v

INASA-CR- 170/53) HIGH-PJSEFOBHANCE

DEPLOYABLE SlfUClCfitS FOR 1EE SUEFOHT OF

HIGH-CONCENTBATICN EATIO SOLAB ASSAY MODULES

iinal Report (Astio Aerospace Corp.) 79 p

HL A05/Mf A01 CSCL 13b G3/3 1

N86-16413

Unclas

04940

DEC 1985

RECEIVED

A SPAR COMPANY

ASTRO AEROSPACE CORPORATION

6384 Via Real. Carpinleria. CA 93013-2993

Telephone 1805) 684-6641

TWX 910-336-1144 FAX (805) 684-3372
HIGH-PERFORMANCE DEPLOYABLE

STRUCTURES FOR THE SUPPORT OF

HIGH-CONCENTRATION RATIO SOLAR ARRAY MODULES

by

Mehran Mobrem

FINAL REPORT

AAC-TN-1142

31 October 1985

Prepared for

NASA Marshall Space Flight Center

Under Contract No. NAS8-36043

Prepared by

Astro Aerospace Corporation

6384 Via Real

Carpinteria, California 93013
TABLE OF CONTENTS

SECTION 1: INTRODUCTION 1

SECTION 2: MISSION SELECTION/DESIGN CRITERIA 2

2.1 High-Concentration Ratio Solar Array 2

2.2 Deployable Structure 2

SECTION 3: CANDIDATE STRUCTURES 5

3.1 Stiffness 5

3.2 Small Relative Mass 5

3.3 Attachment of Solar Array to the Structure 5

SECTION 4: PARAMETRIC ANALYSIS AND SELECTION OF STRUCTURE 6

4.1 Extendible Support Structure Concept 6

4.1.1 Structural Properties 6

4.1.1.1 Dimensions 6

4.1.1.2 Mass 9

4.1.1.3 Truss Member Size 12

4.1.2 Acceleration Capability 14

4.1.2.1 Deployed Structure 14

4.1.2.2 Partially Deployed 15

4.1.3 Dimensions of Stowed Configuration 16

4.1.4 Deployment/Retraction Mechanism 16

4.1.5 Results 19

4.2 STACBEAM Concept 28

4.2.1 Structural Properties 28

4.2.1.1 Dimensions 28

4.2.1.2 Mass 31

4.2.1.3 Truss Member Size 32

4.2.2 Acceleration Capability 33

4.2.3 Dimensions of the Stowed Configuration 33

4.2.4 Deployment/Retraction Mechanism 34

4.2.5 Results 34

4.3 Comparisons 38

4.3.1 Attachments of the Solar Array to the Structure . 38

4.3.2 Package Size 38

4.3.3 Deployment 38

4.3.4 System Mass 39

4.3.5 Selection 39

SECTION 5: POINT DESIGN STUDY 40

5.1 Natural Frequency Analysis By Finite Element Method 40

5.2 Ground Handling 40

5.3 Critical Components 51

5.4 Rought Cost Estimates 51

11
TABLE OF CONTENTS (concluded)

SECTION 6: SUMMARY 53

REFERENCES 54

APPENDIX A: STACBEAM DEPLOYER MASS Al

APPENDIX B: ESS SYSTEM FINITE ELEMENT INPUT DATA Bl

APPENDIX C: ESS SYSTEM MODE SHAPES Cl

APPENDIX D: ESS SKETCHES Dl

in
LIST OF TABLES AND FIGURES

Table 1.

Table 2.

Table 3.

Table 4.

Table 5.

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17a.

Figure 17b.

Deployable Structure Baseline Requirements

ESS Basel i ne Desi gn

STACBEAM Baseline Design

Natural Frequencies of Vibration of the ESS System

ESS Design for t/d = 1/20

Extendi ble Support Structure (ESS) supporting Seasat SAR

Extendible Support Structure (ESS concepts)

Joint mass reduction

Depl oyi ng ESS

Depl oyed ESS

ESS truss member outside diameter

ESS mass

ESS system natural frequencies

ESS system stowed dimensions

ESS system attached to Space Station, stowed configuration ..

ESS system attached to Space Station, partially deployed ....

ESS system attached to Space Station, deployed configuration

STACBEAM concept

Depl oyed STACBEAM

STACBEAM depl oyer concept

ESS system finite element model

ESS system first mode shape (perspective)

ESS system first mode shape (y-z plane)

4

27

37

42

50

7

8

11

17

18

20

21

22

23

24

25

26

29

30

35

41

43

44

IV
LIST OF TABLES AND FIGURES (concluded)

Figure 18a. ESS system second mode shape (perspective) 45

Figure 18b. ESS system second mode shape (y-z plane) 46

Figure 19a. ESS system third mode shape (perspective) 47

Figure 19b. ESS system third mode shape (x-y plane) 48

Figure 20. Synchronized joint 52
SECTION 1

INTRODUCTION

This Final Report summarizes a study conducted by Astro Aerospace

Corporation (Astro) for NASA Marshall Space Flight Center (MSFC) on HighPerformance Deployable Structures for the support of High-Concentration Ratio

Solar Array Modules.

Serious consideration is being given to the use of high-concentration

ratio solar array modules for LEO applications such as Space Station. These

concentrator solar array designs offer the potential of reduced cost, reduced

electrical complexity, higher power per unit area, and improved survivability.

Arrays of concentrators, such as the miniaturized Cassegrainian concentrator

modules (see Ref. 1), present a serious challenge to the structural design

because their mass per unit area (5.7 kg/m^) is higher than that of flexible

solar array blankets, and the requirement for accurate orientation towards the

Sun (±0.5 degree) requires structures with improved accuracy potentials. In

addition, use on Space Station requires relatively high structural natural

frequencies (see Ref. 2) to avoid deleterious interactions with control

systems and other large structural components.

The objective of this study is to identify and evaluate conceptual

designs of structures suitable for deploying and accurately supporting highconcentration ratio solar array modules.

Section 2 of this report describes the mission selection and design

criteria which were used to select the two structural concepts: the

Extendible Support Structure (ESS, a synchronously-deploying structure) and

the STACBEAM (Stacking Triangular Articulated Compact Beam, a sequentiallydeploying mast). Sections 3 through 5 describe the candidate structures,

parametric analysis and point design study, respectively. A summary is

presented as Section 6.
SECTION 2

MISSION SELECTION/DESIGN CRITERIA

A Space Shuttle launch and the Space Station orbit were selected by MSFC

for the baseline environmental requirements.

2.1 HIGH-CONCENTRATION RATIO SOLAR ARRAY

The baseline requirements for the solar array size are:

o A power of 15-kW BOL (Beginning of Life) per wing

o An aspect ratio of 2.46:1 (present Space Station solar array aspect

ratio, Ref. 2)

 :

The Cassegrainian and SLATS (Ref. 3) concentrator concepts have been

evaluated as high-concentration ratio solar array modules. It was concluded

that the requirements for the SLATS concentrator are not as critical as those

for the Cassegrainian concentrator. A pointing accuracy of 0.5 degree over

the entire array was established as a design requirement.

The Cassegrainian concentrator is capable of generating 160 W/m^ BOL

(current technology, Ref. 1); hence, a solar array with dimensions of 6.2 by

15.25 m is required.

2.2 DEPLOYABLE STRUCTURE

The general requirements for the deployable structure are based on the

Space Shuttle launch, the Space Station environment, and the required size and

pointing accuracy of the solar array.

The primary load during a Space Shuttle launch is due to random vibration

(Ref. 4). The deployable structure in the stowed configuration is compact

with its truss elements sitting on top of each other. Also, there will be

some type of launch restraint to prevent any unwanted vibration responses.

Hence, the launch environment will not be the primary design criteria for

deployable structure strengths and stiffnesses. At this point, it is assumed

that the deployable structure in the stowed configuration will be mounted to

the hard points of the STEP pallet. If the launch of the present Space

Station configuration (Ref. 2), however, is considered, the deployable
structure in the stowed configuration will be mounted to the stowed transverse

boom of Space Station inside the Space Shuttle. In that case, the required

dimension of the deployable structure in the stowed configuration, including

the deployer, will be a design driver, due to the available space inside the

Space Shuttle.

For Space Station environments, the deployed structure will be mounted to

Space Station as a solar array mast. The following load conditions were

considered (see Ref. 2):

r^

o Gravity-gradient torques

o Aerodynamic drag and torques (at 200 nmi)

o Docking/berthing

o Crew motion •:,••.

o RCS reboost firing

The acceleration due to RCS reboost firing will generate the highest

bending moment (452 ft-lb) on the deployed structure (see Ref. 2) and was

chosen as a primary requirement, with a safety factor of 5, to establish the

required bending strength of the deployed structure. The fundamental

vibrational natural frequency of the solar array mast given in Ref. 2 is about

0.16 Hz. Note that the computed natural frequency in Ref. 2 decreases to

about 0.11 Hz if the solar array mast is attached to a tensioning-type solar

array. The required pointing accuracy for the deployed structure is 0.5

degree (see Ref. 1). The deployable structure baseline requirements are given

in Table 1.
TABLE 1. DEPLOYABLE STRUCTURE BASELINE REQUIREMENTS.

Minimum

Requirement Design Goal

Length, m (ft) 15.25 (50) 15.25 (50)

Bending strength, m-N (ft-lb) 614 (452) 3068 (2260)

Fundamental vibrational natural 0.11 0.16

frequency, Hz

Pointing accuracy, degrees 0.5 0.5
SECTION 3

CANDIDATE STRUCTURES

The Extendible Support Structure (ESS, a synchronously-deploying

structure) and the STACBEAM (Stacking Triangular Articulated Compact Beam, a

sequentially-deploying mast) truss structures have been considered for

deploying and supporting high-concentration ratio solar array modules.

The primary reason for selecting the above structures is that their

deployments are trans!ational and they do not rotate about their longitudinal

axes during the deployment or retraction. Hence, the solar array can be

attached directly to the structure at each bay, both in stowed and deployed

conditions.

In order to consider the merits of each in an unbiased manner, certain

ground rules have been established.

3.1 STIFFNESS

It has been assumed that the solar array panels (solid panels) do not

contribute to the overall stiffness of the support structure. Therefore,

changes in solar array panel design have little effect on the structural

behavior.

3.2 SMALL RELATIVE MASS

The mass of the solar array and its structure is small in comparison to

the total spacecraft mass. Therefore, the cantilever vibration frequency

approximates the lowest frequency mode.

3.3 ATTACHMENT OF SOLAR ARRAY TO THE STRUCTURE

The -solar array will be attached to its support structure along its width

at the two nodal points of the array's first vibrational free-free mode.

Therefore, the solar array local natural frequency along its width would be

maximum.

Hence, the ratio of the structure width w to solar array width b should

be about 0.56.
SECTION 4

PARAMETRIC ANALYSIS AND SELECTION OF STRUCTURE

4.1 EXTENDIBLE SUPPORT STRUCTURE CONCEPT

The Extendible Support Structure (ESS) concept, originally developed by

Astro Aerospace Corporation (Astro) to support the synthetic aperture radar

antenna, was flown on the Seasat spacecraft. The ESS concept for deployment

and support of .a solar array panel is shown in Figures 1 and 2. The structure

is of width w, depth h, and bay length &. It is composed of truss members of

diameter d and wall thickness t. For the Seasat applications, rigid solar

panels were an integral part of the structure in both the packaged and

deployed state and the same principle is applied for this case.

4.1.1 Structural Properties

4.1.1.1 DIMENSIONS

The minimum required length L of the structure is given in Table 1. The

bay length £ of the structure depends on the number of solar array panels n

(or number of bays) and is

» - -Jr d)

The width of the structure w is obtained from Section 3.3 as

w = 0.56b (2)

The structure depth h can vary and will be selected on the dimensional

requirements of the stowed structure.
ORIGINAL PAGE IS

OF POOR QUALITY

• >- * -I

x .,

' , x

> '''

Figure 1. Extendible Support Structure (ESS) supporting Seasat SAR.
C

X

CDUCOowN^X0)o

S-i

4-1

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,

o.,

3to•HX)C0)a

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00

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4.1.1.2 MASS

The mass of the ESS system includes the masses of its truss members and

joints and the solar array payload itself, or

MS = Mt + Mj + Ma (3)

4.1.1.2.1 Mass of Truss Members

The mass of the truss members is determined by multiplying the linear

density by the structure length, or

Mt = mtL (4)

The structure consists of longerons, face and side diagonals, and face and

side battens so that

mt ' "I* rafd+ msd* mfb + msb

w / w \ . / h \ (H)

 + (i)

where p is the material bulk density, and A is the truss member crosssectional area.

4.1.1.2.2 Mass of Joints

The joint mass is expressed as a function of tube mass by

M -

k = JL + i
The joint factor k, multiplied by the truss member mass, gives the structure

mass Mst and is estimated by investigating the Seasat ESS assembly. The joint

mass in the ESS for Seasat was 8 kg, over a length of 10.7 m, so that

mj Seasat = 0.75 kg/m

The truss member diameter was 0.0127 m with a 0.00075-m wall thickness. The

graphite tube mass per length is determined to be 0.40 kg/m. Therefore, for

Seasat,

k = 2.88

This joint factor, obtained for an assembly having comparatively high

wall thickness, should be greater for joints connecting thinner wall tubing.

Efforts directed toward decreasing the Seasat joint weight (see Figure 3) have

succeeded in lowering the factor. Projecting from these results, the

following joint factors are assumed:

Truss Member Wall

Thickness, t (mm) Joint Factor k

1.00 1.6

0.75 1.9

0.50 2.2

10
ORIGINAL PAGE IS

OF POOR QUALFTY

Object on right Joint J2-1 used on Seasat

ESS structure. Mass: 92 gm.

Object on left: Joint J2-1 lightened as follows

Web reduced from 0.30 to 0.08

inch; hole diameter increased

from 0.25 to 0.30 inch.

Mass: 46 gm. Reduction: 50

percent.

Figure 3. Joint mass reduction,

1-1
4.1.1.2.3 Mass of Solar Array Panels

The mass of the solar array panels Ma is

Ma = ma Aa

= ma bL (6)

where ma and Aa are the area density and the area of the solar array panels,

respectively.

ma = 5.7 kg/m2 (see Ref. 1)

4.1.1.3 TRUSS MEMBER SIZE <:

The truss member sizes are based on both the minimum bending strength and

natural frequency requirements presented in Table 1. At first, the truss

member sizes are calculated to satisfy the bending requirement. Then the

natural frequencies are calculated based on the computed dimensions from the

bending requirements. If the computed natural frequency satisfies the

requirements, then the calculation is complete. Otherwise, the order of

calculation should be reversed and the truss member size should be based on

the natural frequency requirement.

4.1.1.3.1 Bending Strength

The bending moment M is reacted by axial load P. in the longeron

M

P = - (7)

h

The axial load in the longeron should be less than its buckling load Pcr

P TT2 (EI)£

cr = * *

12
where (El) is the bending stiffness of the longeron

(9)

Substitution of Eqs. (8) and (9) into Eq. (7) results in

\1

, . (10)

JEth,

Note that the length of the back longeron A is two times the bay length.

X»

4.1.1.3.2 Natural Frequencies

Bending Natural Frequency

The fundamental bending natural frequency f^ of the ESS system with

cantilever boundary condition is given by

1

2

where the structure bending stiffness El is given by

El = | h2 (EA)A (12)

(EA)j, = the axial stiffness of longerons.

Torsional Natural Frequency

The fundamental torsional natural frequency f^ of the system with

cantilever boundary condition is given by

f

 = 1-57 / Gk \ 2

T

t 2ir J I

13
where Gk is the structure torsi onal stiffness and is given by (Reference 5)

2 'fd

 -

w

3 <E

%

 1

^ TEAT

fb

The mass moment of inertia Js is the sum of structure and solar array mass

moment of inertia.

Js = Jst

 + Ja : (15)

Assuming that all of the structure joints are located along the longerons,

then the structure mass moment of inertia:.-;.; is given by the following

approximation

/ 2 . 2 \

+ (Mt - 4pAjlL) ( j2+f- ) (16)

The mass moment of inertia of the solar array is given by

(

t

2

 ? ? \

_L±_b_4. h 1 ,-m VO

 + "Q I U7

)

id y /

where ta is the solar array panel thickness.

4.1.2 Acceleration Capability

4.1.2.1 DEPLOYED STRUCTURE

For a structure (beam), the limits on the acceleration are generally

governed by the bending strength M of the structure; however, if the pointing

accuracy is a requirement, then the limits on the acceleration are determined

by the maximum response slope of the structure. The latter one usually refers

to the accelerations during the normal operation. The translational and

rotational accelerations for a structure with cantilever boundary condition

are given as follows.

14
4.1.2.1.1. Translational Acceleration

The maximum acceptable translational acceleration aa is

-

 2M

and the maximum translational acceleration a0 during the operation is

°o • ?

where e is the maximum slope (pointing accuracy) of the structure.

4.1.2.1.2 Rotational Acceleration

The maximum acceptable rotational acceleration aa is

aa - ^2 (20)

MsL

and the maximum rotational acceleration OQ during the operation is

8EI§ un 3 (21)

MsL

4.1.2.2 PARTIALLY DEPLOYED

The structural capability of the ESS structure during the deployment has

not been determined by analysis. From past experience (Seasat project),7

however, the ESS structure alone can be deployed under 1 g load without any

antigravity compensation when the load is acting along the X axis (see Figure

2). As a conservative assumption, 0.2 g is taken as the limiting acceleration

capability of the ESS structure during deployments. Thus, the limiting

acceleration capability of the ESS system during the deployent is given by

(0.2 x 9.81) Mst

a

d

 = M"

15
4.1.3 Dimensions of Stowed Configuration

The ESS system dimensions in the stowed configuration along three axes

are given below (see Figure 2).

Axis Dimensions

X b

Y n (ta + d)

Z ~

4.1.4 Deploynent/Retr action Mechanism

The ESS deployment mechanism consists of latching clamps which hold the

packaged assembly rigidly together. Upon release of these clamps, the

assembly is free to expand and does so in a controlled; fashion by motorized

extension of the rear scissors longeron (see Figures 4 and 5). There are

three clamps, one for each stack of hinges, which make a direct load path to

the spacecraft. Such an assembly is expected to have a mass approximately

equal to the joint mass.

The retraction is made possible by retracting the rear scissors longeron.

Note that at the start of retraction, the side battens should be buckled. The

buckling of the side battens is done by the use of a synchronized joint which

controls the motion of side battens with the motion of the rear scissors

longeron.

16
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4.1.5 Results

For the baseline design, an eight-panel solar array is selected. In

addition, the following physical data were used in the analysis:

n = 8

L = 15.25 m

b = 6.2 m

M = 3068 Nm

E = 2.75 x 1011 N/m2 "VHM graphite/epoxy"

; p = 1520 kg/m3 "VHM graphite/epoxy"

t = 1 mm

ta = 15 mm

Aa = Afd = Asd = Afb = Asb :v;

Substitution of the above data into Eqs. (1), (2), and (6) results in

a = 1.91 m ..;;:

W = 3.472 m

Ma = 539 kg

Equation (10) is solved for several structural depths h and results are

presented in Figure 6. Note that h = 3.006 m corresponds to a structure with

equilateral cross-section. Also, the plot of structure mass Mst versus the

structure depth is presented in Figure 7. Note that the deployer mass is

estimated by the joint mass or

Mass of Deployer = M . (l - p-1 st y K/

The above results were used to calculate the natural frequencies and ESS

system stowed dimensions. The results are given in Figures 8 and 9. The

resulting natural frequencies are above the required values; thus, the design

drive for the truss members cross section is the bending strength requirement.

For the baseline, a structure with the depth of 1 m is selected which

satisfies not only STEP available space but also it satisfies the present

space station in stowed configuration (see Figures 10, 11, and 12). Its

properties are given in Table 2.

19
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26
TABLE 2. ESS BASELINE DESIGN.

Bay number, n 8

Length, (m) 15.25

Width, (m) 3.472

Depth, (m) 1

Bay length, (m) 1.91

Truss member diameter, (mm) 34.6

Truss member thickness, (mm) 1

Mass (kg) 46.4

2

Mass moment of inertia (kg-m ) 69 ./•••'

Bending stiffness, (N-m2) 1.94 x 107

 ;

Torsional stiffness, (N-m2) 4.36 x 106

Natural frequency (Hz)

Bending 1.72

Torsion 3.1

Stowed dimension (m)

X 6.2

Y 0.4

Z 2.15

Acceleration capability

Translational, (m/sec2) 0.69

Rotational, (rad/sec2) 0.07

Pointing error due to

maximum acceleration (degree)

Translational 0.046

Rotational 0.054

Acceleration capability

during the deployment,

(m/sec2) 0.077

Deployer Mass (kg) 17.4

27
The maximum acceptable trans!ational and rotational acceleration are

given in Table 2. The pointing error due to the above accelerations are also

given in Table 2.

Note that the response bending moments due to the above accelerations are

five times larger than the res pose bending moment of the solar array mast of

the present space station configuration.

The maximum acceleration capability during deployment is much higher than

accelerations resulting from normal operation of the space station

(docking/berthing and RCS reboost firing are not considered).

The above analyses were repeated for variation in the truss member

thickness from 0.7 to 1.1 mm. Since there are no drastic changes in the

result, the 1-mm thickness remained the baseline.

4.2 STACBEAM CONCEPT

The STACBEAM (Stacking Triangular Articulated Concept Beam) concept for

deployment and support of solar array panels is shown in Figures 13 and 14.

Special characteristics of the STACBEAM structure are as follows:

o It deploys sequentially, one-bay-at-a-time by unfolding and locking

hinges provided at the midpoint of each longeron and diagonal.

o The batten moves linearly, without rotation, during this deployment,

o All hinges are single-degree-of-freedom.

The panels are attached at each bay through standoffs to the two corner

joints of the STACBEAM by hinges. At the time of full deployment, the

midhinge of the panels would be locked to prevent any motion of the panels in

a direction normal to its plane.

4.2.1 Structural Properties

4.2.1.1 DIMENSIONS

In the existing STACBEAM design, the bay length is equal to its radius

R. The width of the structure w is determined in Section 4.1.1.1 and is 3.472

m. Since the cross-section of the STACBEAM is equilaterally triangular, then

its radius is 2.004 m and consequently, its bay length is 2.004 m. The

depth of the structure h is

h = 1.5R = 3.006 m

28
Figure 13. STACBEAM concept. 85-L114

29
Figure 14. Deployed STACBEAM. 85-L113

30
The minimum required length of the structure L is 15.25 m (see Table 1).

Hence the number of bays should be eight which results in a STACBEAM with

16.032-m length.

4.2.1.2 MASS

The mass of the STACBEAM system includes the masses of its truss members

and joints and the solar array payload itself, or

Ms = Mt +

4.2.1.2.1 Mass of Truss Members

(22)

The mass of the truss members is determined by multiplying the linear

density by the structure length, or

Mt = mt L (23)

The structure consists of longerons, diagonals, and battens so that

mt = m + ny + 1%

= 3pA£ + 6PAd +3 3 pAb

= 14.2PA for A£ = A,d = Arf = Afa (24)

where p is the material bulk density and A is the truss member cross-sectional

area.

4.2.1.2.2 Mass of Joints

The joint mass in the STACBEAM is 75 percent of truss member mass (see

Ref. 6). Then the joint factor

is assigned the value of k = 1.75.

31
4.2.1.2.3 Mass of Solar Array Panels

The mass of a solar array panel is given in Section 4.1.1.2

4.2.1.3 TRUSS MEMBER SIZE

The procedure to determine the truss member size is given in Section

4.1.1.3.

4.2.1.3.1 Bending Strength

For the simplicity of design, it is desired that the length of the stowed

STACBEAM and stowed solar array be equal. In order to satisfy the above

condition, the longeron diameter d should be equal to the solar array

thickness ta (see Section 4.2.3). Since the longeron diameter is now limited

to the solar array thickness, then the ratio of longeron diameter to its

thickness may not be large enough to use Eq. (9).

Equation (9) is modified to

(El) =^ (d4 - d4) (25)

I 64 i

where di is the inner diameter of the longeron.

Substitution of Eqs. (25) and (8) into Eq. (7) results in

2

A 4 d

i

 = d --rM

 (26)

1 J

4.2.1.3.2 Natural Frequencies

Bending Natural Frequency

The fundamental bending natural frequency of the STACBEAM system with the

cantilever boundary condition is given by Eqs. (11) and (12).

32
Torsional Natural Frequency

The fundamental torsi onal natural frequency of the STACBEAM system with

cantilever boundary condition is given by Eq. (13).

The torsional stiffness 6k of STACBEAM is given by

Gk = R - - + + _J_ (27)

4

where B = batten-diagonal angle = 30 degrees.

The mass moment of inertia Js is given by Eqs. (15), (17), and

J = /3pA L + (k-1) M \R2 + (M - 3pA L) - (28)

\ 0 \ * st \ s, t t t, 9

4.2.2 Acceleration Capability

The trans! atipnal and rotational acceleration capability of STACBEAM are

given by Eqs. (18) and (20). The pointing accuracies are also given by

Eqs. (19) and (21).

4.2.3 Dimensions of the Stowed Configuration

The STACBEAM system dimensions in the stowed configuration along three

axes are given below (see Figure 13).

Axes Dimensions

X b

Y 2nta or 2nd (whichever is larger)

Z h t. U + = 2R + U

where n is the number of bays or solar array panels, and U is the space

required between the STACBEAM and the solar array panels due to the deployer.

Note that the above dimensions do not include the deployer. The

dimensions for an existing deployer concept with the STACBEAM system

integrated into it are:

33
Axes Dimensions

X b

Y >«,

Z 2R + U + dd

where dd is the diameter of the main support tube of the deployer.

4.2.4 Deployment/Retraction Mechanism

The existing concept for the deployment/retraction mechanism (see Ref. 6)

is presented in Figure 15. The deployer height is at least one bay length.

Prior to deployment, the deployer itself is deployed to its minimum required

height, one bay length plus stack height.

The deployment is initiated by the rotation of three lead screws which

are threaded through the corner fittings of the top batten frame and are

attached to three main supports of the deployer. The top batten frame is

lifted with the rotation of the lead screws until the top bay is fully

deployed; then, the second batten frame which was held by synchronized latches

is released and engaged into the lead screws. The deployment is continued

until full deployment.

The deployment/retraction mechanism retracts the STACBEAM system one bay

at-a-time. The retraction of each bay, initiated by the simultaneous motion

of a series of linkages and levers, pushes the longerons, diagonals and the

solar array panel to unlock their mid-hinges. The estimated mass for the

deployment/retraction mechanism is given in Appendix A.

4.2.5 Results

The following data were used in the analysis:

M = 3068 N-m

, ia = 2.004 m

h = 3.006 m

E = 2.75 x 1011 N/m2 "VMM graphite/epoxy"

P =1520 kg/m3

 "VHM graphite/epoxy"

d = 0.015 m

A

5, =

 Ab = Ad

The results are given in Table 3.

34
Figure 15. STACBEAM deployer concept.

85-L115

35
The resulting natural frequencies are higher than the design goal. Thus

the design drive for truss member cross section is the bending strength

requirement.

The stowed dimensions are larger than the available space of the STEP and

the present Space Station stowed configuration. The maximum space available

of the STEP along its width (z-axis) is 106 inches or 2.69 m. In order to fit

the STACBEAM system with its deployer into the STEP, the following dimensions

are required:

£ = R = 1.23 m

n = 13

W = 2.13 m

Thus, the ratio of the STACBEAM width to that of the solar array is about

0.34.

36
TABLE 3. STACBEAM BASELINE DESIGN.

Bay number, n 8

Length, (m) 16.032

Width, (m) 3.472

Depth, (m) 3.006

Bay length, (m) 2.004

Truss member diameter, (mm) 15

Truss member thickness, (mm) 1.55

Mass (kg) 40

p

Mass moment of inertia (kg-m ) 105.4

Bending stiffness, (N-m2) 1.085 x 108

? 7 Torsional stiffness, (N-m ) 1.58 x 10

Natural frequency (Hz)

Bending 3.78

Torsion 5.1

Stowed dimension (m)

X 6.2

Y 2.004

Z 4.24

Acceleration capability

Trans!ational, (m/sec2) 0.66

Rotational, (rad/sec2) 0.062

Pointing error due to

maximum acceleration (degree)

Trans 1ational 0.009

Rotational 0.01

Deployer Mass (kg) 33

37
4.3 COMPARISONS

The two structural concepts for the support of the solar array panels are

evaluated by using several bases of comparison: attachment of the solar array

to the structure, package size, simplicity of deployment, and system mass.

4.3.1 Attachment of the Solar Array to the Structure

One of the primary purposes of the deployable structure is to support the

solar array panels accurately when it is fully deployed. For that reason, it

is important how and at what location the solar array is attached to the

structure.

o The solar array will be mounted directly on the ESS at any two

locations along its width without being constrained by the package

requirement. The solar array will be an integral part of the ESS and

its relative position to the front face of the ESS will not be changed

during deployment.

o The solar array will be mounted on the STACBEAM through standoffs due

to the deployer constraints. The width of the STACBEAM is constrained

by the package requirement; thus, the two mounting points (corner

fittings of the STACBEAM) cannot be selected arbitrarily. Since the

relative position of the solar array to the front face of the STACBEAM

changes during the deployment, the solar array is mounted at its end

on the standoff by hinges and also has two midhinges.

4.3.2 Package Size

The two concepts have two distinct package shapes. The ESS system

package is a flat box, and its dimensions have no constraints on the ESS

width. The STACBEAM system package is a triangular prism plus a flat box, and

its dimensions have constraints on the STACBEAM width. The dimensions are

given in Sections 4.1.3 and 4.2.3.

4.3.3 Deployment

Aspects of deployment which are factors in the evaluation are simplicity,

reliability, and natural frequency during deployment. The simplicity and

relative reliability of deployment of each concept can be compared by

considering their special characteristics:

o The ESS deploys by simultaneously opening all bays so that each member

receives its deployment force by transmission through the assembly.

38
o The STACBEAM requires synchronized engagement and lifting of the three

corners of each triangular batten frame. This can be accomplished

electronically or mechanically.

Since the full stiffness of the ESS is not developed until it is

completely deployed, the system frequency is degraded .during deployment. This

situation is not encountered in the other system.

4.3.4 System Mass

The two structures have basically equal masses. The mass of the two

structures with the same depth (h = 3.006 m) is used for comparison:

Mass of ESS = 37 kg

Mass of STACBEAM = 40 kg

The estimations for the deployer mass are also

Mass of the ESS deployer = 13.9 kg

Mass of the STACBEAM deployer = 33 kg

4.3.5 Selection

The ESS structure is selected over the STACBEAM for the reasons given in

Sections 4.3.1 and 4.3.2. In addition, note that the deployment mechanism for

each ESS structure is much simpler than the one for STACBEAM.

39
SECTION 5

POINT DESIGN STUDY

5.1 NATURAL FREQUENCY ANALYSIS BY FINITE ELEMENT METHOD

As a part of point design, the ESS system's natural frequencies were

analyzed by the finite element method using the COSMOS 7 Program.

The finite element model contains 23 nodal points and 61 truss elements,

each representing a single truss member as represented in Figure 16. To

account for the mass of the hinges and connections at the joints, the truss

member material density was increased by the joint factor, k = 1.6.

Furthermore, the mass of the solar array panels was accounted for by

including additional lumped masses at only those nodes on the solar array

surface. The solar array panels were assumed not to contribute to the

structural stiffness. Appendix B lists the input data to the COSMOS 7

Program.

The first ten natural frequencies of the ESS system were determined by

the subspace method and are listed in Table 4.

Appendix C lists coordinate displacements of the structural nodes for the

normal mode shapes corresponding to the first ten natural frequencies. Also

presented in Figures 17, 18 and 19 are various views of mode shapes

corresponding to the first three natural frequencies. The first natural

frequency is the first bending about the x-axis and agrees very closely with

the one given in Table 2. The second natural frequency is the first torsional

frequency and is about six percent (6%) lower than the one given in Table 2.

5.2 GROUND HANDLING

During the ground handling (1 g) of the deployable structure, it may

become necessary to handle the truss members with special care to prevent any

damage or fracture to them. If the special handling of the truss members

become a problem, it can easily be solved by increasing the ratio of the truss

member thickness to its diameter.

40
0

0

O) -aocaiO)

"ai

C/) ooO) O)

41
TABLE 4. NATURAL FREQUENCIES OF VIBRATION OF THE ESS SYSTEM

Mode No. Natural Frequency, Hz

1 1.76

2 2.93

3 5.23

4 8.84

5 9.31

6 14.58

7 18.97

8 19.93

9 21.67 v

10 24.11

42
oO) Q

.

co

s_0)Q

.

O) Q

.

(OO) » — .

-O N S- r— £ II .E r- O) q—

4-» x_^

CO>>CO oo

(/>UJ•f8a)s-3

C7>

X

43
->

>

O) Q

.

.(/)

•o

QJ C(ONIO

.

(O

Nvo

+-> r--

co •

•i— • 4- u O) 4JooLUJDO)

44
C

D>O0)a

.

(/>s_CDQ- Q. CO0) -a --^ O N T3 CO c cn O • O C\J a;

c/> n O) co(OCO<ua>

CM

45
(U

c

ON

I

0)

o.

to

•o

o

e

•a

c

o

o

Q>

4->

i/V

CO

LU

CO

tu

CD
OJoo>O_

(/> ' S_O) CLOJ ~oO"O ro S_ CVJ

•1^ •

-C Lf)

-l->

11

<U CO

4-> t-

V>>

r

ISI

(/) oo<o 01O) X47
OJ c(0QJ CXraS- C

O

•r- 00

ECD 4J10ooooenO) CD

CO

48
In order to investigate the effect of the above change on the overall

behavior of the ESS system, Equation 10 is modified to

(29)

where c = t/d.

The ratio c was increased from 1/34.6 (see Table 2) to 1/20; the results

are given in Table 5.

As expected, the deployable structure mass was increased by twenty

percent (20%), but the stiffnesses and natural frequencies were also

increased.

49
TABLE 5. ESS DESIGN FOR t/d = 1/20

Bay number, n 8

Length, (m) 15.25

Width, (m) 3.472

Depth, (m) 1

Bay length, (m) 1.91

Truss member diameter, (mm) 30.2

Truss member thickness, (mm) 1.51

Mass (kg) 56

p

Mass moment of inertia (kg-m ) 83.34

Bending stiffness, (N-m2) 2.49 x 107

Torsional stiffness, (N-m2) 5.61 x 106

Natural frequency (Hz)

Bending 1.93

Torsion 3.51

Stowed dimension (m)

X 6.2

Y 0.36

Z 2.15

Acceleration capability

Trans 1ational, (m/sec2) 0.68

Rotational, (rad/sec2) 0.066

Pointing error due to

maximum acceleration (degree)

Translational . 0.036

Rotational 0.04

50
5.3 CRITICAL COMPONENTS

The operation and reliability of the synchronized joint controlling the

motion of the side battens with the motion of the rear scissors longeron is

the primary concern. Its operation is not only required for the retraction,

but it is essential to a synchronized deployment. The synchronized joint

presented in Figure 20 has been used in the Seasat project and its operation

and reliability have been demonstrated. Note that the Seasat synchronized

joint was controlling the motion of the side diagonal with the motion of the

rear scissors longeron since there were no retraction requirements, but the

basic principles are the same. Presented in Appendix D are sketches (Class C

drawings) of the overall configuration of the ESS structure.

5.4 ROUGH COST ESTIMATES

Cost estimates for both the engineering development of a mission specific

design and the recurring unit costs have been developed on the basis of the

following assumptions:

o Cost plus fixed fee contract (full requirements not defined)

o Costs in 1985 dollars

o Non-recurring costs include:

Mission specific design (analysis, specification and drawings)

Preliminary Design Review at Astro1s facility

Engineering model fabrication

Functional and life cycle tests

Critical Design Review at Astro's facility

o Recurring unit costs include:

Manufacturing of flight hardware (twelve units)

Qualification of testing including vibration, thermal vacuum, E.M.I

Refurbishment of qualification unit as flight spare

Acceptance tests and documentation

Brush-type dc motor

Standard Astro quality plan

Shipping container

F.O..B. Carpinteria, Californi a

On this basis, the non-recurring costs are estimated at $750,000 and the

recurring costs at $650,000 per unit.

51
Figure 20. Synchronized joint.

52
SECTION 6

SUMMARY

The Extendible Support Structure (ESS,, a synchronously deploying

structure) is selected to deploy and accurately support the high-concentration

ratio solar array modules, such as the miniaturized Cassegrainian Concentrator

Solar Array.

The ESS structure provides high stiffness, high strength and low mass

(less than a tenth of the solar array modules' mass). The ESS system (ESS

structure plus the solar array modules) can stand the space station

environment under the worst conditions with a safety factor of five, and its

fundamental vibrational natural frequency is about 1.7 Hz. Due to its high

stiffness, the pointing error under worst conditions is 0.054 degree. The ESS

system in the stowed condition can be attached to the stowed transverse boom

of the space station inside the space shuttle.

53
REFERENCES

1. Patterson, Robert E.: Study of Multi-Kilowat Solar Arrays for Earth

Orbit Applications. TRW Document No. 38172-6001-UE-OO, 15 October 1983.

2. Space Station Reference Configuration Description. JSC-19989, August

1984.

3. SLATS Concentrator Exploratory Development Program Status, April 1985;

package sent to Astro by General Dynamics, Convair Division.

4. Space Shutte System Payload Accomodations. JSC 07700, vol. XIV, Rev. H,

16 May 1983.

5. Preiswerk, Peter R. and Stammreich, John C.; Extravehicular Activity

Translation ARM (EVATA) Study, Astro Document No. AAC-TN-1064,

14 July 1978.

6. Adams, Louis and von Roos, Angelika I.; STACBEAM II, Final Report,

Phase VI, Astro Document No. AAC-TN-1134, 23 April 1983.

54
APPENDIX A

STACBEAM DEPLOYER MASS

Al
APPENDIX A

STACBEAM DEPLOYER MASS

The deployer mass is estimated as the sum of several masses, as follows:

o Primary support. It is assumed that the deployer itself is truss-like

with stiffness equal to that of the beam. The mass of this component

is taken as the mass of an equivalent length of beam, or 5 kg.

o Lead screws. These are assumed to be composite graphite/epoxy and

titanium so that thermal effects are minimized. The mass of three

0.02-m diameter screws is calculated to be about 4 kg.

o Lead screw drives and supports. Includes upper and lower bearings,

three mid-span supports, and gearing on each of the three lead screws.

Assume 2 kg.

o Corner posts. These posts provide substantial backing for the lead

screw supports so that the beam is held with full stiffness at any

intermediate deployment position. Graphite/epoxy tubes of 0.08-m

diameter and 0.004-m wall thickness used for this purpose have a mass

of 3 kg each. Total of 9 kg.

o Motor. Two kg.

o Synchronization. Two composite tubes, transferring rotational motion

from the single motor-driven assembly to each of the two slave

assemblies. Associated gearing. Total of 2 kg.

o Retraction. Mechanisms required for retraction include three longeron

pushers, three diagonal pushers, three escapements (synchronized

latches) and a stack mover. The longeron and diagonal pushers would

be triggered by beam motion through the deployer. Longeron pusher

. linkages would be close to the corner posts and of relatively low

mass: 1.5 kg total. The diagonal pusher linkages must extend to the

area between the posts, and the two situated away from the payload

would total 2 kg. The third diagonal pusher must be free-standing

(because of the beam-pay!oad connections) and would have a mass of

perhaps 3 kg. Escapements are driven by lead screws; total of 0.5 kg.

The stack mover keeps the top of the stack at the lead screw entrance

level and would consist of three separate racks at the corners, driven

by the lead screws, and having 2 kg mass. Total retraction mass: 9

kg.

The total deployer/retractor mass is therefore 33 kg.

A2
APPENDIX B

ESS SYSTEM FINITE ELEMENT INPUT DATA

Bl
PAGE IS

QE POOR QUALFTY

Appendix R

i

2

3

4

5

6

7

' 3

9

10

11

12

13

14

15

16

17

18

19

20

21

23

23

24

55

26

27

23

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

DO

51

52

53

54

50

MARSHALL HPD3

*CONTrcOL, 23, 61

Ml, 3D, L, E

M2, 1, 0, 16, 0

M3, 1

•^RENUMBER

*PLOT

ANODES

C, 1,3, 1,NM

C, 19, 19, 1, NM

1, 0. 0, 0. O, 0. 0, 3

17, 0. 0, 15. 25, O. 0, 0

2, 3. 472, 0. 0, 0. 0, 2 i

18, 3. 472, 15. 25, 0. 0, 0

19, 1. 736, 0. 0, -1. 90625. O I

20, 1. 736, 1. 90625, -1. , 1

23, 1. 736, 13. 34375,-1. , O

AMASSES !

MM, 3, lib, 1. 33. 68, 33. 63, 33. 63 '

NM, 17, 18, 1, 16. 84, 16. 84, 16. 84

*• TRUSS, L, 61

1,1,1,0

1.

2. 75E11, O, 1. 0556E-4, 2432. , 0

1, 1, 3, 1, O, 0, 0, 1 |

17, 1, 2, 1, 0, 0, 0, 2 ;

26, 1, 4, 1, 0, 0, 0, 2

34, 19, 20, 1, 0, 0, 0, 1

38, 1, 20, 1, 0, 0, 0, 1

39, 2, 20, 1, 0, 0, 0, 1

40, 3, 20, 1, 0, 0, 0, 1

41, 4, 20, 1, 0, 0, 0, 1

42, 5, 20. 1, 0, 0, 0, 1

43, 6

44, 5

45 6,2]

1, 0, 0, 0, J

0. 0, O, 1

. 0, 0, 0, 1

0, 0, 0, 1

1, 0, 0, 0, 1

1, 0, 0, 0, 1

49, 10, 21, 1, O, 0, 0, J

50, 9, 22, 1, 0, 0, 0, 1

10, 22, 1, 0, 0, 0, 1

11, 22, 1, 0, 0, 0, 1

12, 22, 1, 0. 0, 0, J

13, 22, 1, 0, 0, 0, J

55, 14, 22, 1, 0, 0, 0, J

56, 13, 23, 1, 0, 0, 0, 1

57, 14, 23, 1,

15, 23, i,

20,

21, 1,

il. 1,

46, 7, 21, 1,

47, 8, 21,

48, 9, 21,

51,

52,

53,

54,

, O, 0, O, t

0, 0, 0, J

16, 23, 1, 0, 0, 0, J

17, 23, 1, 0, 0, 0, )

53

59

60

61, 18, 23, 1, 0, 0, 0, J

•^FREQUENCIES

12, S, 1000. , 0, 1, 1, O, 0, O

^FINISH

B2
APPENDIX C

ESS SYSTEM MODE SHAPES

Cl
Appendix C

ORIGJNAl PAGE IS

fiE POOR QUALmr

MOD E SHAP E N O

NODE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

X-DISP.LACEMENT

Cm

0.OOOOOOE+OO

0,OOOOOOE+OO

0. 541264E-03

0.486291E-03

0.110029E-02

0.104383E-02

0.151732E-02

0. 14577 IE-OP.

0.193886E-02

0.187604E-02

0.222442E-OP

0.215B40E-02

0.250393E-02

0.243439E-02

0.2&B690E-02

0.261533E-02

282307E-02

278266E-02

0.OOOOOOE+OO

-0.417953E-04

-0.385174E-04

0.3011OOE-04

0. 146118E-03

0.

0.

Y-DISPLACEMENT

fm)

0.OOOOOOE+OO

0.OOOOOOE+OO

-0.682360E-03

-O.735139E-03

-0.138063E-02

-0.14532BE-02

-0.179243E-02

-0.189978E-02

-0. 221651E-02

-0.233105E-02

-0.239085E-02

-0.252348E-02

-0.257213E-02

-0. 270483E-02

-0.2D9579E-02

-0.273402E-02

-0.262008E-02

-0.275787E-02

0.OOOOOOE+OO

0. 998420E-03

0.322041E-02

0.437B5&E-02

0. 471648E-02

Z-DISPLACEHENT

(m)

0. OOOOOOE+OO

O. OOOOOOE+OO

0.142115E-02

-0. 510122E-03

0.78126BE-02

0.394488E-02

0. 181919E-01

0.12SB72E-01

0. 300691E-01

0.234213E-01

0. 438964E-01;

0. 363B33E-01

0. 58141&E-01

0.498613E-01

O. 723174E-01

0.&41096E-01

6,B7090BE-01

0.7B1184E-01

0. OOOOOOE+OO

0.407250E-03

0.154691E-01

0.400343E-01

0.683191E-01

C2
MOD E SHAP E NO . 2

NODE X-DISPLACEHENT

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

IB

19

20

21

22

23

0. OOOOOOE+OO

0. OOOOOOE+OO

-0. 47250AE-0?

-0.304699E-02

-0.994316E-02

-0. 83523BE-02

-0.153748E-01

-0.139349E-01

-0. 207157E-01

-0.19483BE-01

-0.257127E-01

-0.247407E-01

-0.301474E-01

-0.294772E-01

-0.338318E-01

-0.33495OE-01

-0.367729E-01

-0.366928E-01

0.OOOOOOE+OO

0.126667E-02

0.947002E-03

-O.149437E-02

-0.546333E-02

Y-DISPLACEMENT

Cm)

0.OOOOOOE+OO

0.OOOOOOE+OO

-0.772501E-03

0. 9490HE-03

-0.104837E-02

0.13S443E-02

-0.150028E-02

0.208793E-02

-0.154360E-02

O. 232B94E-02

-0. 172786E-02

0.276156E-02

-0.16572BE-02

0. 285470E-02

-0.168189E-02

0.302587E-02

-0.165033E-02

0.303703E-02

0.OOOOOOE+OO

0.244951E-03

0.803281E-03

0.110448E-02

O. 119501E-02

Z-DISPLACEMENT

(m)

0.OOOOOOE+OO

O.OOOOOOE+OO

-O.103527E-01

0.759707E-02

-0.1S3507E-01

0.169114E-01

-0.266111E-01

0.277390E-01

-0.323614E-01

'O. 362B05E-Q1

-0.37B639E-01

0.443091E-0!

-0.410935E-01

0.507422E-01

-0:427522E-01

.0/554845E-01

-b:424795E-01

0. 576O13E-01

0. OOOOOOE+OO

0.833276E-04

0.1B1189E-02

0. 430477E-02

O.663736E-02

C3
MOD E SHAP E NO .

NODE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

X-DISPLACEHENT

0.OOOOOGE+OO

0.OOOOOOE+00

0.713473E-04

0.674043E-03

0.373437E-02

0. 421684E-02

0. 106270E-01

0. 109240E-01

0.200766E-01

0.201822E-01

0.315174E-01

0.314595E-01

0.441560E-01

0. 440107E-01

0. 573343E-01

0.572487E-01

0. 705719E-01

0.705205E-01

0. OOOOOOE+00

0. 257961E-02

0. 209115E-01

0. 463564E-01

0. 737344E-01

Y-DISPLACEMENT

0.

0.

0.

•0.

0.

-0.

0.

-0.

O.

-0.

O.

-0.

0.

-0.

0.

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-0.

0.

0.

0.

0.

0.

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OOOOOOE+00

306364E-02

29207 1E-02

629080E-02

602280E-02

B18425E-02

784455E-02

101177E-01

976258E-02

109587E-01

1062BOE-01

117355E-01

114681E-01

118775E-01

116651E-O1

119601E-01

117829E-01

OOOOOOE+00

363762E-04

140947E-03

219779E-03

250957E-03

Z-DISPLACEMENT

0.

0.

-0.

0.

-O.

0.

-0.

0.

-0.

0.

-0.

0.

-0.

0.

-0.

0.

-0.

0.

0.

-0.

-0.

-0.

O.

(m)

OOOOOOE+00

OOOOOOE+00

441225E-02

333223E-02

143028E-01

130606E-01

1S2236E-01

173456E-01

240926E-01

234662E-01

261447E-01

26029 5E-01

27B8B2E-01

283251E-01

283387E-01

292743E-01

27B580E-01

292883E-01

OOOOOOE+00

11 1490E-04

176610E-03

107262E-03

345158E-03

C4
M 0 D E

NODE

1

2

3

4

5

b

7

3

9

10

U

12

13

14

15

li>

17

IB

19

20

21

SHAP E NO .

X-DISPLACEMENT

0.OOOOOOE+00

0.OOOOOOE+00

-0. 118293E-01

-O.791935E-O2

-0.206904E-01

-0.1B3101E-01

-0.225369E-01

-0.223974E-01

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-0.20107&E-01

-0.836442E-02

-0.119222E-01

0. 2S5589E-02

-0.964885E-03

0.112822E-01

0. 847680E-02

0. 148S05E-01

0. 13767SE-01

0. OOOOOOE+00

0. 272549E-02

0. 197013E-02

-0. 568Q60E-02

-O. 133754E-01

Y-DISPLACEMENT

(m)

0.OOOOOOE+00

0.OOOOOOE+00

O. 441397E-03

O. 261908E-02

0. 180931E-02

0. 390346E-02

O.112010E-02

0.287947E-02

-0. 124705E-03

0. 160755E-02

-0.105166E-02

-0. 111030E-02

-O.329085E-02

-O. 268947E-02

-0. 353977E-02

-0.410951E-02

-0.416646E-O2

-0.445011E-02

0.OOOOOOE+00

-0.126421E-02

-0.66S200E-03

0.44ia48E-02

0.748992E-02

Z-DISPLACEMENT

(m) 0.OOOOOOE+00

O.OOOOOOE+00

-0.295790E-01

O.155319E-01

-0.539089E-01

0. 2O1317E-01

-O.732905E-01

0.142023E-01

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0.OOOOOOE+00

-0.341730E-02

-0. 2S5294E-01

-0.257615E-01

0.136821E-01

C5
MOD E

'NODE

1

2

3

4

5

6

7

8

9

10

11

. 12

13

14

15

16

17

18

19

20

21

22

23

SHAP E N O

X-DISPLACEMENT

(m)

0. OOOOOOE+OO

O. OOOOOOE+OO

-0. 740B95E-02

-0. 465305E-02

-O. 119491E-01

-0. 110113E-01

-0. 133983E-01

-0. 14730SE-01

-0. 100000E-01

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-O. 384156E-02

-0. 759716E-02

0. 243364E-02

-0. 548109E-03

0. 670&66E-03

0. 576923E-02

0. 754456E-02

0. 7920S4E-O2

0. OOOOOOE+OO

0. 219309E-02

0. 226409E-02

-0. 276079E-O2

-0. 79B365E-02

Y-DISPLACEMENT

(m)

0. OOOOOOE+OO

0. OOOOOOE+OO

-0. 193822E-02

-0. 38&B07E-03

-0. 3149fc9E-02

-0. 175838E-02

-0. 135955E-02

-0. 124683E-03

0. 101767E-03

0. 128244E-02

0. 253723E-02

0. 25278&E-02

0. 406377E-0.2

0. 451150E-02

0. 464329E-02

0. 431497E-02

0. 492322E-02

0. 47B836E-02

0. OOOOOOE+OO

0. 24i437E-02

0. 21B726E-02

-0. 663630E-02

-O. 122341E-01

Z-DISPLACEMEN1

(m)

• 0. OOOOOOE+OO

0. OOOOOOE+OO

-O. 114B97E-01

0. 180550E-01

-0. 29914BE-O3

0. 495228E-OJ

0. 159037E-01

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0. 317050E-01

0. 729169E-01

0. 343307E-01

0. 449592E-01

0. 241522E-01

O. 1 19253E-02 |

-0-: 123777E-02

70,.523283E-01

-0. 339619E-01

-0. 909267E-01

0. OOOOOOE+OO

0. 556466E-02

0. 425604E-01

0. 35055BE-01J

-0. 266987E-01I

C6
MOD E

NODE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

SHAP E NO .

/-DISPLACEMENT

(m) 0.OOOOOOE+0 3000^ 0

0. OOOOOOE+00

0.179142E-01

0.127481E-01

0.179519E-O1

0.203398E-01

-0.478622E-03

0.735046E-02

-O.211341E-01

-0.146677E-01

-0.250002E-01

-0.259456E-01

-0.839329E-02

-0.157965E-01

0.143037E-01

76357CE-Q2

260144E-01

240778E-01

0. OOOOOOE+00

-0.765519E-02

-0.&40714E-02

0.351336E-02

-0.490301E-02

0.

0.

0.

Y-DISPLACEMENT Z-DISPLACEMENT

'ml

0. OOOOOOE>00

0. OOOOOOE+00

0. 578430E-03

0. 166696E-02

0. 160232E-02

0. 898937E-03

O. 143147E-02

0. 830753E-03

0. 141467E-02

0. 66301SE-03

0. 277679E-02

0. 754469E-03

0. 255004E-02

0. 219280E-03

0. 302492E-02

0. 310299E-02

0. 216044E-02

0. 329176E-02

0. OOOOOOE+00

0. 893652E-04

0. 122530E-03

0. 549047E-04

0. 10261BE-02

0.

0.

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513244E-01

507512E-01

1572S6E-01 .

215115E-01

355442E-01

286181E-01

528006E-01

568674E-01

165509E-01

279033E-01

301B68E-01

299603E-01

471128E-01

581795E-01

OOOOOOE+00

450307E-03

414219E-02

104547E-02

564044E-02

C7
MOD E

NODE

1

*•>

3

4

5

6

7

8

V

10

11

, 12

13

14

15

16

17

18

19

20

21

SHAP E NO .

X-DISPLACEMENT

(m)

DCOO^

Y-DISPLACEMENT

0.OOOOOOE+00

O.OOOOOOE+00

-O. 834984E-02

-0.782959E-O2

0.203419E-O2

-0.628708E-O2

0. 126427E-01

0. 577384E-02

0. 596501E-02

B78313E-02

7S0029E-02

152336E-03

-0.108919E-01

-0.86148&E-02

186423E-02

32.0593E-02

129668E-01

833935E-02

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533028E-02

433125E-03

331049E-02

0.

-0.

-0.

0.

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0.

0.

0.

0.

0.

O.

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IOOOE

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0. OOOOOOE+00

0. OOOOOOE+OO

-0. 230507E-02

-0. 769967E-03

-O. 485383E-O2

-O. 3190O1E-02

-O. 324263E-02

-0.194406E-O2

-0.115129E-02

0. 439514E-03

-0.530925E-02

-0. 248452E-02

-0.896972E-02

-0.671721E-02

-0.109679E-01

-O.104715E-01

-0.137495E-01

-0.124872E-01

0.OOOOOOE+00

0. 152446E-02

-0.935S52E-02

-0.9133S7E-02

0.544324E-02

Z-DISPLACEMENTI

(m) !

0. OOOOOOE+00:

O. OOOOOOE+OOj

-0. 1O3454E-01I

0. 437823E-01j

0. 443433E-01

O. 655859E-01

0.704248E-01

0.350316E-01

0. 135543E-01

-0.989655E-02

-0. 5S5667E-01,

-0.291764E-01

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-0.163933E-01

0. 11 1073E-01

0.'-245510E-02

"0. 802758E-01

0. 200699E-01

0.OOOOOOE+001

0. 148432E-OJ i

0.394274E-01'

-0.311272E-01;

0.143645E-02

C8
MOD E

NODE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

13

19

20

21

H A P E NO.

X-DISPLACEMENT Y-DISPLACEMENT Z-DISPLACEMENT

0.

0.

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234380E-01

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194055E-01

6&4518E-02

33262SE-02

314791E-03

713714E-02

1S5637E-01 '

13B591E-01

149968E-01

203356E-01

994360E-02

305799E-02

26929SE-01

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507007E-02

192497E-01

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332716E-03

291473E-02

158760E-02

764740E-02

181352E-02

130743E-01

214S14E-02

156764E-01

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540037E-02

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0.

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292793E-01

711673E-01

266663E-01

458577E-01 '

21366OE-02.

375966E-01

102005E-01

617225E-01

577429E-02

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169923E-02

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732922E-02

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190895E-01

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C9
MOD E SHAP E MO .

NODE

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

X-DISPLACEMENT

Cm) 0.OOOOOOE+00

0.OOOOGOE+QO

-0. 112354E-01

-0. 578946E-02

-0.339855E-01

-0. 274014E-01

-0.4S3409E-01

-0.464343E-01

-0. 450766E-01

-0. 472901E-01

-0.264977E-O1

-0.259Ba7E-Ol

-0.126324E-01

-0.848345E-02

0. 159840E-01

0.150061E-01

0. 539696E-01

0. 517092E-01

0. OOOOOOE+00

-0.185978E-01

-0. 537126E-01

-0. 452300E-01

0.257623E-01

Y-DISPLACEMENT

(ml

0.OOOOOOE+00

0. OOOOOOE+00

-0.331019E-02

0.432406E-02

-0. 443O40E-02

0.776B85E-02

O. 412559E-02

O.373654E-02

0. 129816E-01

-0. 207312E-02

0.2138SOE-01

-0.118462E-01

0.29S304E-01

-0.200009E-01

0.326494E-01

-0..231487E-01

0. 333014E-01

-0.255941E-01

0.OOOOOOE+00

O.153045E-02

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0.304446E-02

0.823337E-02

Z-DISBLACEMENT

(ml I

0. OOOOOOE+00 '

0.OOOOOOE+00

0. 163490E-01

-O.264350E-01

0.107345E-01

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0.254874E-01

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0.153&52E-01

0.306101E-03

0.348512E-01

-0.45&994E-01

-0.156999E-01

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-0. 205616E-01J

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0. 175450E-02'

0.260583E-01:

0.OOOOOOE+OO,

0. 600096E-03:

0. 11532SE-01:

-0. 399&93E-02;

0.147763E-03

CIO
MOD E

NODE

3

'4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

SHAP E NO . 10

X-DISPLACEMENT

0.

0.

-0.

-0.

(m)

OOOOOOE+0OOE-t 0

OOOOOOE+00

146228E-O1

144201E-01

0. 353514E-02

-0. 541648E-02

-0.376248E-02

0.439690E-02

-0.300489E-01

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-0. 183943E-01

0.22B116E-01

0. 1B2919E-01

0. 392054E-02

0.160286E-01

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0. OOOOOOE+00

0. 329564E-02

-0. 188692E-01

-0.501107E-02

0.6311O5E-02

Y-DISPLACEMENT

(m)

0.OOOOOOE+00

0.OOOOOOE+00

-O.332774E-02

0. 5431B&E-03

-0.851627E-02

-0.180959E-02

-0.970295E-02

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0.OOOOOOE+00

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Z-DISPLACEMENT

(m)

0.OOOOOOE+00

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-O.328957E-01

0.469168E-01

0.436372E-01

0.970471E-02

0.332324E-01

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0. 635397E-01

0. OOOOOOE+00

O. 560990E-02

-0.467254E-03

-0.465713E-02

O.450445E-02

I

cn
APPENDIX D

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OF POOR QUALITY

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POOR QUALITY

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