A Reproduced (~opy€¦ · NASA-CR-173215 19840008497 A Reproduced (~opy OF ;Y!l5/l CR-'/73 J 2...
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NASA-CR-173215 19840008497 A Reproduced OF ;Y!l5/l CR-'/73 J 2 .. .. ------ Reproduced for NASA by the NIASA Scientific and Technical Facility :( 111111111111111111111111111111111111111111111 NF01450 FFNo 672 Aug 65 i ANGLF:Y .1.1\11 dl' "11\:';/\ HPt!I'.PfON, ViI<GINIA https://ntrs.nasa.gov/search.jsp?R=19840008497 2020-04-18T14:56:11+00:00Z
Transcript of A Reproduced (~opy€¦ · NASA-CR-173215 19840008497 A Reproduced (~opy OF ;Y!l5/l CR-'/73 J 2...
NASA-CR-173215 19840008497
A Reproduced (~opy OF
;Y!l5/l CR-'/73 J 2 ~/S-' .. -,-.~ .. ------
Reproduced for NASA
by the
NIASA Scientific and Technical ~nformation Facility ~) :(
111111111111111111111111111111111111111111111 NF01450
FFNo 672 Aug 65
i ANGLF:Y Rr'~;r/\W'" .1.1\11 dl' LlBi~MIV "11\:';/\
HPt!I'.PfON, ViI<GINIA
https://ntrs.nasa.gov/search.jsp?R=19840008497 2020-04-18T14:56:11+00:00Z
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CSd. 131
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DEPARTMENT OF HECJ:1ANICAl. 1,~NmNgERr.NG AND HeCHANICS SCHOOL OF rmGmE!~I:UNG OLD DOMINION UNXV'i!;1UHTY NORPOLR. VIRGINIA
SELF-SHADOHING OF ORB!TING TRUSSES
By
Jack Mah~ney
and
Earl A. Thornton, Principal Invest igator
Progress R~port I?or the period end ing Hay 15t 1983
Pr.epared for the National Aeronautics and Space Administration Langley Renellrch Center Hsmpton, Virginia
Under Research Grant. NAGl-257 L. liernard Garrett. Technical M:lnitor Space Systems Division
Submitted by th~!
Old Dominion University ReIJct1rch Foundation P.O. Eox 6369 Norfolk. ~irgiuia 23508
Augu.st 1983
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SEU~-SUADownm OF OREITING TRUSSES
By
SUHHARY
Ptlrpose Determine nhadowing reductions on hattting of orbiting trusses
Detennination of heating ratea \'lith Illeuder member shadowing effel:t:s included
TIlennal response of shadowed member
Analysis ~~proach
1. I)etermine shado~ring
2. Heating analysis
J. Thcl.lIIal analysis
4. Structural analysis
1 Graduate Msist:/mt. Department of ~12ch[mical Engineering and Milchanics. Old Dominion Univm:eity, Nor.folk, Virginia 23508.
2 ASBocint(! PrOf;!S8or. Department of Hechauical Engineering and HBdwuicB. Old Dominion University, Norfolk, Virginia 23508.
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FINITE ELE~~~ENT THERivlAL-STRUCTURAL ANALYSIS
OF CABLE 5PACE STRUCTURES
41' ANALYSIS INCLUDES:
( a) CABLE PRESTRESS
( b) APPLIED SURfACE HEATING
(c) NONliNEAR TRANSIENT THERMAL ANALYSiS
( d) NONl\ NEAR LARGE DEFORMATION STRUCTURAL ANALYSIS
~ HOO? COLUMN EXAMPLE. IS USED TO DEMONSTRATE. THE. ANAL'fSIS .
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APPROACHES:
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INVESTiGATE THREE. AF'PROACHES FOR. THERMAL-
STRUCTURAL ANALYSIS Of CABLE STlffENE.D
SPACE STRUCTURES.
(0 LINEAR SMALL DISPLACEMENT STRUCTURAL
ANALYSIS WITH PRETENSION.
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(2) liNEAR" STRESS -STIFFENING SMALL
DISPLACEMENT STRUCTURAL ANALYStS.
j (3) NON-LINEAR LARGE. DlSPLACEME.NT STRUCTURAL
ANALYS!S WiTH PRETENSION •
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ANALYSIS PROCEDURE~
HEATING RAT£ ANAl~-~IS-1
ELEMENT
HEATING
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PRETENSION ANAL '(SIS THERMAL ANALYSIS
PRETENSIONS
LARGE DEfORMATION
STRUCTURAL ANALYSIS
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LARGE DEFORMATION CABLE ANALYSIS
,. ~TRA1N - DISPLACEMENT RELATION ~ G
E = 2
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NONLINEAR TERM
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G FINITE ELE.ME.NT FORMULATION j
ESTABLiSH ELASTiC STRAIN E.NERGY EXFRESSION
PERFORM MINIMIZATION WRT. NODAL DISPLACEMENTS
10 OBTAIN F.E.. E.QS. IN THE. FORM:
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LOADS - f'~E.TENS10N EFfECT
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SOLVE. THE. ABOVE. NONLlNE.AR EQS. USING ITERATIVE TECHNIQUE ~g
( NEWTON - RAPHSON ITERATION). "'titS 0::;; o~ A1,-. .0..., C):!, Pl,;) !:Tl1 -' ..... -<~
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CABLE ELEMENTS WITl; THERMAL STRAH'\j Af\lD PRE STRESS
STRESS
t 4> 5TRESS- STRAIN RELATION:
cr =-- E" (€. - Eo) -t 0-0 T f7
WHERE Eo - TH e: RMAL STRAIN
era - PRe: -STRESS
DO I' r I l I • I I I
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.. DER~VA"'ON OF F. E· £QS.';
- ESTABL\SH ELASTiC STRAIN ENERGY
u "" ~ J (?-- ~)l£- e .. ) &v -+ J 00 E dv V ~
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_EXPRE.SS STRA1N €. IN TERMS OF DISPLAC.EMENTS
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e ::STRAI N::: \..\3. -UI L-
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TI1ERt-'i'\L STRAIN PReSTRESS
'---- .-/ T-"
~Ot)AL_ LoADS
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CABLE ELEf·v1ENT V'JiTH THERMAL STRAiN AND
~ SOLUTiON M;::'TWf':,!". .. .,._ .. 'I ~ ....... ,..,
_ APPLY NEWTON -RAPHsoN ALGORITHM TO OBTAIN EQS.
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THEg~.rLA.L -STRUCTURAL ANALYSIS OF HOOP COLUMN
(IDEALIZED 2-D MODEL)
i:
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I CAeLE
. (QUARTZ)
82 m. V COLUMN (G.dar)
N \D
t ! I I i !
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PRETE.NSION ANALYSIS
e USING A COMPUTE.? CODE DEVELOPE.!? J CABLE. PRETE.NSIONS A ....... I'\Kt=. COMPUTED
W N
,.
SUCH THAT THE STRUCTURE. IS IN:
REQUIRED GE.OMETRY
EQUILIBRIUM
e CAf)LE PR.ETE.NSIONS OBTAINED ARE. TRANSfE.RRE'.P DiRECTLY TO THE
LARGE. DEFORMATION STRUCTURAL ANALYSIS PROGRAM (AS· PRETENSio'N<><
E.FFECT ) WHICH WILL BE INCLUDED IN THE. FiNAL DISPLACE.MENT AND
STRE.SS COMPUTATiONS.
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TYPICAL RESULT OF CABLE PRETENSiONS
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i!
t 362.5 N "> or 11: ••
( 13.2. E6 N/m2.) <::; 2 jC~r.
poX
\.- 199.7 N t ~ ., Ib.
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RESULT Of CABLE PRETENSIONS
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ELEMENT ('CRCE
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f 141
.2 152
3 170
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4-
I 200
.5 452
6 43
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a I .33 ...
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10 140
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12 -511
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STRESS •. ; :2. lN/m}
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HEATING RATE 'ANALYSIS
~ HEAT SOURCES INCLUDE j
SOLAR
EARTH EMI.5SION
EA.RTH ALBEDO
~ ELEME.NT HEATING RATES ARE COMPUTE.D AT DifFERENT ORaiTAL POSITIONS
FOR AN ORBIT.
() THESE ELE.MENT HEATING RATES ARE TRANSFE.RRED DIRECTLY TO THE.
THERMAL ANALYSIS PROGRAM fOR COMPUTATION OF ELEMENT TEMPERATURE
RESPONSES.
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TYPICAL CABLE 5URFACE HEATING RATES
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HEATING ==
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OR.BITAL POSITION ~) DEGREES W 0\
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THERMAL ANALYSiS
o ASSUME. ISOTHE.RMAL ELEMENT TEMPERATURES.
• ANALYSIS (NONLlNE.AR TRANS1E.NT) INCLUDE.S:
APPLIED SURfACE HEATING
SURFAC.e. RAD!ATION TO SPACE
00 -":A5 -oS 02 OJ;,'> AIr'" .()"'O C";P ~::> 0 C~
::!w
e ELEMENT TEMPE.RATURE-S ARE COMPUTED AT DIfFERENT ORt'>\TAL PosnlOI\lS
FOR AN ORBIT.
e ELEMENT TEMPE.RATURES ARE. TRANSFERRE.D TO THE LARGE. . DEFORMATiON
oN ....,
STRUCTURAL ANALYSIS PROGRAM (AS THERMAL EFFECT) fOR
DISPLACEME.NT AND STR.ESS COMPUTATIONS.
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STRUCTURAL ANAL'l'SIS
o ANALYSIS INCLUDES:
LARGE DEfORMATION (NONLI NEAR)
THERMAL EfFECT
PRE.TE.NSION EFFECT
o DISPLACEMENTS AND STRESSE.S ARE. COMPUTED AT DIFfERENT
ORBITAL pOSiTIONS FOR. AN ORf)IT ( QUASI - STATIC)
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PLANS:
& COMPLETE DEVELOPMENT OF PRETENSION PROGRAM.
e PERFORM 2-D HOOP COLUMN MODEL WITH:
(0 LINEAR ANALYSIS .. ,t
(2.) LlNE.AR STRESS - STI FfENING ANALYSIS
o PE.RfORM .3-D HOOP COLUMN MODEL WITH:
(1) LINEAR ANALYSIS
(V " u LINEAR STRESS - STIFFENING ANALYSIS
(3) NON-LINEAR ANAL '(SIS
G MEMBRANE. r-.FFECTS (?)
:-":··~·~:·~~!:c~·~:··: ~.:~~
THERMAL ANALYSIS
STRUC.TURAL ANALYSIS
:; ~
(ANS'($ )
" ? ,l4 .>'- \.:
End of Document
