wing design ion

8/3/2019 Wing Design ion

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American Institute of Aeronautics and Astronautics

Multidisciplinary Design Optimization Of A Regional Aircraft Wing Box

G. Schuhmacher, I. Murra, L. Wang,

A. Laxander, O. J. OLeary

#and M. Herold

**

Fairchild Dornier GmbH, 82230 Wessling, Germany

MDO team leader, Dr.-Ing., Engineer

MDO team, Ph.D., Engineer, member AIAA

MDO team, Dr.-Ing., EngineerAeroelastics group, Dr.-Ing., Engineer#MDO team, Ph.D., Engineer**MDO team, Dr.-Ing., Engineer

ABSTRACT

Multidisciplinary Design Optimization (MDO) tech-

niques were successfully applied in sizing the wing

boxes of the newly developed Fairchild Dornier re-

gional jet family. A common finite element model for

the whole aircraft was used for the static and aero-

elastic optimization and analysis purposes. A detailed

design model in the order of thousands of design

variables was constructed. All relevant sizing re-

quirements for structural strength, aeroelastic behav-

ior and manufacturing, resulting in over 800,000 con-

straints, were applied under all loading conditions.Many auxiliary tools for automating the process of

preparing the huge amount of required input data, as

well as the rapid assessment of results, were devel-

oped. Most of these tools were developed in close

coordination with the MSC Software GmbH, since

the MDO implementation process is centered around

the optimization procedure in MSC.Nastran SOL 200.

A new MSC.Nastran feature called External Server

was utilized to integrate company specific wing buck-

ling constraints into the Nastran optimization loop. An

independent and comprehensive analysis of the con-

ceived wing boxs structural sizes confirmed the va-

lidity of the results.

1 INTRODUCTION

The structural design of an airframe is determined by

multidisciplinary criteria (stress, fatigue, buckling,

control surface effectiveness, flutter and weight etc.).

Several thousands of structural sizes of stringers,

panels, ribs etc. have to be determined considering

hundreds of thousands of requirements to find an

optimum solution, i.e. a design fulfilling all require-

ments with a minimum weight or minimum cost re-

spectively. The design process involves variousgroups of the airframe manufacturer and its suppliers,

and requires the application of complex analysis pro-

cedures to show compliance with all design criteria.

Traditionally the structural sizes of a wing box are

determined by the stress group of the airframe manu-

facturer or its supplier. This is done by analyzing the

stress and buckling reserves for a few selected load

cases and modifying the sizes, until the strength crite-

ria are satisfied. The major shortfalls of this approach

are:

Modification of the structural sizes usually affects

not only local stresses but also the internal load dis-

tribution. Therefore, this approach requires an itera-

tive, complicated and time-consuming process.

Since the design process is performed with a few

dominating load cases only, there is a risk of not

meeting the design criteria for the complete set of

design driving load cases. Furthermore, fatigue re-

quirements are only considered on an approximate

basis. This can result in re-work and additional costwhen the full set of load-cases and fatigue criteria

are considered later in the design process.

Due to resources and time limitations, the manual

iterative process is usually stopped after achieving a

design which is feasible, from a strength viewpoint,

and which is close enough to the target weight. This

design is not necessarily a minimum weight design.

Aeroelastic requirements regarding elastic control

surface effectiveness, aileron reversal and flutter are

usually not considered by the stress engineers de-

termining the structural sizes. In most cases there

are significant time-delays until the design deter-mined by the stress engineers is available for aero-

elastic analysis. Shortfalls in the aeroelastic behav-

ior then require significant additional efforts in or-

der to find feasible solutions. Those solutions are

usually non-optimal, expensive repair-solutions,

which have to be introduced fairly late in the design

process.1

Due to program requirements, the development

cycles shrink continuously whilst the technical de-

mands grow. These contradictory requirements can

not be fulfilled by traditional sequential engineering

practice.

Because of its size and complexity and the problems

explained above, there is a clear need for advanced

tools integrating and accelerating the design process.

Efficient model management and harmonization of

analysis procedures play an important role in im-

proving the workflow in multi-national projects.2


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However, the problems encountered by multi-national

projects result primarily from poor coordination or

poor communication between all partners, rather than

the inherent challenges of the structural design proc-

ess. Multidisciplinary Design Optimization (MDO)

Methods have proven to provide an efficient and

powerful basis for integrating all disciplines and de-termining a feasible, minimum weight design. Within

the last 20 years, several in-house MDO programs

have been developed by the aircraft industry.3,4,5,6 A

commercial software, capable of solving multidisci-

plinary aircraftdesign optimization problems (in-

cluding aeroelastic requirements), is MSC.Nastran

SOL 200. Despite the successful demonstration of the

power and efficiency of these tools in solving various

benchmarks and industrial applications, there is still a

significant lack of comprehensive, real-life aerospace

applications. This is due to technical as well as to

cultural aspects. Several obstacles, which have pre-

vented the broad application of MDO in aerospace

projects are:

Simultaneous consideration of all relevant criteria

and analysis procedures requires several changes

compared to that of the traditional, sequential de-

sign process. And generally speaking, change to es-

tablished procedures and already defined responsi-

bilities is usually met with strong resistance.

The hierarchy of traditional aerospace companies

usually does not have a functional unit performing

the MDO tasks and organizing the required coop-

eration between all involved parties.1

Each discipline (e.g. stress, aeroelastics etc.) typi-cally tailors FE-Models according to their individual

requirements. For MDO these models must be har-

monized to avoid unnecessary data handling com-

plications.

Development of MDO software requires tremendous

resources. This is due to the fact, that it must be able

to treat all relevant analysis and sensitivity calcula-

tions very efficiently within an integrated computa-

tional process, in order to optimize real-life, large

scale aerospace applications.

Due to the limited amount of detail within global

aircraft FE-models, the strength and buckling analy-sis can not be performed based purely on FE-

analysis methods. The detailed strength and buck-

ling analysis is generally performed based on semi-

analytical, company confidential procedures, which

must also be incorporated in the optimization proc-

ess. This is crucial, since a design will never be ac-

cepted by a stress group so long as it is not fully

compliant with their design criteria.

A lot of effort and persuasion are required to over-

come these obstacles. Nevertheless, the contradiction

of continuously growing design complexity, requiring

the integration of aerodynamics, structures, aeroelas-tics, flight controls and system design, on the one

hand, and continuously shrinking development times

on the other, can only be solved by such advanced

design tools and processes as represented by the

MDO.

The implementation of the MDO process at Fairchild

Dornier (FD) started in March 2001. Since then, it has

been successfully applied to the preliminary sizing of

the wing box structure of the FD regional aircraft

family (728-100/200/300, 928-200). The implemen-tation of the whole process is centered around the

optimization procedure SOL 200 of MSC.Nastran.

The main merit of the work reported in this paper is to

demonstrate the benefits of MDO techniques for the

preliminary sizing of the wing box and other structural

components.

The produced structural sizes for the above mentioned

wing components satisfy the minimum weight re-

quirement and are capable of carrying all the applied

loads without violating any of the imposed various

design requirements. These design criteria included

various stress, buckling, fatigue, manufacturing, light-

ning protection and aeroelastic (flutter, aileron rever-

sal) requirements. In the MDO process all design

conditions and applied loads were simultaneously

considered. A detailed design model having thousands

of design variables representing all the structural

components treated in the sizing process was used.

Due to computer storage and memory limits as well as

the required real time for such a large optimization

problem, the sizing due to the aeroelastic require-

ments was subsequently performed after achieving an

optimum design with respect to all other design con-

ditions. The conceived design for the total wing was

subjected to detailed analysis under all loading andaeroelastic conditions, to ensure the validity of the

sizing process. The result of this analysis will be

briefly discussed.

2 The Structural Analysis and Design

Process - Traditional and Today

Various departments and external suppliers are in-

volved in the structural analysis and design process,

(see Fig. 1). In general, Fairchild Dornier (FD) takes

responsibility for all whole aircraft aspects (aerody-

namics, aeroelastics, loads, overall stiffness and stress

distribution etc.), which can only be analyzed and

assessed by considering the interaction of all compo-

nents within a whole aircraft analysis model. The

suppliers take responsibility for the detailed analysis

and design of single components (e.g. wing, empen-

nage, tail-cone, engine etc.) based on the loads and

criteria defined by FD. Within the FD aircraft de-

velopment process, the conceptual design department

determines the general aircraft configuration (wing

size, engine position, fuselage cross-section, design

masses etc.), whilst the aerodynamics group shapes

the loft. Based on this information the structural de-sign process starts by creating a simplified Beam

Aircraft Model (BAM), which represents the esti-

mated global stiffness distribution as well as the


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Fig. 2: Today's Design Process automated by Multidisciplinary Design OptimizationTechniques

Fig. 1: The "Traditional" Structural Analysis and Design Process at Fairchild Dornier

Dynamic Aircraft Model

DAM

BAM

WAM

Loads

Aeroelastics

Su lier 1 Su lier 3 Su lier

Structures / Strength Design

Detailed Strength Analysis and Design

Stress Results and

Executable Models

for Suppliers

....

Updated FE-

Component

Models from

Suppliers

Flutter speed

Aeroelastic Effectiveness

Supplier 2

Payload

Fuel

Weights

Structural- &

Systems Weight

Weights

Panel and

Beam Model

Whole

Aircraft

Model

(WAM)

Loft DAM

Unsteady-Panel Model

for Gustloads

Loads

Aerodynamics

L

O

A

D

S

Beam AircraftModel (BAM)

Unsteady-

Panel Model

Results

Final Design

WAM

Structural- and Sensitivity-Analysis

U-PAM,

S-PAM

Constant

Design Loads

Limit, ultimate

& fatigue stresses

Flutter &

Effectiveness

Evaluation Model

Objective: weight, etc.

Constraint Functions:- Limit & Ultimate Stress

- Fatigue Stress

- Various Buckling Crit.

- Flutter & Effectiveness

Optimization Algorithm

1. Set-up substitute problem

2. Solve substitute problem

3. Check convergencecriteria

Design Model

FE Properties:

-Thicknesses

-Stringer Sizes

Geometry not yet

considered as

design variables

Loads

Structures

Aeroelastics

Optimization

Multidiscipl. Team

Structural responses

(stresses, flutter

speeds, etc)

Sensitivities of structural

responses w.r.t. changes of

the design variables

Functions & Sensitivities

Objective and Constraints

Definition of

Design Criteria

Structural

Analysis-

Models &

Loads

Definition of

Design Model

Selection of

Optimization

Algorithm

and Criteria

Improved Set of

Design Variables

Start

Updated Set

of Analysis

Model Pa-

rameters

End

Optimum

Design

Design

Loads

External

Server

Buckling

Criteria


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global mass distribution (Fig. 1 shows a schematic

mass representation which is substantially simplified

compared to the real model). The BAM is coupled

with an aerodynamic panel model to analyze all rele-

vant aeroelastic effects (flutter, control surface effec-

tiveness etc.). Furthermore, it is used by the loadsgroup to calculate external loads resulting from the

relevant flight and ground maneuvers as well as other

design driving scenarios (fan blade off, bird strike

etc.). The loads are usually partitioned into aerody-

namic, inertia and concentrated loads and are supplied

to the structures group as running loads along the

elastic axes of fuselage, wing, control surfaces etc.

In parallel to the process of calculating the external

loads, a more detailed Whole Aircraft Shell FE-Model

(WAM) is generated by the stress group in coopera-

tion with the suppliers. The stress group also converts

external loads into FE-Forces and -Moments to be

applied to the WAM. With the loaded WAM, the

internal loads (grid point forces and stresses) can be

calculated and used as a basis for strength design. The

internal loads and partially condensed models are then

transferred to the various suppliers responsible for the

detailed design of a specific substructure (wing, fuse-

lage, empennage etc.). The WAM is a relatively crude

model (250,000 degrees of freedom) which is never-

theless sufficiently accurate to determine the internal

load-flow and the global stress distribution. Stress

concentrations due to notches or local design details

need to be analyzed with refined numerical or analyti-

cal models. The internal loads determined by theWAM are fed into locally refined analysis models

containing all relevant details of the design. Based on

these detailed models, the reserve factors for limit,

ultimate, fatigue stresses and all kinds of buckling

criteria are calculated and used to assess and deter-

mine the detailed design. Once detailed design sizes

have been established and introduced into the FE-

models, FD assembles and updates the WAM. The

updated WAM is then used to derive a BAM with

equivalent stiffness in order to start a new loop of

aeroelastic, loads and stress analysis followed again

by detailed design. Through this iterative process, the

effects of all changes (stiffness and mass distribution,refined aerodynamics due to wind-tunnel results etc.)

are accounted for. The complete loop has to be cycled

several times until the process is converged.

The traditional work share described above is typical

for most airframe manufacturers. One of the most

important shortfalls of this approach is, that the de-

tailed design process considers only static require-

ments, since the aeroelastic behavior can only be

analyzed and assessed on a whole aircraft level. The

consequences of this shortfall have already been de-

scribed in the introduction. An additional problem is

the tremendous amount of man-power and time re-

quired to determine the several thousands of design

sizes subject to several hundreds of thousands of

strength constraints.8 Due to the limited development

time, the process cycle shown in Fig. 1 is continued

without waiting for the WAM to be re-sized. This

means, that the process cycle i+1 is performed based

on a WAM, which is sized for the loads of cycle i-1.

Since man-power and time are expensive and limited,

the traditional design process is usually stopped be-fore a minimum weight design is achieved. These

shortfalls can be overcome by automating the design

process through MDO techniques.

Fig. 2 shows how the MDO process has been orga-

nized at FD based on MSC.Nastran SOL 200. The key

role for successful application is a Multidisciplinary

Team consisting of representatives of all involved

disciplines. Before the numerical optimization loop

can be started, the design must be parameterized and

all disciplines must make available their analysis

models and design criteria. A very flexible approach

of describing the design in parametric form is to util-ize "constructive design models".

5,10However, the FD

wing box sizes can also be parameterized by simply

assigning design variables to the FE-properties (cross-

sections, thicknesses). The linking scheme between

FE-properties and the independent design variables is

represented by the Design Model and it is based on

constructive, manufacturing as well as numerical

considerations. Structural Analysis provides all rele-

vant structural responses based on the analysis models

and the current set of design variables. The Sensitivity

Analysis calculates the first derivatives of all re-

sponses w.r.t. the independent design variables. A

very important new feature of MSC.Nastran is theExternal Server, which allows the integration of user-

defined design criteria described by Fortran routines.

It therefore can be used to integrate various detailed

design constraints, which are dependent on

NASTRAN responses (stresses, displacements etc.).

All detailed FD wing buckling criteria (skin, stringer,

and column buckling and stringer crippling) have

been implemented within this External Server. The

objective function and all constraints are mathemati-

cally defined in the Evaluation Model based on

structural responses. They are then transferred to the

optimization algorithm to find an improved set of

design variables. This set is converted into a new set

of FE-Properties in order to initiate the next cycle. As

a result of the non-linear relationship between the

constraints and design variables, the full process must

be repeated several times until an optimum design is

found.


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Aileron

Pylon

Engine

Outer Wing

Inner Wing

Center

Wing

Front Spar

Rear Spar

Fig. 4: FE-Model of the wing (93,000 DOF)

tST

hST

t2t1

Skin

Stringer

StringersTruss Ribs

Machined Ribs

Rear Spar

Front Spar with

vertical and hori-

zontal stiffenersLower

Skin

Fig. 3: General layout of the outer wing box


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3 Wing Box Design

Figure 3 shows the lower panel, the spars and the

internal ribs of the outer wing box. The panels consist

of a skin stiffened by rectangular stringers. The num-

ber of stringers decreases from inboard to outboard

due to wing taper. Ribs are connected both to spars

and panels. The panels and spars carry global bending

and torsional loads, whilst the primary function of ribs

is to stabilize the whole structure and transfer the local

air load into the wing box. Since the panels and the

spars are machined from solids, the sizes of skin and

stringers can change between each pocket surrounded

by two stringers and two ribs. It is even possible to

have a varying skin thickness or varying stringer

height within a pocket to provide the locally required

strength and stiffness with a minimum weight. This

results in several thousands of independent parametersdefining the whole wing box design.

4 The Finite Element Model

The level of meshing detail of the wing model is

shown in Fig. 4. This model is the same finite element

model that is typically used for sizing by traditional

methods. The wing box model mainly consists of

Shell and Beam elements representing skin and

stringers/stiffeners, respectively. The whole wing

model with its major substructures (center, inner and

outer wing) is given in Fig. 4. Combining wing box

with fuselage and empennage FE models results in a

WAM of approximately 250,000 degrees of freedom.

A finite element model common to the stress, aero-

elastics and the MDO group is used. This FE model

satisfies the requirements of all groups involved.

Harmonization of the initially different FE models

proved to be very important to allow rapid and effi-

cient exchange of data between all groups within the

MDO process.

5 The Design Model

The most important structural sizes of the wing box

comprise the skin thickness and the stringer height

and thickness. This applies to the panels as well as to

the spars. Linear equations define the relationship

between the independent design variables (DV) and

the FE-Properties representing skin and stringers

sizes:

ti = ti0 *xk; Aj =Aj0 *xk; I1j =I1j0 *xk

with ti =skin thickness of element i

Aj = area of stringer j

I1j = 1st moment of inertia of stringer j

xk = design variable k

ti0, Aj0 ,I1j0 = constants

For the purpose of applying buckling constraints, the

upper and lower surfaces of the wing are subdivided

into so called Buckling Fields. Each buckling field

consists of the finite element mesh between two adja-

cent span wise ribs and two chord wise adjacent setsof stringers. Mechanically speaking, this corresponds

to each stiffened sub-panel on the wing. The skin

elements within each buckling field were linked to-

gether and represented by a single design variable.

The same applies to the stringer properties. Theoreti-

cally, the changes in stringers sizes should also affect

second moment of inertia and the stringer offset.

However, these effects are neglected during the opti-

mization process for two reasons: firstly, their influ-

ence on the mechanical behavior is small; secondly,

their consideration would cause a tremendous increase

in the computational effort required for sensitivity

analysis, as a consequence of their non-linear relation-ship to the design variables. Nevertheless, the stringer

offset and the second moment of inertia are updated

after the optimization before the analysis of the new

sizes takes place.

The sizes of the internal ribs and vertical spar stiffen-

ers are not considered in the optimization process,

since their impact on the internal load flow and global

stiffness is negligible. The overall design model of the

whole wing was structured corresponding to the major

wing sections. Each of these components was subdi-

vided again into upper and lower panels, front and

rear spar, as well as skin and stringers. With this ar-rangement the total number of design variables

reached 2515 as shown in Table 1.

Table 1: Design variables

Component No. of DV per wing section

Center Inner Outer Total

Upper skin 88 127 180 395

Lower skin 84 123 189 396

Upper stringers 168 244 336 748

Lower stringers 162 238 350 750

Front spar web 13 13 20 46

Front spar stiff. 18 12 40 70

Rear spar web 11 13 20 44

Rear spar stiff. 14 12 40 66

Total 558 782 1175 2515

Minimum and maximum sizes due to manufacturing

or lightning protection were considered as lower and

upper bounds for the FE-Properties. Special PCL

(PATRAN Command Language) tools were devel-

oped to automate the creation and update of all corre-

sponding design model input data for Nastran SOL

200.


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6 Design Criteria

The mathematical objective of the optimization pro-

cess is to find a minimum feasible weight. All relevant

wing box sizing criteria comprising of limit, ultimate

and fatigue stresses, buckling criteria, manufacturingrequirements, control surface effectiveness and flutter

criteria were applied in the form of in-equality con-

straints. The buckling constraints were communicated

to NASTRAN during the optimization process by the

External Server(see Section 2). Fatigue stress con-

straints were applied to all fatigue sensitive areas of

the wing box. These areas included the lower skin

panels, major wing box joints (inner and outer wing

joint, lower front and rear panel joints), front spar web

at the pylon attachment and rear spar web at the

landing gear attachment. Due to manufacturing re-

quirements, a minimum stringer thickness to heightratio had to be adhered to. Furthermore, the relative

step size of the stringer height was limited in span-

direction to prevent excessive out-of-plane bending

stresses. Table 2 gives an overview of all constraints.

Table 2: Wing box design constraints

Number of ConstraintsWing Box

Substructure

Constraint Type

Center Inner Outer

Number of

Load Cases

Constraints

Total

Skin elements von-Mises stress 416 1132 562 96 Ultimate 202560

Stringer and horizontal

stiffener elements

Axial, Tension and

Compression stress

476 985 622 96 Ultimate 199488

Spar web elements Shear stress 148 525 280 96 Ultimate 91488

Buckling field skin Panel buckling 147 251 364 96 Ultimate 75552

Buckling field skin Crippling 147 251 364 96 Ultimate 75552

BF stringers Stringer buckling 147 251 364 96 Ultimate 75552

BF skin and stringer Euler buckling 147 251 364 96 Ultimate 75552

Lower panel skin Principle stress 384 1042 508 3 Fatigue 5502

Panel joints Principle stress 20 108 42 3 Fatigue 510

Spar web elements Principle stress 408 3 Fatigue 1224

Height of adjacent

stringers

Maximum step size 120 199 115 434

Stringer thickness to

height ratio

Minimum ratio 431 995 538 1964

Outer wing box skin Aileron effectiveness 3 Trim cases (zero aileron effectiveness) 3

Inner wing box skin Lowest flutter speed 1 Flutter speed limit 1

Total Number of Constraints 805402

The aileron effectiveness constraint is incorporated

via a roll performance criterion which is required to

be greater than or equal to zero at maximum true air

speed. The applied Doublet-Lattice method (line-

arized aerodynamic potential theory) is not valid in

the transonic flight regime, particularly at maximum

true air speed. Therefore, equivalent conditions at

lower Mach numbers had to be found. A set of threetrim cases, i.e. pairs of Mach number and dynamic

pressure, has been defined from which, on an empiri-

cal basis, the zero effectiveness curve can be ex-

trapolated to maximum true air speed by a 2nd order

polynomial.

The flutter constraint is defined such that the lowest

flutter speed, i.e. a flutter mode with zero damping,

must not be lower than a prescribed limit velocity

which depends on the flight altitude. All normal

modes up to 50Hz are taken into account in the flutter

analysis using the PK-method. The range of air speeds

used for the flutter response is limited to a minimumrequired set. Because of the high computational effort

required for flutter optimization, a pre-selection of

very few critical flutter cases is indispensable.

In order to get an indication for these cases, a com-

prehensive flutter check covering the entire flight

regime (i.e. a systematic variation of payload mass,

fuel mass and flight level) is performed preceding the

optimization runs.

As can be seen from the above table, large amounts of

input data for the optimization process had to be pre-

pared in the correct format for MSC.Nastran SOL

200. The total amount of data required to describe the

optimization model is multiple times greater than the

FE-Model. Also a large amount of optimization re-

sults needed to be processed in a fairly short time.

Therefore, many auxiliary tools had to be developed.

Most of these tools have been programmed by a rep-

resentative of the MSC Software GmbH as PCL utili-

ties within MSC PATRAN, to allow efficient data

exchange between the Optimization Model and the

FE-Model.


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7 RESULTS

As mentioned above, because of computer storage,

memory restriction and the required real time for such

large optimization problems, sizing with respect to

aeroelastic requirements was performed after achiev-

ing an optimum design with respect to all strength,

stability and geometric design criteria. Equally, for the

same reasons the outer, inner and center wing were

sized separately using several computers in parallel.

A property update for the whole model corresponding

to the optimization results was usually performed

using a specially developed update tool. The con-

ceived design for the total wing was subject to a de-

tailed analysis under all loading and aeroelastic con-

ditions to ensure the validity of the sizing process.

Typical results from this analysis are presented in this

section. Several tools were also developed for the

purpose of post-processing the results of such ananalysis. These tools enable the user to rapidly display

the various results in tabular and graphical format to

give a clear picture of all the parameters of interest.

A typical sizing result for skin thickness and stringer

heights for the outer wing are shown in Fig. 5 and

Fig. 6. Similar graphs along with corresponding tabu-

lar display of all other sized wing box structural com-

ponents are also produced. Another valuable means of

displaying the results is shown in Fig. 7. In this figure,

the driving load cases that design a given section withrespect to column buckling of the outer wing are dis-

played. The driving cases are resulting from symmet-

rical maneuvers at different speeds, altitudes, flap

settings etc. Similar plots for other wing sections and

other buckling criteria are also produced.

In order to satisfy the aileron reversal constraint the

stiffness of the outer wing was locally increased. Fig.

8 shows the increase of panel thickness in the upper

skin to achieve this stiffness increase.The skin thick-

nesses obtained from static optimization were taken as

lower bounds. Significant changes are essentially

restricted to a zone reaching diagonally from the ai-leron attachment area inboard to the leading edge,

close to the inner wing connection. Similar results

have been obtained for the lower skin.

Fig. 5: Outer wing upper panels thickness Fig. 6: Outer wing upper stringers height

11-12

13-14

15-16

17-18

19-20

21-22

23-24

25-26

27-28

29-30

S14-FS

S11-S12

S8-S9

S5-S6

S2-S3

0,00

5,00

10,00

15,00

Thickness

[m

m]

Rib Position

Stringer

Position

11-12

13-14

15-16

17-18

19-20

21-22

23-24

25-26

27-28

29-30

S12

S9

S6

S3

0

20

40

60

He

ight

[m

m]

Rib Position

Stringer

Position

Fig. 7: Critical load cases, outer wing upper panels, column buckling criteria

11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22 22-23 23-24 24-25 25-26 26-27 27-28 28-29 29-30 30-31

S14-FS

S13-S14

S12-S13

S11-S12

S10-S11

S9-S10

S8-S9

S7-S8

S6-S7

S5-S6

S4-S5

S3-S4

S2-S3

S1-S2RS-S1

300112

symmetrical manoeuvre

(256,7 KTAS)

300121

symmetrical

manoeuvre

(519,6 KTAS)

300120 symmetrical manoeuvre

(519,6 KTAS)300117symmetrical manoeuvre

(538,8 KTAS)

300119

symmetrical manoeuvre

(538,8 KTAS)300115

symmetrical

manouvre

(485,9 KTAS)

300110 symmetrical manoeuvre (488 KTAS)

Rib Position

StringerPosition


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Fig. 8: Skin thickness increase of outer upper wing

to satisfy aileron reversal

Flutter optimization results are presented in Fig. 9 andFig. 10. A critical flutter mode (No. 12, see Fig. 9)

essentially determined by symmetric outer wing

bending and pylon/engine pitch/yaw modes occurs

particularly for low payload and fuel mass configura-

tions at low flight altitudes. Although the instability in

mode 12 is not severe, the instability onset was con-

sidered too early. The flutter speed was increased to

the prescribed flutter speed limit by stiffening the

inner wing at a minimal weight increase.

Fig. 9: Flutter instabilities before optimization

Fig. 10: Optimized flutter behavior (flutter speed

of mode 12 increased)

SUMMARY AND CONCLUSIONS

The first stage of implementing and applying MDO

techniques at FD has been successfully completed.

The achieved sizing results of the wing box proved,

that it is very efficient to apply MDO in a real lifeaircraft design cycle. Once all the tools for pre- and

post-processing were in place, it became clear that the

sizing process could be completed in a much shorter

time than that of traditional means. At the same time

all relevant load cases and all design conditions in-

cluding aeroelastic requirements were taken into ac-

count. Furthermore, the MDO sizing process pro-

duced the much desired minimum weight design with

its economic and performance benefits. The main

factors that contributed to the successful implementa-

tion of the MDO process at FD were:

The setting up of a special team dedicated for

MDO process implementation and application.

The application of a common finite element

model for all disciplines involved (statics and

aeroelastics) which allowed a smooth data trans-

fer between all groups and enabled rapid per-

formance of entire flutter and aileron reversal

checks.

The development of various pre- and post-

processing tools which automated most of the in-

put data preparation and the post analysis pro-

cess.

The new capability of Nastran SOL 200 which

enabled the application of the in-house bucklingcriteria by means of theExternal Server.

A detailed design model accommodating all de-

sign and manufacturing requirements.

The close coordination and cooperation of all

design groups involved.

The implementation of the MDO process for other

aircraft structural components is under development.

ACKNOWLEDGEMENT

The authors acknowledge the valuable cooperation

with Erwin Johnson and his Optimization Develop-

ment group from MSC Software Corporation. The

speed and efficiency with which most of the auxiliary

tools were programmed by Rainer Illig, MSCs on site

consultant, are greatly acknowledged. The close par-

ticipation of the Stress, Fatigue and Aeroelastics

groups were very valuable. The tireless efforts and

dedication coupled with high enthusiasm by all mem-

bers of the MDO team is acknowledged. Finally,

without the support and encouragement of Fairchild

Dornier Engineering management in introducing the

new methods, the results reported in this paper wouldnot have been achieved.

11-12

13-14

15-16

17-18

19-20

21-22

23-24

25-26

27-28

29-30

S14-FS

S11-S12

S8-S9

S5-S6

S2-S3

0.00

1.00

2.00

3.00

4.00

5.00

Thickness

[mm]

Rib Position

Stringer

Position


10/10

10


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