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FLEXIBLE WINGSVIA NASTRAN

hESIS

AFIT/GAE/AA/82D-16 Kim Jones1Lt USAk'" DTIC .

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DEPARTMENT OF THE AIR FORCE-.- AIR UNIVERSITY (ATC)c5 AIR FORCE INSTITUTE OF TECHNOLOGY

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STATIC AEROELASTIC AN,%LY--;SOF

FLEXIBLE WINGSVIA NASTRALN

THESIS

AFIT/GAE/AA/82D-16 Kim JonesiLt USAF

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AFIT/GAR/AA/8 2 D-16

STATIC AEROELASTIC ANALYSIS

OF

FLEXIBLE WINGS

VIA NASTRAN

PART I

THESIS

Presented to the Faculty of the School of Engineering

of the Air Force Institute of Technology

Air University

in Partial Fulfillment of the

Requirements for the Degree of

Master of ScienceAccession por,NTIS GRA&I

DTIC TAB

By Dtstr.b ,tiol

Kim Jones, B.S.A.E. Avajlrbi14 t Codes

lLt USAF Dist A mjo

Graduate Aerospace Engineering

December 1982

*l Approved for Public Release; Distribution Unlimited

o ° -,. -~ - .-, ., .* o-... -

Preface

This thesis is a continuation of the research done by

Captain Lance P. Chrisinger in his M.S. Thesis at AFIT in

1980. The first part contains the theoretical development

of the sequence along with the results of a survey of wing

models. The survey determined the characteristics of

average wing models that the procedure must be able to

tolerate. The second part develops a procedure for

designing and testing a NASTRAN module. Then the module

used for the aeroelastic sequence, GIAS, is used as an

example. The logical procedures in GIAS are then

explained. Finally, a detailed description of the

aeroelastic sequence is given along with a description of

how to implement it.

I would like to extend my gratitude to

Captain Hugh C. Briggs, who has understood and put up with

me while guiding me through this thesis.

I would also like to thank Michael Bernier and

Jim Trace for their help with the cor., u-L.r.

A very special thanks goes to my wife, Valerie, whose

patience and understanding has helped greatly with my stay

at AFIT.

ii:

a Contents

Part I. Page

Preface . . . . . . . . . . . . . . . . . . . .

List of Figures . . . . . . . . . . . . . . . . . . iv

Abstract . . . . . . . . . . . . . . . . . . . . . . v

I. Introduction .................... 1

.. II. Background. . . . . .................. 2

Dual-Program Method .................. 2FLEXLOADS. . . . ................ 3FLEXSTAB . . ....... ........... 3Via NASTRAN. . . 4. ............ 4

III. Theory. . . . . .................... 5

Iterative. ............ . . 5Noniterative .. .............. 7Comparison . . . . . . . . 9

IV. Capabilities ................... 11

V. Procedure . ................. . 13

VI. Survey. . . . . . . . ........... 14

Characteristics to be Determ' ned ..... .. 14Characteristics of Wings in Survey . . .. 16Effects of Characteristics ......... 25

Bibliography. . . . . . . . . . . . ....... 29

Part II.

I. Introduction .... . . .......... 1

II. Designing and Testing a NASTRAN Module . ... 2

III. Example of a New NASTRAN Module, GIAS .... 9

IV. Logical Procedures Within GIAS .......... ... 18

V. Running the Flexible Wing Solution Sequence 22

iii

" - " . ... .. . . . . ' . .. . ' . - m . -- -- . "- ., , w a . -- ' - -

- - . , ]

List of Figures

Figure Page

Part I.

1 Graphical Description ofT-37 Wing Model. .. .. ............ 17

2 Graphical Description ofT-Wig Woel. n g... .. d el.. 19

3a Graphical Description of*Egi ig e . . .U ..... 2

3b Graphical Description of"ElnWing" Model (Wing Tip) .. ........ 22

4a Graphical Description ofB-1 Wing Model (Inboard Substructure) . . . 23

4b Graphical Description ofB-i Wing Model (Outboard Substructure) .. 24

Part II.

2 Determining AQAP . . . . . . . . . . . . . . 24

iv

AFIT/GAE/AA/82D-16

Abstract

+3/

The purpose of this study was to expand theK capabilities of the Static Flexible Wing Aeroelastic

Sequence that-~Captain Lance P. Chrisinger developed for

NASTRAN as his Master'. Thesis at AFIT. Captain Chrisinger

developed a basic procedure to enable NASTRAN to analyze

flexible wing airloads and stresses. That capability is

expanded to enable analysis of standard wing models.

A subroutine was incorporated into NASTRAN to

eliminate extensive band-calculation of transformation

matrices.

IV

The capability to tolerate control surfaces was

discovered. Also, a survey of wing models in the Air Force

inventory was taken to determine the cuaacacteristics of the

average wing model. This was used to determine where the

aeroelastic procedure was lacking in its ability to analyze

wing models.

V

STATICAEROELASTIC ANALYSIS

OFFLEXIBLE WINGSVIA NASTRAN

PART I

I. Introduction

An improved aeroelastic package has been developed to

calculate stresses, displacements, and aerodynamic

coefficients for flexible wings undere-oing computer-

generated airloads. The package is based on the readily

available NASTRAN computer program and can tolerate

moderately complex wing models with secondary structure.

The need for such a package became evident as aircraft

wings were designed with more structural flexibility. The

changes in displacements caused by the airloads, and the

changes in airloads caused by the displacements became

significant enough to warrant attention. As a result,

several aeroelastic analysis packages have been designed,

such as FLEXLOADS and FLEXSTAB. However, all of the

packages designed so far contain deficiencies that prevent

them from efficiently solving complex wing structures.

This package is an attempt to design an aeroelastic

analysis program that does not have any serious drawbacks.

-4

....................... . ...

II. Background

The aeroelastic flexible wing problem is a study in

fluid-structure interaction because the airloads on the

structure are dependent on the displacements of the

structure. Several packages have been designed to solve

this interaction problem for aircraft wings.

Dual-Program Method

One type of solution technique uses an airloads

generator computer program and a structural analysis

package. The advantage of this method is that its parts

are already in existence. However, there are some serious

drawbacks to this solution technique. Much time is

consumed in transforming the generated airloads into forces

for the structural analysis package. Also, the

displacements from the structural analysis package must be

transformed into displacements for the airload generator.

An additional problem with this method is the duplicate

computer work required. As iterative passes are made

through the airloads generator and structural analysis

package the same equations are assembled and decomposed.

This results in the same work being done with each pass

through the system.

2 .. ..!. .

FLEXLOADS

Another solution technique aimed at solving the

. flexible wing problem involves a single program using an

iterative solution. The program, FLEXLOADS, was developed

by General Dynamics where it is currently being used to

analyze several bombers and transports. They are also

modifying FLEXLOADS to use with nonlinear aero theory in

order to investigate the separation and stall flight

I.I regimes. Northrup is using FLEXLOADS in their analysis of

L. several fighters. The advantages of FLEXLOADS are that it

is a relatively small, easily manageaLile program and that

it contains several different aero theories to choose from.

A disadvantage is its size restriction of 165 degrees-of-

freedom (DOF), which will limit the complexity of the

models that can be analyzed. An attempt is being made at

San Antonio Air Logistics Center (SAALC) to use Guyan

Reduction to reduce the number of DOF of a T-37 wing model

from 850 to 165 DOF and still keep its accuracy. They are

currently having difficulty finding a representative set of

nodes that leaves the natural frequencies and static

displacements unaltered.

FLEXSTAB

Still another way to solve the flexible wing problem

is to use FLEXSTAB, a computer program developed by Boeing.

FLEXSTAB was originally designed as a stability analysis

package but can also analyze structures. It is currently

being used at Nasa-Dryden an Nasa-v igley. The primary

3. --. . . . . .

disadvantage of FLEXSTAB is that it gives only

approximations of the stresses and displacements because it

uses equivalent beam elements rather than the detailed

model.

Via NASTRAN

Captain Lance Chrisinger, in his Master's Thesis at

AFIT, had previously done all the preliminary work of

comparing these various solution techniques (Ref 3). The

problems a solution technique must be able to tolerate in

order to effectively solve a flexible wing are: a wide

variety of element types, any odd characteristics of

typical wing models such as node number resequencing

(SEQGP) cards, and large numbers of elements. After

looking at these requirements and the characteristics of

all the available solution techniques it became apparent

that there is a need for yet another solution technique.

The s-'ution technique must involve a complete, self-

contained computer program. All of these qualities were

-found in the NASTRAN computer program. The one

disadvantage that this program does have is that it is

rather large and unwieldy. However, with the recent

inclusion of an airload generator, NASTRAN has all the

requirements to effectively solve a flexible wing. In

addition, Captain Chrisinger built an instruction sequence

for solving the flexible wing problem for a simple generic

wing box (Ref 3).

4

b-7-

III. Theory

There are two approaches to solving flexible wings.

Both are based on the same assumptions but differ in

methodology. In one scheme iterative passes are made

through a sequence of steps while in the other the process

is assembled into a single equation to be solved (Ref 2).

Iterative

The iterative solution consists of three parts: a

pre-processor to set up the operations, an iterative loop

that terminates when a specified tolerance is reached, and

a post-processor to recover the output.

Definitions

* -* general matrix multiplier

Us the change in structural deformation

(the first value is the initial structural

displacements representing the initial

angle-of-attack)

IUw, - The cumulative structural deformation

Q - The change in forces on the structural

grid

- The cumulative forces on the structuralI:'2rgrid

- The changes in airloaWd on the aero grid

Q - The cumulative airloads on the aero grid

5

Procedure

set U. = Angle of Attack ini. angle of

set Ur = - Angle of Attack attack so the

initial angle of

attack will not be

included in summing

the deformations

set Q = 0

set QT = 0

top of loop

UA = G * Us G - transformation

matrix from struc-

tural displacements

to aero displace-

ments

Q, = A * UA A - matrix of aero

coefficients

"" G G* - transformation

matrix from airloads

on aero grid to

forces on structural

grid

U - * Q K - stiffness matrix

U, L. + U6 cumulating structur-

al deformation

changes

6",o -- - -. . -

S Q + Q cumulating changes

in forces on struc-

tural grid

QA= OAT +Q1 cumulating changes

in airloads on aero

grid

go to top of loop unless the norm of the change

" - in structural displacements is less than

the tolerance

output

Usr

Qs-

aerodynamic coefficients

Noniterative

The noniterative scheme uses the same assumptions

but it is ordered differently (Ref 2):

Definitions

* - general matrix multiplier

K - the stiffness matrix

Us - structural deformations

O'- structural forces

G - the transformation from aero forces to

structural forces and also from structural

deformations to aero deformations

AOA - initial angle of attack

U4 - aero deformations

4 7

-aero forces()A -cofiinsoaeofrs

CPA - coefficients of aero presue

DlJK - matrix of aero coefficients, real

part of complex aero wash

D2JK -matrix of aero coefficients, imtaginary

part of complex aero wash

A=. matrix of aero influence coefficients

SKJ -matrix of areas of the wing

Q -dynamic pressure

Procedure

CP A j.* lJK + i(D2JK)) U4

CQ4 =SKJ CPA

therefore

Q5 Q G SKJ A k [DJK +i (D2JK)j* Gr% U.,

but

D2JK -0 only concerned with

static, zero frequency

and

F -G *SKJ * AOA rigid bodyQ., due to

AQA

- and

FDEF G*SKJ*A' xD1JK xG T Q due to

deformations

there fore

'Q - Q * [(F * AOA)+(FDEF * US)]

*if.:.:"'-'U 5 -KIC * Q.

then

U, - Q * K 1 * (AOA * F) + (FDSF * US)

'1- (Q * K' * FDEF) * U --Q * K" * F * AOA

finally

U. K l(Q,-I' FDEF)' *Q*K *F *AOA

The last equation is the one that is used for the

noniterative scheme.

- Comparison

There are two points to be considered when deciding

which solution scheme to use for a particular problem.

Both the accuracy and the expense (in terms of time to

compute) is discussed. The accuracy of the iterative

solution scheme can, at best, equal the accuracy of the

noniterative solution. This is because they both make the

same approximations but the iterative solution has an

additional inherent error. The iterative solution takes a

shorter time to assemble and decompose than the

noniterative scheme but then also involves the time in

going through the iteration loop. The noniterative scheme

takes longer to assemble and decompose but once this is

done, the equations are solved only once. Therefore, it

the time to assemble and decompose the equations for a

* particular model in the iterative solution is significantly

9-o . .. . . . . b . . .

shorter than that for the noniterative solution, then the

iterative solution will take less time. In order for this

Ali to work, the assembly and decomposition time for the

iterative solution has to be shorter than the noniterative

solution by the amount of time it takes for the iterative

solution to complete all the iterative passes. Recent

experience indicates typically 3-6 passes are required for

simple models. For the present work, the iterative scheme

'A has been employed.

10

I .'. .

F--.

IV. Capabilities

The discussion of the capabilities of the current

solution technique is broken into two parts. The first

gives an outline of the applicable characteristics of

NASTRAN. The second describes the capabilities of the

instruction sequence.

As outlined in the background section, the primary

disadvantage in using a program such as NASTRAN is its

large size. Because of this the instruction sequence is

more difficult to manipulate. Another disadvantage is that

NASTRAN uses only one aero theory, a Doublet-Lattice

Method. This theory does not generate any rotational

forces; therefore, any bending elements in the model will

not have forces along their rotational DOF due to the

airloads. Despite these disadvantages, NASTRAN was chosen

as a host program because of its several advantages. The

most important of these is NASTRAN's ability to tolerate

very large problems efficiently. Anot.ner major advantage

is the wide variety of element types already available in

NASTRAN. In addition, many options to the instruction

sequence are easily implemented. These three advantages

lend a great deal of flexibility to any instruction

. .

sequence implemented with NASTRAN. This is essential when

S"'dealing with the wide range and variety of wing

characteristics encountered.

This second section outlines the capabilities of the

instruction sequence. The ultimate goal for the sequence

is to be able to solve for the stres -tt, displacements, and

aerodynamic coefficients of an entire flexible aircraft.

Currently, a restricted type of flexible wing can beN solved. Provisions have been made to calculate internally

all of the transformation matrices and other derived input

data. This enables the user to analyze a wing using an

existing model with minimum additional input data. The

instruction sequence is capable of solving deflected

control surfaces as long as the deflections are small

enough to stay within linear aero theory. Substructuring

has not been attempted while using the instruction

sequence. The only wing surface element type that can be

used by the instruction sequence is the CQDMEM2 element.

Provisions have yet to be made to tolerate grid point

number resequencing (SEQGP) cards. Wing-fuselage

aerodynamic interaction can be modeled by constructing an

aero model of the fuselage near the wing root.

12

V. Procedure

This section is included in the event that someone

with an understanding of the instruction sequence has a

desire to use it. Within this section is an overview of

additional input data that must be included with a standard

model in NASTRAN format. The details of each additional

piece of data are covered in Part II.

The instruction sequence requires that two subcases be

run. The first subcase generates the initial angle of

attack and the second subcase actually goes through the

iterations. There are several PARAM cards that must be

added. These are concerned with various dimensions of the

wing model, the angle of attack, and the error deemed

adequate for the iteration convergence. SPC cards are

required for both subcases to help determine the AOA and to

partition out the rotational DOF of the model. ASET cards

are needed to narrow down the analysis set to just the

Z DOF of every free node. A CAERO ca± i and its support

cards are needed to determine the flight regime. An EIGR

card is needed to help set the initial angle of attack.

SPLINE and SET cards are needed to build the transformation

matrix from the displacements on the structural grid to the

displacements and slopes on the aero grid. Finally, a

table (TOSEL - Top Surface Element List) must be input in

the Bulk Data Deck.

13. . . . . . . . . . . .

VI. Survey

In order for the instruction sequence to run

efficiently with standard wing models their characteristics

must be known. To this effect a survey of several wing

models in the Air Force inventory was taken. The answers

to a list of questions were compiled to determine the

characteristics of the average wing model. Though several

wings were surveyed, only four will be presented here.

These depict typical wing models. The rest are not

presented because of repetition.

(Characteristics to be Determined

The characteristics investigated were:

1. The number of grid points and DOF. This is an

estimate of the size of a typical wing model.

2. Whether the model has leading and/or trailing edge

secondary structure. Since the aero and

structural models should both have the same

planforms structural models without the secondary

structure will require modification.

3. If the model has been validated with only the

Z-DOF in the analysis set. The inodel1 can be

S.. validated either by known static deformations or

by known natural frequencies. This should have

14

been done because the current NASTRAN aero

theories allow only the Z-Do-' in the analysis

.. set (Ref 1).

4. The existence of any stresses, displacements,

basic aerodynamic coefficients, and distri-

butions for flight test data and standard

computer analysis. This provides a measurement

standard for judging the accuracy of results.

Computed versions of these items can be generated

by the solution sequence to provide accuracy

checks at various points in ':he sequence. The

data from a standard computer analysis could be

used to check the sequence before it enters the

iterative loop. The flight test data provides a

check for the final results from the solution

sequence.

5. Types of area elements on the wing surface.

Currently, only certain element types on the wing

surface can be analyzed by the solution sequence.

6. If there are any bending elements in the model.

This will affect the validation described in

question 3 since the analysis set for the solution

sequence is condensed to only translational DOF

by Guyan reduction.

7. If there are any SEQGP cards. This would affect

the internal equation numbering which in turn

affects the calculation of some of the transforma-

tion matrices (Ref 1).

15

8. If the wing model includes wheel wells or other

cutouts. This will become significant when aero

theories are implemented that panel 3-D

structures. The current theory uses 2-D lifting

" surfaces and is only affected by the curvature of

mean camber surface (Ref 1).

9. Is it in NASTRAN format. Considerable time and

money can be spent in reformatting data to NASTRAN

format.

Characteristics of Wings in Survey

Several wing models were evaluated with respect to the

criteria. These models are T-37, T-38, B-l, C-5, and

KC-135. Also, a wing model termed the "Eglin Wing" was

C included in the survey. The four win,7s presented in detail

are the T-37 wing, the T-38 wing, the uglin Wing," and the

B-i wing.

The T-37 is illustrated here because it is a typical

early subsonic wing type (Fig 1). It only has two spars

and a thin skin. Unlike modern fighters, the T-37 wing has

a high aspect ratio and a complex wing carry-through

connected to the fuselage. This carry-through will present

some problems in determining the wing root boundary

conditions for this type of wing. The T-37 wing model has

319 grid points with 850 DOF. The model has no leading or

trailing edges and, therefore, no control surfaces. This

particular wing model has been validated in the Z-DOF only.

' "This is unusual, typically wing models contain rotational

16

117

DOF. The T-37 wing model is validated under such

S"-. conditions due to the Guyan Reduction efforts being done at

SAALC on the T-37 wing model for the FLEXLOADS program.

There is very little flight test data because the T-37 was

built when extensive tests on new aircraft were not done.

[I There is some aerodynamic computer analysis for the T-37

wing, primarily by the airloads program called USSAERO.

Several types of area elements are used on the wing

surface. There are very few bending elements encountered

in the T-37 wing model, they are only in the wheel well.

The T-37 wing model contains SEQGP cards because the grid

numbers are encoded position coordinates. Finally, the

T-37 wing model is already in NASTRAN - r,,at.

The T-38 wing is a typical modern fighter-type wing

having several spars, thick skin, a low aspect ratio and

388 grid points with 1564 DOF (Fig 2). It does have a

leading edge structure but no trailing edge because the

control surfaces are typically analyzed separately from the

wing. The model has not been validated using only the

Z-DOF. There are large amounts of flight test data and

computer analyses to provide check data for the solution

sequence. There are four types of area elements on the

wing surface, some of which are plates, and there are

additional bending elements within the wing. There are

SEQGP cards included in the model. Wheel wells are present

in the model but the wheel covers have not been modeled.

18

-40

-4

04

C

190

Analyzing the wing is simplified by the fact that it is in

NASTRAN format and has been analyzed in several static load

conditions.

The Eglin Wing is presented because it is a typical

damage tolerance wing model (Fig 3). These tend to be more

complex because they have to closely trace the stresses

throughout the wing. As a result, the Eglin Wing has 542

grid points with 2710 DOF. The model has both leading and

trailing edges, the trailing edge consists partly of the

control surfaces. It has not been validated with only the

Z-DOF. The check data available is a minimum with only a

small amount of computer analysis pro.'ided. There are

several types of area elements on the wing surface in both

triangular and quadrilateral shapes. The Eglin Wing does

have bending elements. A large number of SEQGP cards are

present which will affect the transformation matrices. The

model also contains wheel well cutouts whose covers will

have to be modeled if a 3-D aero theory is implemented. As

with the T-38 wing model, the Eglin Wing is also in NASTRAN

format and has been run in several static load cases.

Despite the effects of the wing pivot area, the B-1

wing model is taken as a typical "heavy-aircraft" type

wing. These effects do not interfere with the present

analysis so swing wing aircraft can also be analyzed. The

outboard sections of the wing are fairly typical to other

"heavy-aircraft" wings. Because the wing is large and

complex, there are a great number of grid points and DOF,

5116 grid points with 24,361 DOF (Fig 4). Fortunately,

20

-4A

IINI 0

04

'-40

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21"

r-4

0'

0'4-

p-4

4

U)

22)

k4-

.0

Ub)

C9C

230

w 'I

4'0zL

c'a

240

wings of this size can be analyzed using substructuring.

S -. The largest substructure in the B-i wing model has 1605

grid points and 5479 DOF. This is sti.l large but it is

much more manageable than the entire wing. All parts of

the wing are represented by the substructuring, including

the leading and trailing edges, with the control surfaces.

The B-I wing model has not been validated using only the

Z-DOF. There has been a lot of flight test data and

computer analysis done on the B-1 wing. There are four

types of area elements on the wing surface. The model

includes bending elements, but no wheel wells or other

cutouts. Since the B-i model is not in NASTRAN format,

SEQGP cards are not applicable.

Effects of Characteristics

Considering the wide range of characteristics of the

wings in the survey, it is evident that compromises must be

made. While the overriding concern in designing the

solution sequence is to make it user-oriented, it is not

possible to design the sequence for every characteristic.

At times certain models will have to be altered to fit the

sequence. The average size of wing models is fairly large

and requires the sequence to use computer space

efficiently. However, after the usage has been trimmed

down as far as possible, there will still be some wing

models that will be too large for the computer used. In

these cases, either substructuring should be used or the

complexity of the model lessened by Guyan Reduction

25*.. . . . . . . . .".%.

techniques.

If the structural wing model does not have leading

and/or trailing edges, then two courses of action can be

taken. One method is to alter the solution sequence to

artificially transfer the loads from the leading and

trailing edges to the structural wing box. However, this

requires large amounts of the user's time. The second

course of action would be to put leading edges on the wing

model. This is the easier of the two in that, once done,

--it automates the load transfer from the edges to the wing

.box.

Since most wing models are not validated in the Z-DOF,

there will be some error in using these models. The error

can be measured by restricting the model to the Z-DOF,

performing the validation procedures, and calculating how

far off the model with only Z-DOF is from the actual

structure. If the error determined is unacceptable, the

model should be adjusted to give accurate values in the

Z-DOF. Another course of action can be taken to reduce the

error but it requires extensive rebuilding of the solution

sequence. The only reason the models put through the

solution sequence are reduced to Z-DOF is the aero analysis

within the sequence cannot tolerate any displacements

except out-of-plane translations. If desired, a different

aero theory can be implemented into the solution sequence

but it would require many months of effort to rebuild and

4debug the altered solution sequence.

Most wing models only use three or four area element

26

r. types on the wing surface. Given these element types, no

problem is encountered with the solution sequence.

However, if an element type different from those normally

L. used is put on the wing surface then problems can arise.

It is a simple matter to add that element type to the

capabilities of the solution sequence, if sufficient

knowledge of how the solution sequence works is available.

LacKing that, it is advisable not to include the new

element type in the wing surface.

* •Virtually every wing model contains bending elements.

As with the validation of the models in the Z-DOF, the

restriction of using bending elements in the solution

sequence lies within the aero model. The bending elements

will not be loaded by the aero forces in the rotational

DOF. If the error incurred is unacceptable the recommended

solutions are the same, either replace the bending elements

or implement a different aero theory.

Most of the large wing models contain SEQGP cards in

an effort to improve the bandwidth of the matrices

involved. Currently there is no capability to tolerate

SEQGP cards in the solution sequence so care should be

taken in choosing the form of the input data for the wing

model.

Most wing models contain wheel wells or other cutouts.

This is not a problem with the present aero theory but it

will need to be considered if a different aero theory is

implemented. The most obvious solution is to include the

wheel covers in the model. This will ailow the wheel well

27

.. .. ... .

.', --

doors to be included as part of the lower wing surface.

A problem not previously mentioned is the aerodynamic

interaction between the wing and other aircraft structures.

If the wing is modeled alone then these effects are not

taken into account. The aircraft structure that most

Icommonly interacts with the wing is the fuselage. If the

F fuselage tends to be flat and vertical at the wing root,

then the centerline symmetry condition of the wing alone

will be a reasonable approximation. However, if the

'fuselage-wing root structure is rounded and smooth then

there can be a great deal of crossflow. Other structures,

such as engine inlets, engine exhaust, and winq mounted

stores, can also affect the airflow across the wing.

Wing-fuselage aerodynamic interaction can be modelled by

constructing an aero model of the fuselage near the wing

root.

The solution sequence can tolerate most of the

characteristics of the average wing model. However,

further revisions to the sequence would broaden its

capabilities and applicability.

28

* Bibliography

*1. NASA SP-222(04). The NASTRAN User's Manual (Level17.0). National Aeronautics a-nd Space Administraion,December 1979.

2. Ford, Douglas A., Advanced Development Projects,Lockheed Aircraft Corporation (Personal Interview).Lockheed, California, October 21, 1982.

3. Chrisinger, Lance E. Calculation of Airloads for a* Flexible Wing via NASTRAN. M.S. Thesis.

DTIC AD A094770, Wright-Patterson AFB, Ohio:Air Force Institute of Technology, December 1980.

29

AFIT/GAE/AA/82D-16

STATIC AEROELASTIC ANALYSIS

OF

FLEXIBLE WINGS

VIA HASTRAN

PART II

'-ESIS

Presented to the Faculty of the School of Engineering

of the Air Force Institute of Technology

Air University

in Partial Fulfillment of the

Requirements for the Degree of

Master of Science

By

Kim Jones, B.S.A.E.

lLt USAF

Graduate Aerospace Engineering

December 1982

Approved for Public Release; Distribution Unlimited

* . -,

S.-Contents

Part I. Page

I. Introduction ... . ........ . 1

Ii. Background. . . . . . . ............. 2

III. Theory. . . . . . . . . . .................... 5

IV. Capabilities. . . . . . . ........ . 11

V. Procedure . . . . . . ........... . 13

VI. Survey. . . . . . . . . ............ 14

Part II.

Abstract. . . . . . . . . . ............ iiI. Introduction. . . . . ................

II. Designing and Testing a NASTRAN module . 2

III. Example of a New NASTRAN Module, GIAS . . .. 9

IV. Logical Procedures Within GIAS .......... ... 18

Output Datablocks. . . . . ......... 18Logical Procedures . . . . ........... 19

V. Running the Flexible Wing Solution Sequence 22

Logical Procedures . . ............ 22Implementation . ................ .... 26

SBibliography . .. .. .. .. .. .. .. .. . .. 31iVita . . . . . . . . . . . . . . . . . . . . . . . 32•

Appendix A: GIAS and Environment ............ 33

Appendix B: Sample Input Data and Illustration . . 79

I.

|--i

AFIT/GAE/AA/82D-16

Abstract

This thesis is a continuation of the research done by

Captain Lance P. Chrisinger in his M.S. Thesis at AFIT in

1980. Captain Chrisinger developed a basic procedure to

enable NASTRAN to analyze flexible wing airloads and

stresses. That capability is expanded in this report to

enable analysis of standard wing modeis.

A subroutine was incorporated into NASTRAN to

eliminate extensive hand-calculation of transformation

matrices.

The capability to tolerate control surfaces was

discovered. Also, a survey of wing models in the Air Force

inventory was taken to determine the characteristics of the

average wing model. This was used to determine where the

aeroelastic procedure was lacking in its ability to analyze

wing models.

~iii

m" ' m "I m' u --":,, . , # --- . ..h.-,.. . .. .

i -STATICAEROELASTIC ANALYSIS

OFFLEXIBLE WINGSVIA NASTRAN

PART II

I. Introduction

This part presents a detailed account of the

procedures associated with the NASTRAN instruction sequence

for flexible wings. However, the presentation presumes a

level of knowledge about NASTRAN and its organization. In

order to fully understand the majority of this part, the

reader must understand the organization of NASTRAN, to

include datablocks, modules, links, and overlays. The

reader should have taken, or have notes of, a course

dealing with NASTRAN System Programming (Refs 3,4).

This part is organized into three sections. The first

two describe a recommended procedure for designing and

testing a module to be put inside NASTRAN. This will also

include, as an example, the module designed to work within

the NASTRAN instruction sequence to solve flexible wing

problems. These two sections were included to illustrate a

set of steps not given elsewhere on designing and testing a

NASTRAN module. The third section in this part is a

detailed account of how to run this instruction sequence,

with an explanation of additions to tiU. liulk Data Deck.° 9.°

II. Designing and Testing a NASTRAN Module

The following is a recommended procedure for designing

and testing new NASTRAN modules. The procedure carries

through from the initial conception of the need for a new

module to the final testing of the module once it is inside

NASTRAN. The procedure pulls together information from

various NASTRAN publications to preseiL complete, logical

sequence of steps to design and implement a module. These

steps are designed to insure the most error free module in

the least amount of time. These will minimize the

debugging required while manipulating the entire NASTRAN

0? package. To do this the module must be tested in an

environment as close to NASTRAN as possible before the

module is entered into NASTRAN. The recommended steps in

designing and testing a NASTRAN module are:

1. Recognition of the Need. In designing a new

DMAP sequence or running an extensive DMAP

alter the user might recognize that none of the

DMAP statements, nor any combination of them,

provide him with a procedure he needs.

The first thing he must do before considering

adding a module is be sure that there is no other

way to accomplish the procedure, even by a round-

S..about method. The time and effort required to

2

design, test, and implement a new NASTRAN module

is enough to make it a last resort. If it is at

. all reasonable to operate without the module then

that course of action is recommended. In con-

sidering a DMAP to solve his problem the user

might compare MSC NASTRAN to COSMIC NASTRAN.

The MSC version contains many more modules

and might have the proper DMAP modules where

the COSMIC version did not.

2. Development of the logic process and recognition

of required inputs. These two steps are lumped

together because the logic processes inside the

module must operate within the NASTRAN

environment. Some of the inputs that would be

ideal for the procedure might just not be

there, or might exist but in a format that

will increase the complexity of the

module's logic. To determine exactly what

is needed by the sequence from the module,

and also to check the sequence, run the sequence

with the module and its outputs replaced by hand-

generated data.

3. Determine where to get the inputs.

There are several ways that inputs are available

to a module. They can either be: an existing

datablock, a datablock that can be built in the

3

DMAP before the module is executed using DMAP al-

ters or the data that can be user supplied through

PARAM, DTI, or DMI cards. Datablocks can be

either matrices or tables. The way the data

reaches the module will have an effect on its

logic processes and on the amount of user input

needed. It is desirable to require as little as

possible from the user. This will reduce input

errors.

4. Write the module with all of its NASTRAN-

necessary parts. NASTRAN uses the Fortran IV

computer language. Any limitations with this

language must be taken into account when writing

the module. The module will be operating in an

tP environment with common staLCi,. nts, open core

arrangements, and various other subroutines

to which it has access. Depending on. the

design of the module, the use of these will

have to be carefully planned out so as to

minimize the module's use of computer time and

. space. This must be considered because the large

variation of problem types encountered will cause

the solution sequence to tax the capabilities of

most any computer.

5. Build a file of the data the module will receive.

*" This will be the input to a simulated environment

built to debug the module as thoroughly as

4

I 1Apossible before it is put inside NASTRAN. The

content of the data should be from several sample

cases to which the correct (or at least expected)

answers are known. The form of the data can be

up to the user but it should contain all the

information that will reach the module, not just

what the module will use. The procedures to

develop this file are determined by how the

module will get the data when it is incorporated

into NASTRAN. To get the data that the user will

supply to the module when it is incorporated into

NASTRAN is relatively simple. Just put the data

on the input file as it would appear in the Bulk

Data Deck. The other data, those that are gener-

ated inside NASTRAN before the module, will

require a different approach. A solution

sequence nearly identical to the one that will

use the module should be run. This solution

sequence should not have the call to the module

being developed. It is not necessary for the

sequence to run until completion. All that is

required is to derive the data that the module

will use. This data should be punched out of a

NASTRAN run onto a file. It is advisable to do

this right after the last DMAP statement before

the new module is called. It is easier to do

this with a DMAP alter. The specific cards that

5.= .- . . .

- --. .. . . .. .. .- .. -. -i " : - -'' .. . /'i : ' - " - * 1

need to be inserted in the DMAP depends on the

form of the data. If the data is in table

format use the TABPCH module. If it is in

matrix format use MATPUN.

6. Build environment around the module to simulate

the NASTRAN environment. Ideally, this

should be done with as few changes to

the module as possible. The form of the

module should be as close as possible to the form

it will have when inside NASTRAN. The environ-

ment should consist of several subroutines,

including the module, with a master sequence of

commands whose job it will be to call an ini-

tialization subroutine and ttei, the module.

The module, in turn, will call utility sub-

routines. The environment should simulate all

the common statements, open core, functions, and

subroutines that the module will see while

inside NASTRAN. The environment subroutines

need not do exactly what the equivalent NASTRAN

subroutines do, but they must return the same

response to the module. Some of the subroutines

the module calls may hare to be copied from

NASTRAN source code and put into the environment

rather than just building similar ones. How-

ever, caution should be used in doing this

because the subroutines pulled from NASTRAN will

6

have to have their NASTRAN environments simu-

lated also. Their environments can be as simple

as another utility subroutine or they can require

an assortment of common statements, open core,

functions, and subroutines of their own.

7. Run several test cases to debug the module in the

environment. The test cases should use the input

data described in Step 5. It is helpful here to

put internal check statements within the environ-

ment. Perhaps printing out a simple statement

telling which subroutine the program is in. The

module must be debugged until the environment's

output data is exactly what the user wants NASTRAN

to see once it finishes executing the module.

8. Put the module inside NASTRAN.

The procedure to do this can be found in the

NASTRAN Programmer's Manual, in most any other

NASTRAN system programming text or from someone

who has done it before and i; knowledgeable

about the NASTRAN system. The module must be

put in a link that will allow it access to the

subroutines and common areas the module needs.

9. Run additional tests on installed module until

satisfied. These should begin with the same test

cases run before, in Step 7. However, it might be

a good idea to run additional cases. It could be

helpful to have various matrices and tables

7

. . . . .. . . .. . . . . . . . . . .

printed out at key locations within the DMA.P. Of

* - course, to run these cases, the trial DMAP should

have been altered to include the call for the

module.

ia

'.. .....

III. Example of a New NASTRAN Module, GIAS

This section uses the NASTRAN module GIAS as an

example of the procedure to design a module.

GIAS was designed to build various matrices used to

solve the flexible wing problem. Beforehand, the matrices

were manually calculated and entered into the program via

DMI cards. The overriding concept in GIAS is to minimize

the. work the user must do. As many matrices as possible

are built within GIAS. This leaves only one matrix, other

than the normal model data, to be built by hand. As

development on GIAS continues, this matrix will also be

g built inside NASTRAN.

The following is a reiteration of the steps necessary

to design a module for NASTRAN, with specific application

to GIAS.

1. Recognition of need. The solution sequence for

solving flexible wings requires several transfor-

mation matrices and moment arm vectors. The

procedure used to generate these matrices is much

too detailed and complex for NASTRAN to accomplish

it with DMAP. Therefore, in order to signifi-

cantly reduce the amount of udLa to be entered by

the user a new module is needed to calculate the

extra data.

.... .....

2&3. Development of logic process, recognition of

required inputs and where to get them. Since the

object of the module is to reduce the user's work

most of the input data to the module already

exists in NASTRAN while it is running. At this

time there is only one additional table that

needs to be input by hand. Those that already

exist in NASTRAN are:

SIL - Scalar Index List

BGPA - Basic Grid Point definition table,

Aerodynamics

GPLA - Grid Point List, Aerodynamics

ACPT - Aerodynamic Connection and Property

Table

6' ECTA - Element Connection Table, Aerodynamics

Descriptions of the existing datablocks can be

found in the NASTRAN programmer's manual.

The user-supplied table is:

TOSEL - Top Surface Element List

TOSEL contains a list of area element numbers on

the top surface of the wing. The datablock is

needed because the loads generated by the aero-

dynamic model in the solutivri 6equence are only

applied to the nodes of the elements listed in

TOSEL. TOSEL contains one record for each

type of area element on the upper surface.

The records are arranged so that the element type

10

- I' - ; ? - , - : - ' i . - . i i : i i : . i -i . . . . . . .

code numbers are in increasing order. The first

entry in each record is the BCD name of that

element type. The entries following that, within

each record, are the element numbers of that

element type on the upper surface in increasing

order. TOSEL cannot be derived inside NASTRAN;

currently there is no method available to

isolate the upper wing surface elements in a

general wing model.

4. Write the module with all of its NASTRAN-

necessary parts. The entire module is listed

in the back of this volume (Appendix A). There

are various items that need to be included in the

module to allow it to operate within NASTRAN. For

GIAS the NASTRAN-necessary -rlrt are:

COMMON statements

COMMON//A - Obtains the variable "A" out of

the blank common. "A" is the

bottom of blank common.

COMMON/SYSTEM/IBUF - IBUF is the required

length of GINO buffers

COMMON/PACKX/TYP IN, TYPOUT, IROW, NROW, INCR -

Various parameters for the PACK

subroutine

COMMON/ZOPEN/Z(l) - Designates a common area

for working

,q11

DATA statements

DATA NAME/4HGIAS,4HREAD/ - Assigns a BCD

value for NAME, a parameter for

the MESAGE subroutine, an error

utility

DATA statements are also used to assign

inputs the consecutive numbers 101-106. In

addition, data statements are used to assign

outputs the consecutive numbers 201-209.

Functions

CORSZ(Z,A) - Determines amount of open core

available from the field length

specified for the program run"Subroutines

GOPEN - Opens a d~cablock in order to

read from it or write into it

CLOSE - Closes a datablock

READ - Reads from a datablock

PACK - Writes to a datablock

RDTRL - Reads the trailer of a datablock

WRTRL - Writes the trailer of a

datablock

t4ESAGE -Prints selected fatal

errors as they occur

12

SSPLIN - Produces dn interpolation matrix

A more detailed descrip-ion of the

subroutines can be found in the NASTRAN

Programmer's Manual (Ref 2).

5. Build a computer file of the input data the module

will receive. A listing of the input data to the

simulated environment for a test case is included

in this volume. TABPCH cards were inserted in the

solution sequence near line 104; this is where

GIAS was later put. Datablocks ACPT, TOSEL, ECTA,

GPLA, BGPA, and SIL were output to logical

file PUNCH. This file was then manipulated,

along with the initialization subroutine

(see subroutine INIT, Appendix A), to put these

datablocks in a form where the rest of the simu-

lated environment can use them.

6. Simulate the NASTRAN environment. All of the

items discussed in Step 4 must be duplicated

within the simulated environment. In the simu-

lated environment they do not have to do exactly

what the subroutines in NASTRAN do, but they must

return the same response to the module being

tested. The following are the simulated items in

the environment for GIAS; they have the same names

as the items in Step 4.

"3

.,.

-,- . ---. ;-'

Function CORSZ(Z,A) - Returns a predetermined

number to be the size of the

Z array.

COMON/SYSTEM/IBUF - Returns a predetermined

arbitrary number to be the

size of the buffers, the

buffers used in the simula-

tion.

Subroutines

INIT -The initialization subroutine, reads

the input file into internal arrays

for use by the subroutines READ and

RDTRL.

GOPEN -Prints out the statement "Datablock

### openedN to announce the position

of the program, but it really does

nothing to the datablock.

CLOSE -Prints out the statement "Datablock

### closedN to announce the position

" of the program, but it really does

nothing to the datablock.

READ - Fetches all or part of the datablock

contained within a set of arrays

prepared by subroutine INIT. It is

more complex than an average read

statement so it can handle any

14

-...- .. .. , . ... ._ . % . . . . . , , /

errors it encounters, such as being

asked to read past an End-of-File or

an End-of-Record.

PACK -Prints out the narm of the specified

datablock along with its values, for

inspection but does not create any

files.

RDTRL -Reads the trailer of the datablock

specified from the set of arrays

prepared by INIT.

WRTRL - Prints out the trailer of the data-

block specified.

MESAGE - Prints out the specified error

message.

SSPLIN -Produces an interpolation matrix.

SSPLIN calls two other utility sub-

routines, INVERS and GMMATS. These

must also be included in the

environment. All three of these

subroutines had to be copied

directly from NASTRAN source code.

7. Run several test cases to debug the module. A

simplified wing box was designed and run in

NASTRAN using input entered by hand to replace

15

tv X (a u

Ac IS >

0 0

00 U)z 04d

16

GIAS. Running several variations of this produced

" ;- the required check data for the environment.

8. Put the module inside NASTRAN. Because SSPLIN is

one of the utility subroutines used, GIAS was put

into Link 11 of NASTRAN (Fig 2). The other sub-

routines needed are also available from this

position.

9. Run additional test cases until satisfied. Both

the simplified wing box mentioned in Step 7 and an

intermediate complexity wing were run as final

test cases.

.1

g 4

!1

. --

IV. Loqical Procedures Within GIAS

It was previously mentioned that GIAS created various

transformation matrices and moment arms. This section will

look at each of these datablocks and outline the logical

procedures used to make them. Several of the procedures

overlap within GIAS because several of the output

datablocks use the same input.

Output Datablocks

The output datablocks are:

SAS - A matrix containing ones where areas are

0in the SKJ matrix

GTAK - Surface spline interpolation matrix for

transformation of 4P's at the aero

points to 6P's at the structural nodes

TTTTT - Transformation matrix from AP's at the

structural points to loads at the

structural nodes

VGLS - A vector with ones in the proper positions

so that when multiplied by the structural

loads it sums them. VGLS also condenses

PG down to nonzero terms.

VTMA - Contains the moment arms for the aero-

dynamic pitching moment about the Y-axis.

18

--- --------

VTRA - Contains the moment arms for the aero-

dynamic rolling moment about the X-axis

VTM - Contains the moment arms for the pitching

moment about the Y-axis due to the trans-

formed structural loads.

VTR - Contains the moment arms for the rolling

moment about the X-axis due to the trans-

formed structural loads.

AIDMT - Unit vector of lengtn equal to the number

of aerodynamic boxes.

Logical Procedures

The first datablocks built in GIAS are TTTTT and VGLS.

Even though they are built at the same time the logic to

build each of them wil be considered separately. TTTTT

transforms the 6,P applied to the centroid of each area

element on the upper surface of the wing model to loads on

the upper surface structural nodes. The first step to do

this is to multiply the 6p applied to the element by the

area of the element. Using the geometry of the element the

load over the element is then correctly partitioned out to

each node of the element. The only information needed to

calculate TTTTT is the coordinates of the structural nodes

on the upper surface and which elements they are associated

with. Since VGLS is a list of ones in the Z DOF position

for each node on the upper surface the only information

needed is the upper surface node numbers.

19

The next datablocks built are VTM and VTR. The moment

arms for the structural rolling and pitching moments are

simply the coordinates of each upper surface node. This

information was obtained when TTTTT and VGLS were built.

VTMA and VTRA are built next. The only information

needed for these two is the coordinates of the corners of

the aero boxes. From these the coordinates of the 1/2-span

S. 1/4-chord point of each aero box is found. This is the

point of each box where the lift is assumed to act. The X

and Y values of each of these are the entries in VTMA and

VTRA, respectively.

All the information needed to calculate GTAK is now

available. In order to calculate GTAK the subroutine

SSPLIN needs to know the coordinates of the input and

output points and how many of each there are. The input

points are the points on the aero boxes where the pressure

is assumed to act. The output points are the upper surface

structural nodes. Because GTAK has to be built all at

once, rather than a column at a time like other matrices,

this is the procedure in GIAS that takes up the most

computer memory. In fact, depending on the problem, this

procedure could be the one that governs the amount of

computer memory required for the entire analysis.

The last two datablocks built by GIAS are AIDMT and

SAS. To build AIDMT only the number of aero boxes is

20,--..,.

needed. SAS has ones down two of its diagonals and zeroes

elsewhere. It has as many rows as two times the number of

aero boxes and as many columns as the number of aero boxes.

21

.V. Running the Flexible Wing Solution Sequence

In order to best use a solution sequence it is

advisable to first understand how it works. Therefore,

this section first presents a detailed outline of how the

solution sequence for flexible wings operates. Afterward,

an explanation of the Bulk Data Deck is presented. An

example of the input deck is given in Appendix B.

Logical Procedures

The first part of the solution sequence (from now on,

called DMAP) sets up the tables that de.scribe the

0. structural model. These include ECT (Element Connection

Table) and GPL (Grid Point List). This set of matrices

describes the unconstrained structural model. The

constraints of the first subcase allow only rigid body

pitch about the wing root trailing edge. This will be

found in the eigenvalue analysis and used to set the

initial angle of attack. The frequency limits of 0.0 to

1.0 on the EIGR card ensure that this is the only

eigenvector used. The DOF are then further partitioned

down by Guyan Reduction to only the remaining Z DOF since

the aero model can only tolerate displacements in the

Z-direction. A real eigenvalue analysis is then performed

within a small frequency range around zero. The purpose of

" "the analysis is to obtain the mode shape of the rigid body

22

pitch mode. The Z-displacement of the most in-board

leading edge node, not including the wing root, is then

normalized to one by selection of "point" on the EIGR card.

All displacements are multiplied by a user calculated

parameter, AOAP, in order to set the initial angle of

attack (Fig 1). This procedure determines the zero-camber

initial displacements of all the nodes. The indirect

method of determining this is unavoidable because COSMIC

A STRAN has no module, or simple sequence of modules, that

will do this. Camber is added to the wing, if desired, by

using a parameter ICAMB and a matrix CAMBER. After this,

various transformation matrices are built. The first one

created is GTKA, which is built using the Bulk Data SPLINE

cards. This will be used to transform the displacements of

the structural model to values of slope on the aero model.

These values will then be used by the aero analysis portion

to specify the strengths of the downwash vector, DIJK or

D2JK. This vector is then multiplied by the aero influence

matrix for the Doublet-Lattice aero method, AJJL'e to

determine the rC distribution on the aero model.

Following the calculation of GTKA the module GIAS is called

to determine other transformation matrices and moment arms.

This ends the first subcase of the DMAP.

The second subcase is distinguished from the first by

a change of SPC cards. The structura' ,r.Ael is

reconstrained to allow no rigid body motion. None of the

nodes on the wing root have any active DOF; all the other

23

x

z

AO"P e

AQAP A 2C tan

ft initial AGA

-X-distance from the leading edgenode and the wing root trailingedge

Fig 2.. Determining AOAP

24

7z7-

nodes are limited o only translational DO?. These nodes

are then further reduced to only the Z DOF by ASET cards.

This procedure locks the wing root at the initial AOA as

determined by the eigenvalue analysis and AOAP. Then the

matrices necessary for static deflection analysis are

determined for this configuration. This analysis is then

performed to determine the structural loads due to the

initial AOA.

The next section is the most significant one of the

'DMAP. The iterative loop calculates the displacements,

structural loads, and aero forces due to the structural

deformations. Then the structural deformation due to the

new airloads are calculated. The loop begins by finding

the change in structural deformations due to the airload

vector. On the first iteration the load vector is due to

the initial AOA. On subsequent iterations it is due to the

change in structural deformations. Then the incremental

deformations are transformed to slopes on the aero model

using the GTAK generated from the Bulk Data SPLINE cards.

These slopes are used to determine incrementall(s.. The

incremental 6e, are transformed to an incremental load

vector which is used in the next iterative pass through the

loop. This is accomplished by premultiplying the aCe

vector by GTAK and then by TTTTT. At the end of each

increment the changes in deformations, structural loads,

and aero forces are accumulated. The loop is finally left

when the norm of incremental displacements (VNSR) is less

25

than the user supplied parameter ELOO,?, or a total of ten

incremental passes have been made. The loop gives the

final values for the structural deformations, structural

forces, and 40, vector.

The DMAP then recovers the complete solution for both

the analysis set and the omitted DOF. A complete stress

.- recovery for all the structural elements can be done if

requested by the user. The final section of the DMAP

determines C., CP, C,, due to both the final aero forces

and the final structural loads. Both sets are calculated

to provide a means of checking the accuracy of the force

transformations between the aero and structural models.

Implementation

0In addition to the usual model used in structural

analysis there are a few more cards, and one additional

datablock, needed to run the DMAP. The extra datablock is

TOSEL and is entered via DTI cards. TOSEL is the table of

area element numbers on the upper wing surface. The

records in TOSEL are organized according to element BCD

names. A more detailed explanation of TOSEL is presented

in Section III of this volume. The additional cards needed

are (Ref 1):

ASETI - Defines the DOF in the analysis set. For

the DMAP the analysis set should consist of

only the Z-DOF for every non-wing-root node.

CAERO1 - Divides the aero panels into equal boxes for

the Doublet-Lattice aero theory. The param-

26

eters on this card are determined by the

wing planform and the user's needs.

AEFACT - Divides the aero panels into unequal boxes,

used in conjunction with the CAERO1 card.

PAER01 - Defines associated bodies for the CAER01

card.

EIGR - Lists parameters for the real eigenvalue

analysis. The frequency range of interest

should be from 0.0 to . in order to

include only the rigid body pitch mode.

There is only one estimated and desired

root in the frequency range. The eigen-

vector should be point normalized on the

Z-displacement of the most in-board leading

edge node, not including the wing root.

AERO - Defines the basic aero parameters. The DMAP

uses the parameter Q, the dynamic pressure,

and the mach number frr, m the MKAERO card

instead of the parameters on the AERO card.

Therefore the values on the aero card do not

matter, but they have to be positive to

allow the DMAP to complete the processing of

the AERO card.

MKAERO - Defines the mach number and reduced

frequency for the desired flight condition.

In the DMAP only one mach number and

- reduced frequency are allowed. The mach

27

. . . . . . . . . . . . . . .

number should be subsonic and representative

S-of the desired flight condition. The

reduced frequency should be a positive

number very close to zero.

SPLINEl - Defines the parameters for generation of a

surface spline to interpolate the out-of-

plane displacements on the structural model

to out-of-plane displacements and slopes on

the aero model. The SPLINEI card is used in

exactly the same way as it is in the flutter

analysis rigid format.

SET1 - List of structural grid points to be used

with the SPLINEl card. Normally the list is

only the nodes on the upper surface.

PARAM cards

AOAP - Used to set initial AOA. Real

number. It multiplies the rigid

body pitch mode eigenvector after

the point normalization is done as

specified on the EIGR card.

ELOOP - Tolerance of convergence for the

iterative loop. It is compared to

the norm of the change of deforma-

tions for each iteration. Real

number.

LMODES - Number of modes to be used in the

modal flutter formulation. Since

28

the only desired mode is the rigid

body pitch mode LMODES is one.

LMODES is normally used when

several eigenvectors are consid-

ered in a flutter analysis. In

these cases the different eigen-

vectors are arranged as columns in

a forcing vector for determina-

tion of modal pressures.

LMODES would then be the number

of columns. 'MOVE is a real

number.

Q - Dynamic pressure. Must correspond

to the desired flight condition.

VReal number.

RC -Root chord length. Used in formu-

lating aerodynamic coefficients.

Real number.

WAREA -Planform area of the model. Used

in calculating aerodynamic coeffi-

cients. Real number.

As an .option, camber can be added to the wing. If camber

is required then an additional PARAM card should set

ICAMB = 1. Also, the CAMBER vector must be input via DMI

cards. CAMBER is as long as the number of corners on the

aero boxes. If two or more aero panels are used then the

- common nodes on both panels are counted twice. The values

29.-.

that are in CAMBER are the Z displacement of each aero box

corner due to the camber of the airfoil. In addition, any

control surface deflection can be treated as if it were a

change in camber.

Finally, in order to run this DMAP for aeroelastic

analysis of flexible wings, the case control and executive

card decks must be formulated. The executive card deck

must reflect the fact that a DMAP is being run rather than

a rigid format. The case control deck notes the set

identification number of the EIGR card in the Bulk Data

Deck. The case control lists the two subcases and the SPC

identification numbers for each. In addition, output

requests as needed are specified in the case control. The

values of the first subcase correspond to the initial pitch

configuration; those of the second subcase are a final

result of the iteration loop. All the available output

requests for the static loads analysis rigid format art:

also available for the DMAP.

30

-..

Bibliography

1. NASA SP-222(04). The NASTRAN User's Manual (Level17.0. National Aeronautics and Space Administration,December 1979.

2. NASA SP-223(04). The NASTRAN Procrammer's Manual(Level 17.-O). National Aeronautics and SpaceAdministration, December 1979.

3. Hurwitz, M~yles H. Course Notes of NASTRAN SystemPrograming. MSN Software Services, 1978.

4. Schaeffer, Harry G. Course Notes of Direct MatrixAbstraction Programming (DMAP) in MSC/NASTRAN.Schaeffer Analysis, Inc., 1981.

Lw

31

Vita- --

Kim Jones was born on 28 February 1958 in Weisbaden,

Germany. He graduated from high school in Clearwater,

Florida in 1976 and was subsequently accepted into the Air

Force Academy. A year after receiving a Bachelor of

Science Degree in Aeronautical Engineering, he entered the

'School of Engineering, Air Force Institute of Technology,

in June 1981.

Permanent Address: 837 Island Way

Clearwater, Florida 33515

32

..... ..-

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~Or THIS PAGE (When Dat. EFntered)

REPORT DOCUMENTATION PAGE REA~DISTUCIONS

1REPORT NUMAIER 2. GOVT ACCESSION NO. S. RECIPIENTIS CATA1,OG NUM1BER1

AFIT/GAE/AA/82D-164. TITLE (and Subtitle) S. TYPE OF REPORT & PERIOD COVERED

STATIC AERIOELASTIC ANALYSIS OF US ThesisFEXIBLE WINGS VIA NASI'RAN S. PERFORMING ORG. REPORT MUNGER

7. AuTNOR(e) I. CONTRACT OR GRANT MU1111190e)

Kim JonesiLt.

9. PERFORMING ORGANIZATION NAME AND ADDRESS Ia. PROGRAM ELEMENT., PRJECT. TASK-AREA t& ORK UNIT V%1ER

Air Force Institute of Technology (AFIT-EN)* Wright-Patterson AMB, Ctaio 45433

It. CONTROLLING OFFICE NAME AND ADDRESS I*. REPORT DATE

Decaiiber 198218. MUNGER OF PAGES

13014. MONITORING AGENCY NAME SADOR9SS(Jf differenulf'e. Coelifte OffIo) It. SE9CURITY CLASS. (41 Od e.

Unclassifiedlad. OECDASIFICATION/DOWNGRADIMG

ISI. OISTRIISUTION STATEMENT (of tis Report)

Approved for public release; distribution unlimited

'7. DISTRIDUTION STATEMENT (.1 th* abstraot euatemd I Stck". N, at at. *m Roert)

IS. SUPPLEMENTARY NOTE11

fVrWOLA.. rar 1AW JPU 190.17.

AUr Force Iflswt. t Ioc ivL.. 1 , i

Is. KEY WORDS (Canthnue on reverse aide Iee MaassrOidedntify by Wleek nuiaber)

NASI'RAFlexible-wingsAeroelasticFluid-Structure Interfacing

20. ASISTRACT (CON1111 n fu ewere@ side it neoeavy and Ideadit, by bleak mmWbw)

The purpose of this study was to expand the capabilities of theStatic Flexible Wing Aeroelastic Sequence that Captain Lance P. Qirisingerdeveloped for NASIEAN as his Master's Thesis at AFIT. Captain Chrisingerdeveloped a basic procedure to enable NASIRAN to analyze flexible wingairloads and stresses. That capability is expanded to enable analysisof standard wing models.

D I AM 1473 EDITION OF I NOV so is 0SOLETE UNCU.SSIFIEDSECURITY CLASSIFICATION OF t1"16 PAGE (ohmUsa

FILM7D

3=8