. Thus, the technical rel-evance of the resulting designs identified by the

optimiser can be ensured. The integration of theloads calculation into the optimisation process isespecially important. As the design and sizingof the structure influences its elastic and inertialproperties, it will influence not only its strengthbut also the aerodynamic and inertial loads actingon the structure. By including the loads calcula-tion in the optimisation process, the iterative loopbetween the loads calculation and structural siz-ing, the so called load loops, can be automated.Much of the manual work involved in trimmingthe aircraft for an updated mass distribution andin-flight shape, determining the loads (steady andunsteady maneuvers), applying these to the struc-ture and evaluating the relevant criteria such asstress, strain, stability and other criteria can thusbe fully automated. Furthermore, the sizing toachieve a feasible design is automated by the op-timisation process. This increases overall effi-ciency of the design process with respect to both,time and costs drastically.

However, it also must be mentioned, thatother reasons than stiffness changes will lead tochanges of the design loads. Examples of theseare changes to the design missions or the load en-velope as well as detailing of the design drivingload cases resulting from flight and landing ma-noeuvres, ground handling, failure cases, trans-port loads, fatigue etc.. These externally drivenload changes (which are not resulting from stiff-ness changes) can of course not be updated auto-matically within the optimization process. Theyhave to be considered in a subsequent optimiza-tion run with updated loads input. However, itis important to consider the major design drivingload cases already in the early design phase in or-der to avoid the need of late concept changes.

2 Challenges of Multidisciplinary AirframeOptimisation

A very simplified aircraft design process is de-picted in figure 2(a). After establishing a designconcept and the necessary analysis models to de-termine the relevant design responses, the cen-tral activity in figure 2(a) is the determination ofmodifications based on experience and heuristic

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Multidisciplinary Airframe Design Optimisation

methods to fulfill all design criteria and improveperformance. This results in a manual adjustmentof the analysis models to reflect these changes. Inthe inner loop, changes are made to material se-lection or dimensioning of individual structuralmembers. If these are not sufficient in order tomeet the design criteria, possibly even changes tothe design concept itself may be necessary, whichcan be an extremely time consuming process.

(a) Traditional design process

(b) MDO assisted design process

Fig. 2 The traditional 2(a) and MDO based 2(b)aircraft design processes.

In an MDO assisted design process shown infigure 2(b), however, the determination of designchanges is based on mathematical criteria andperformed automatically. This enables automa-tion of both, the inner sizing loop and partly alsothe outer loop for the structural concept. How-ever, in the following we will concentrate on theautomation of the inner sizing loop rather thanthe automation of the outer concept loop.

Both processes, traditional and MDO assisted

design process, must be supported by a wide va-riety of tools to evaluate the feasibility of the de-sign, by e.g. determining the strength and sta-bility of individual parts. These tools are oftenspecific to the company or even the particularaircraft. In addition, there are company specificanalysis methods for aeroelastic behaviour andloads calculations as well as guidelines and ruleswith respect to design and manufacturing.

Therefore the design of the aircraft, in par-ticular the airframe, will be driven by a largenumber of multidisciplinary design criteria de-termined by various different tools and method-ologies. These will include manoeuvre, gust andground loads, aeroelastic control surface effec-tiveness, flutter speeds, strength and structuralstability criteria, flight control input, dynamicresponses, manufacturing requirements etc. (seefigure 4 and table 3). An acceptable design mustmeet all of these requirements and thus the designprocess must take all of the design driving cri-teria into account simultaneously. This enablesthe determination of an optimum feasible com-promise solution. This means that the integratedairframe design process must combine all dis-ciplines and design criteria driving the airframestructural sizes and composite layup in order todetermine a feasible, minimum weight design.

An important fact is that, on the one hand, thelevel of complexity of applied analysis methods(and models) must fit the design phase (concept,preliminary, detailed), and on the other hand, aharmonisation of applied analysis methods be-tween optimisation and subsequent analyses forcertification purposes must take place, in order togenerate feasible and certifiable designs.

The comprehensive integration of tools andprocesses has been identified by the NATO-RTOas a major enabler increasing the affordability ofair vehicles. According to the RTO technical re-port TR-AVT-093: “Integration of Tools and Pro-cesses for Affordable Vehicles” [1] the key ele-ments of such a process are firstly, the integrationof design information to make data available assoon as they are generated and secondly, accel-eration of the design and decision process by ex-tensive use of mathematical modelling and sim-

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ulation combined with multidisciplinary designoptimisation methods. The report calls for therelevant design information to be provided to allthat need to know in the engineering design or-ganisation whilst maintaining a clear distinctionbetween proposed and approved states of the de-sign. The methods of MDO shall be applied atthe detailed level as well as on the system level inorder to automate and accelerate the overall de-sign process as well as to assist human creativity.

The major benefits to aircraft design throughthis integrated process identified in the report are:improved process integration and automation re-ducing manual effort, reduction in the number ofdesign cycles, improvement in the performanceof the product (mass, flight performance etc.) anda reduction in development time (up to 50% asstated in the report [1]).

2.1 Tools Developed at Cassidian to Meetthese Challenges

Several commercial software packages are avail-able that include physical analysis capabilitiesand optimisation techniques. Within these toolsthe disciplinary analyses are generally based onthe finite element or finite volume methods fore.g. structural or fluid analyses. These toolsare not tailored specifically to the needs of theaerospace industry and do therefore not includeimportant airframe design criteria. Furthermore,it is usually a challenge to include company spe-cific tools in commercial analysis or optimisationtools. However, if important design driving cri-teria are not included in the optimisation criteriamodel, it will most likely result in impractical de-signs being determined by the optimisation pro-cess.

Another approach is followed by commer-cial optimisation frameworks. These allow theuser to link several company specific or commer-cially available design tools into an overall, inte-grated design process. However, as these optimi-sation frameworks have no influence on the inter-nal analysis process of the individual tools, theyare generally limited to working with numericgradients resulting in high computational costs.

This severely limits the number of design vari-ables and constraints that can be included; thisis not mitigated through high performance com-puting since numerical sensitivity analysis over-strains current parallel computing capabilities.

Due to the lack of suitable commercial tools,Cassidian started the development of its own in-house multidisciplinary structural optimisationtool LAGRANGE as early as 1984. In the sub-sequent decades, LAGRANGE has been contin-uously enhanced as well as applied to the designof various military and civil aircrafts includingthe Eurofighter, X-31, A400M, A380, A350, Ta-larion and ATLANTE as well as to future aircraftprojects. An overview of some previous and cur-rent designs developed with the help of this op-timisation procedure can be seen in figure 3. Adescription of its application to the A400M rearfuselage design may be found in Schuhmacher etal. [6].

Fig. 4 Overview of system analyses types avail-able in LAGRANGE.

LAGRANGE consists of a general purpose fi-nite element solver well suited to the thin walledstiffened structures used in aerospace, optimi-sation algorithms and routines for evaluation ofcriteria models. Particular attention is paid tothe modelling of composite structures. Theunique aspects of LAGRANGE, however, whencompared to commercial structural optimisationcodes, are the availability of the fully analyt-

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(a) Eurofighter (≈ 1985): compositewing and fin

(b) X-31A (1990): composite wing (c) Stealth demonstrator (1995): fullaircraft design

(d) Trainer (2000): composite wingand fin

(e) A380 (2003) droop nose (f) A400M (2004 - 2006): rear fuse-lage skin and frames

(g) A350 XWB (2004 - 2006) tail sec-tion

(h) A400M (2006) cargo door (i) A30X (2007) composite wing

(j) A350 XWB (2008) fuselage (k) A350 XWB (2008) vertical tail-plane

(l) Advanced UAV (2006+): compos-ite wing and fuselage

Fig. 3 Overview of past applications of the LAGRANGE software.

ical sensitivities of each system response to agiven set of design variables and the integrationof diverse linear aerodynamic analysis tools foraeroelastic and loads analysis, including analyti-cal sensitivity of aerodynamic and aeroelastic re-

sponses. This enables highly efficient gradientbased search of the design space for the optimumdesign. Several optimisation algorithms are im-plemented in the program to this end, each suitedto a specific type of optimisation problem. These

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• Linear statics

• Linear dynamics (eigenvalues, transientresponse)

• Linear stability

• Steady aeroelastics (including trim-ming)

• Unsteady aeroelastics (flutter and gust)

Table 1 System analysis disciplines in LAGRANGE.

include both, first and second order methods sup-porting a large number of design variables (∼105− 106) and many constraints (∼ 106− 108).The automation of both load analysis and struc-tural sizing process is a key capability for the costefficient development of high-performance flyingaircrafts.

2.2 Analysis, Design Variable and CriteriaModels

LAGRANGE supports the following systemanalyses: linear statics, linear dynamics, linearstability, steady aeroelastics (including trimmingfor automatic generation of equilibrium flightconditions) and unsteady aeroelastics (flutter andgust), see table 1.

Each of these analyses can be coupled withan optimisation model linking physical model pa-rameters to the mathematical design variables ofthe optimisation algorithm. Modifiable parame-ters (see table 2) include cross sectional areas ofbars (e.g. stringers), geometrical sizes and com-posite lay up of various cross sections commonlyused in aerospace, thicknesses of shell elements,ply thicknesses in composites, fibre orientationsin composites, shape variables (currently beingredesigned) and in the case of steady aeroelasticanalyses, the trim variables, i.e. angles of attackof the aircraft and control surfaces.

To complete the picture, a range of designcriteria (see table 3) are available to define themultidisciplinary requirements to be met by theairframe design, and to differentiate between

• Bar cross sectional areas

• Geometric sizes of various (isotropicand composite) bar cross sections com-monly used in aerospace (I, Z, T,Omega etc.) as well as the lay up ofcomposite bars

• Shell or membrane thicknesses

• Composite ply thicknesses

• Composite fibre orientations

• Concentrated masses

• FE node coordinates (shape)

• Shape control points

• Trimming variables (angles of attack ofthe airframe and control surfaces)

Table 2 Physical design parameters in LAGRANGE.

feasible and infeasible designs. Most commonare traditional requirements related to stress inthe structure and appropriate failure criteria forisotropic or composite materials. Additionally, awide range of stability criteria are available basedon analytical buckling formulae covering skinand web buckling for isotropic, orthotropic andanisotropic structures, Euler (column) bucklingof stringers and several company specific vari-ations thereof, sometimes tuned to specific ap-plications. Analytical postbuckling criteria arealso included. Some details may be found inDaoud and Calomfirescu [3]. In addition tostrength and stability requirements, constraintsmay be placed on displacements (requiring min-imum stiffness). W.r.t. dynamics, natural fre-quencies may be confined to given frequencybands and furthermore, displacements, veloci-ties or acceleration responses of FEM-nodes canbe constrained. Aeroelastic criteria include re-quirements on aeroelastic effectiveness and flut-ter speeds. Finally, a range of manufacturingconstraints, particularly with respect to compos-ite structures, are supported.

In order to give an idea of the complexity ofthe software, it currently comprises around 3.5

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• Various strength or failure criteria formetals and composite materials

• Global stability criteria based on finiteelement analysis

• Local stability criteria based on analyti-cal solutions for skin and web buckling(isotropic, orthotropic, anisotropic),stringer column buckling and crippling

• Analytical postbuckling effects

• Displacements

• Natural frequencies

• Accelerations and velocities

• Aeroelastic criteria (control surfacecontrol surface effectiveness, flutterspeeds)

• Manufacturing constraints (e.g. plyshares, ply drop off, stringer / skin stiff-ness ratios, etc.)

• Trim constraints i.e. global force andmoment equilibrium

Table 3 Design criteria within LAGRANGE.

million lines of code. Input of the finite elementmodel uses a NASTRAN compatible input deckallowing any NASTRAN supporting preproces-sor, such as MSC Patran or Altair HyperMesh, tobe used to generate the model. Apart from textfile output, results can also be stored in binaryformats compatible with Altair’s HyperView postprocessor and in the near future in the OP2 for-mat compatible with any post processor capableof reading NASTRAN OP2 result files. In recentyears, a comprehensive modernisation of the en-tire code has been taking place, moving to theFortran 2003 standard, adding parallelisation ofperformance critical routines and improving therobustness and flexibility of the code to integratefurther analysis types in order to meet future re-quirements.

2.3 Integration of Loads Calculation into theOptimisation Process

In the traditional airframe design process, theloads analysis and structural sizing process areperformed sequentially in an iterative loop asshown in figure 5. Because of the strong couplingbetween the deformed shape, mass and stiffnessdistribution of the structure on the one hand andthe aerodynamic and inertial forces acting on iton the other, several iterations (load loops) maybe required. Furthermore convergence to a feasi-ble design is not guaranteed due to time and re-source limitations. In this context, feasible refersto a design fulfilling each of the disciplinary re-quirements with respect to, for example, stress,stability, aeroelastic and manufacturing designcriteria.

Fig. 5 Automated load loops; within LA-GRANGE the trim and loads analysis (using theaerodynamic panel model and the finite elementmodel representing structural mass and stiffness)is automatically conducted at each optimisationiteration, updating the loads and aeroelastic prop-erties for the structural sizing.

The approach at Cassidian to speed up thisprocess and increase its robustness with respectto delivering feasible designs is to combine theloads calculation with the classic sizing processin an overall automated cycle. The determinationof the structural loads dependent on the deflec-tions thus becomes part of the MDO procedurein the LAGRANGE programme.

In practice, this means that in addition tothe structural finite element model (bottom right

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hand corner in figure 5) the aerodynamic influ-ence coefficients from the evaluation of a higherorder aerodynamic panel model (right hand cen-tre in figure 5) are supplied to the program. Fur-thermore, the user supplies a coupling modelto one of the available mesh interpolation algo-rithms in the programme. These create couplingmatrices between the analyses meshes, transfer-ring displacements to the aerodynamic mesh andforces to the structural mesh.

The sensitivity analysis is more involved thanin a standard static loadcase as the applied loadsnow implicitly depend on the structural sizingvariables through aeroelastic effects. The detailsof the coupled sensitivity analysis may be foundin Daoud et al. [4].

Figure 6 shows the traditional design processleading from an external aerodynamic loft and in-board profile to the global finite element model ofthe structure (GFEM) used for the manual loadsand sizing loops. The resulting structure is sub-sequently being used by the stress departmentfor detailed checks. Furthermore, dynamic andaeroelastic criteria have to be checked. In thetraditional airframe design process, usually spe-cific simplified models have been used for thedynamic analysis (flutter, gust etc.), instead ofworking with the GFEM (s. Fig. 6). This resultsin additional effort and delays, in order to incor-porate results from the manual sizing into the dy-namic model. Figure 7 shows how the manualdesign updates can be replaced by the automatedMDO process leading to an optimised GFEM,which will be subjected to detailed checks. Gen-erally, no significant subsequent design changesare required as the relevant design criteria havealready been considered during the optimisationprocess.

In ongoing development work LAGRANGEis being extended to also include dynamic aeroe-lastic loads due to turbulence (gusts), details ofwhich may be found in Petersson [5]. Further-more, in future, the process is to be extendedbeyond the realm of linear aerodynamics by en-abling coupling to high fidelity CFD analyses.

Fig. 6 The traditional sizing process from outerloft and structural concept via global finite ele-ment model (GFEM) and manual loads and siz-ing loops to final stress check.

Fig. 7 MDO design process replacing the manualloads and sizing updates with an automatedMDObased process leading to a fully automated loadcalculation and sizing process.

3 Application Examples

Figure 3 shows an overview on past applications.Below, a couple of application examples of theMDO process implemented in LAGRANGE aredescribed in more detail.

3.1 Aeroelastic Tailoring of A350 Wingbox

Aeroelastic tailoring refers to the tuning of theelastic properties of a structure in a fluid in order

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to influence its deflected shape and, thus, also thefluid forces themselves. A simple example is thatof a clamped plate at a positive angle of attack tothe flow. The lift generated by the plate along itsspan will cause it to bend upward. Modificationof the stiffness properties of the plate to introducecoupling between bending and torsion (e.g. byusing a non-symmetric laminate) will cause theplate to twist as it deflects due to the lift, influenc-ing the local angle of attack and subsequently thespanwise load distribution. A detailed descrip-tion of the theory and application of aeroelastictailoring is given by Shirk et al. [7].

Although aeroelastic tailoring as such is notlimited to composite structures (bending-torsioncoupling is influenced also by purely geometricvariables such as sweep angle, for example, or theorientation of stiffeners such as ribs or stringers)the finely tunable elastic properties of compositematerials make them particularly well suited tothe task.

(a) Aerodynamic mesh (b) Structural FEM model

Fig. 8 Aerodynamic panel model and structuralFEMmodel of the A350 wingbox used for aeroe-lastic tailoring. Differently coloured regions inthe structural model indicate groups of elementswith shared properties influenced by a designvariable.

The A350-XWB will be the first civil aircraftfrom Airbus to use a wing constructed entirelyof composite materials (outer skin and internalsupport structure). The composite wing box ofthe A350 was the subject of a design study per-formed by Cassidian jointly with Airbus to assessthe potential weight savings through aeroelastictailoring.

The study was performed using the two nu-merical models shown in figure 8 for evaluation

of aerodynamic loads, structural displacements,stresses and buckling reserve factors. The designparameters that could be varied by the optimiserwere the cross sectional area of the stringers rep-resented by beam elements attached to the outerskins, the thickness of individual plies in thecomposite skin (homogeneous, non discrete plythicknesses were assumed) and the fibre angles.These are defined in figure 9. A rotation of theentire stack orientation with respect to the base-line structure was defined as a design variable aswell as the angle γ of the diagonal plies.

The parameters of clusters of 4 bucklingfields (2×2 patch in chordwise and spanwise di-rection) were grouped together and controlled bysingle ply thickness design variables with a cor-responding grouping of stringer cross-sections toreduce the total number of design variables. Thisresulted in up to 3000 design variables for thestudies with the greatest design freedom. Somestudies allowed the thickness of the diagonalplies to be varied individually creating unbal-anced lay-ups.

(a) Orientation, β (b) Variable ply angles, γ

Fig. 9 Design variables controlling the wing skinply angles: orientation of the of the 0◦ ply withrespect to baseline design and global structureand diagonal ply angles.

The criteria models implemented in LA-GRANGE were used to define constraints on thebuckling of the anisotropic composite skin, col-umn buckling of the stringers, stress and manu-facturing aspects such as ply drop offs.

For the design studies, 19 load cases weredefined including landing loads (landing gear at-tachment) and aeroelastic load cases for trimmedforward flight and roll manoeuvres. Trim vari-ables included the total angle of attack and de-

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flections of aileron and spoiler. The weight wasdefined as objective function to be minimised.Over 40 optimisation studies were performedwith varying numbers of design variables and set-tings for the bounds of structural sizing parame-ters.

When rotating the stack orientation forwardas a whole by a negative angle β as shown in fig-ure 9 the studies show a reduction in the loadsat the wing root through the wash-out effect ofmoving the elastic axis forward (reducing the lo-cal angle of attack at the tip, moving the lift re-sultant inboard). However, as the rotated stack isless resistant in terms of strength, especially forcomposite lay-ups with fixed minimum and max-imum ply shares, there is a structural penalty topay in the form of increased thickness to satisfystrength criteria.

Increasing the number of variables availableto the optimiser such as allowing it to vary thethickness of individual plies independently ratherthan of the stack as a whole or the angle betweenthe diagonal plies, increases the size of the designspace and reveals designs, where the load allevia-tion effect outweighs the structural penalty. Thisstudy has been performed in 2007.

3.2 Future MALE Aircraft

In the following, the results of a multidisciplinaryoptimisation of a generic MALE1 with aeroelas-tic analysis, sizing and trimming variables anda multidisciplinary criteria model are presented.The aeroelastic analysis includes the simulationof trimmed flight conditions of the design drivingsteady manoeuvres. The study was performed ina conceptual design phase in 2010.

As the objective of the activity is to obtaina feasible, minimum mass airframe design, thewhole fuselage structure is parametrised. Addi-tionally trimming variables are defined for eachmanoeuvre as can be seen in Figure 10b.

The multidisciplinary criteria model can besubdivided into stressing criteria, resulting in alarge number of constraints for each load case, as

1Medium Altitude Long Endurance reconnaissance air-craft

(a) Sizing variables (1.015 in all)

(b) Trim variables (250 in all)

Fig. 10 Parametric design variable model.

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(a) Strength constraints (2.464.550 inall)

(b) Buckling constraints (74.950 in all)

Fig. 11 Stressing criteria model with a total num-ber of 2.539.500 constraints.

can be seen in Figure 11. Furthemore it com-prises criteria such as flutter speeds, displace-ments and manufacturing requirements (see fig-ure 12), which are fewer in number than the stressconstraints, however, the requirements regardingmodelling and mathematical complexity are usu-ally much higher.

In Figures 13 and 14 the thickness distribu-tion and reserve factors of the composite skin andshear walls can be seen.

The results clearly show, that the load levelin the airframe is relatively low compared to afighter aircraft, hence, many areas run to min-imum gage (waste of weight saving potential).The conclusion out of this study was that the cho-sen airframe design concept had to be revised.This shows that results from the MDO designprocess can provide valuable information alreadyin the conceptual design phase where the struc-tural concept may still be adjusted. The study

(a) Trim constraints; an additional flutter constraintfor 1 mass configuration was also included

(b) Displacement constraints

(c) Manufacturing constraints

Fig. 12 Criteria model comprising flight-physics,flutter, displacement and manufacturing.

described above was done with design variablesfor the fuselage only. The optimization of thewing was performed in another study. Further-more, the optimization of the complete airframeis currently ongoing with an updated configura-tion.

Fig. 13 Thickness distribution and reserve fac-tors of composite skin.

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Fig. 14 Thickness distribution and reserve fac-tors of composite shearwalls.

4 Conclusions

MDO increases the amount of information avail-able to the engineer in early design phases regard-ing the behaviour of the system being studied,helps identify design driving requirements and il-luminates the often complex interactions betweenthe various disciplines affecting the performanceof the system. Integration of traditionally de-coupled processes such as loads calculation andstructural sizing in an automated process drivenby MDO methods, reduces the number of man-ual iterations and eases the search for a feasibleoptimum compromise design, fulfilling all designcriteria. The major benefit, therefore, is a tremen-dous reduction in development time and effortand subsequently lower costs.

Commercially available analysis and optimi-sation tools generally suffer from either a lackof flexibility to include company internal disci-plinary tools such as buckling routines or aeroe-lastic solvers or are very limited in the numberof design variables and constraints that can be in-cluded in the optimisation due to being tied tonumerical sensitivity analyses.

In the Cassidian multidisciplinary optimisa-tion tool LAGRANGE these problems are solvedby determining the analytical sensitivity of eachdesign response required to evaluate a criteriamodel with respect to the design variables. Spe-cial disciplinary tools developed within the com-pany to simulate the aircraft response or evalu-ate design criteria are either integrated into thetool directly, or, in the case of aerodynamics, de-liver results in the form of linear influence coeffi-cients from an aerodynamic panel model read by

the programme. A multidisciplinary analysis ofthe response is thus enabled as well as optimisa-tion of the coupled system with a large number ofdesign variables and constraints using efficient,gradient based algorithms. In almost 30 yearsof development and application within the com-pany, the code has been used for a broad range ofcivil and military aircraft projects, from compo-nents through large assemblies to entire aircraft.It leads to feasible designs satisfying all the rel-evant requirements of design driving criteria at aminimum structural weight.

The continued development of LAGRANGEis a strategic decision based on its specialisa-tion for aerospace design tasks not available incommercial off the shelf tools, the ease withwhich an in-house tool can be adapted to newrequirements and technology developments andthe competitive advantage it offers. The fullyintegrated and automated multidisciplinary loadanalysis and sizing process results in an optimalproduct performance as well as a tremendous re-duction in development time and costs.

References

[1] Integration of tools and processes for afford-

able vehicles, Tech. Report RTO-TR-AVT-093AC/323(AVT-093)TP/102, NATO Research andTechnology Organisation, December 2006.

[2] Pietro Chervellera, Integration of optimization

methods into the aircraft structural design pro-

cess at subsystem and component level, Ph.D.thesis, Universitá degli Studi di Padova, 2006.

[3] Fernass Daoud and Mircea Calomfirescu, Opti-

mization of composite aircraft structures in con-

sideration of postbuckling behavior, InternationalJournal of Structural Stability and Dynamics 10(2010), no. 4.

[4] Fernass Daoud, Ögmundur Petersson, Sebas-tian Deinert, and Paul Bronny, Multidisci-

plinary airframe design process: Incorpora-

tion of steady and unsteady aeroelastic loads,14th AIAA/ISSMO Multidisciplinary Analysisand Optimization Conference, AIAA, September2012.

[5] Ögmundur Petersson, Optimization of aircraft

wings including dynamic aeroelasticity and man-

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ufacturing aspects, 5th AIAA MultidisciplinaryDesign Optimization Specialist Conference, 04. -07. May 2009, Palm Springs CA, AIAA, AIAA,May 2009.

[6] Gerd Schuhmacher, Martin Stettner, Rainer Zote-mantel, Owen O’Leary, and Markus Wagner, Op-

timization assisted structural design of a new mil-

itary transport aircraft, 10th AIAA/ISSMO Mul-tidisciplinary Analysis and Optimization Confer-ence, AIAA, AIAA, August 2004.

[7] Michael H. Shirk, Terrence J. Hertz, and Ter-rence A. Weisshaar, Aeroelastic tailoring - the-

ory, practice and promise, Journal of Aircraft 23(1986), 6 – 18.

4.1 Copyright Statement

The authors confirm that they, and/or their company or

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that they have obtained permission, from the copy-

right holder of any third party material included in this

paper, to publish it as part of their paper. The authors

confirm that they give permission, or have obtained

permission from the copyright holder of this paper, for

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the ICAS2012 proceedings or as individual off-prints

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MULTIDISCIPLINARY AIRFRAME DESIGN OPTIMISATION