NASA Technical Reports Server (NTRS) 20030002752: Dynamics of a 4x6-Meter Thin Film Elliptical Inflated Membrane for Space Applications

6 Pages·0.49 MB·English

by  NASA Technical Reports Server (NTRS)

AIAA-2002- _s'_7
DYNAMICS OF A 4x6-METER THIN FILM ELLIPTICAL INFLATED MEMBRANE
FOR SPACE APPLICATIONS
Matthew J. Casianot Hamid R. Hamidzadeh$
Fluid Physics and Dynamics Group/TD63 South Dakota St. University
Subsystem and Component Development Dept. Mechanical Engineering Department
NASA Marshall Space Flight Center Brookings, South Dakota
Huntsville, AL 35812
Michael L. Tinker*
Structural Dynamics and Loads Group/ED21
Structures, Mechanics, and Thermal Department
NASA Marshall Space Flight Center
Huntsville, AL 35812
Abstract Introduction and Background
Inflatable structures have been the subject of renewed
Dynamic characterization of a thin film inflatable
elliptical structure is described in detail. A two-step finite interest in recent years for space applications such as
element modeling approach in VISC/NASTRAN is communications antennas, solar thermal propulsion, and
utilized, consisting of (1) a nonlinear static pressurization space solar power (Figs. I-2). A major advantage of
procedure used to obtain the updated stiffness matrix, and using inflatable structures in space is their extremely light
(2) a modal "restart" eigen solution that uses the modified weight. An obvious second advantage is on-orbit
stiffness matrix. deployability and subsequent space savings in the launch
Unique problems encountered in modeling of this large configuration. A recent technology demonstrator flight
for inflatable structures was the Inflatable Antenna
4x6-meter lightweight inflatable arc identified, including
considerable difficulty in obtaining convergence in the Experiment (IAE) that was deployed on orbit from the
nonlinear finite element pressurization solution. It was Shuttle Orbiter. Although difficulty was encountered in
found that the extremely thin pol¢imide film material the inflation/deployment phase, the flight was successful
(.001 in or I mil) presents trerrendous problems in overall and provided valuable experience in the use of such
obtaining a converged solution when internal pressure structures (Ref. 1).
The Solar Orbital Transfer Vehicle (SOTV), discussed
loading is applied. Approaches utilized to overcome these
difficulties are described. in Ref. 2, and Solar Thermal Upper Stage (STUS),
Comparison of finite element predictions for frequency described in Refs. 3-5, are possible technology
and mode shapes of the inflated structure with closed-form demonstrator flights for solar thermal propulsion. The
solutions for a flat pre-tensionec_ membrane indicate basic concept behind solar thermal propulsion is to utilize
reasonable agreement. sunlight or solar energy as a means of heating a working
fluid (propellant) to provide thrust at increased specific
impulse. As described in Ref. 6, thrust is produced by
expanding the heated propellant through a nozzle. No
combustion occurs, and the thrust level is low. For this
reason, solar thermal propulsive systems are mainly
tAerospace Technologist,
applicable for orbital transfer vehicles. The engine system
_Professor of Mechanical Engi_leering; Fellow
envisioned for the STUS is designed to utilize hydrogen
ASME
propellant to produce a thrust level of about 2 lbf. Two
*Structural Dynamics Lead Engineer; Associate
inflatable parabolic collectors could be used that would be
Fellow AIAA
rotated and gimbaled for focusing sunlight into an
absorber cavity (Fig. i, from Ref. 5). The collectors
Copyright O 2002 by theAmerican institute of Aeronautics would be inflated after separation of the upper stage from
the launch vehicle.
and Astronautics, Inc. No copyright is asserted in the United
States under Title 17, U.S. Code. The J.S. government has a Many investigators have considered the use of
royalty-free license to exercise all rigl_ts under the copyright inflatable structures for space applications. Perhaps the
claimed herein for Governmental purl:oses. All other rights earliest was Frei Otto (Ref. 7), who in 1962 published
are reserved by the copyright owner. ideas for inflated tubular frames for use in structures such
as orbiting platforms. A more recent proposed application
involves the use of inflatable beam segments to replace
i
American Institute of Aeronautics and Astronautics
solidsegmenotsftheSpaceShuttleremotemanipulator
systemandthusreducsetoragsepacaendinertiaoftheann
(Ref.8).
Modeling Approach and Results
Severaplaperosnstaticstructuraalnalysiosfinflated
cylinderhsavebeenwrittend,escribindgifferentetchniques
The finite element modeling technique involved two
suchaslineasrhelltheorya,ndnonlineaarndvariational
main steps: 1. Nonlinear static analysis, in which the
method(Rsefs.9-17)b, utverylittleworkhadbeendone
internal pressure loading was applied to the lenticular
indynamicosfinflatablsetructureusntilrecenytears.In
element and a pretension applied to the catenaries, and 2.
1988Leonar(dRef.18)indicatetdhatelastibceambending
modal analysis utilizing the results of step 1. Such a
modescouldbeutilizedin approximatinlogwer-order
procedure is needed due to the impossibility of active
frequencioefsinflatablbeeamsM. ain,etal.wroteavery
forces in an eigensolution. In step 1, the stiffness matrix
significan1t995papedrescribinrgesultsofmodatlestsof
inflatecdantilevebreamasndthedeterminatioofneffective of the model is updated to capture the tensioning of the
thin film material caused by internal pressure. This two-
materiaplropertie(sRef.19). Changesin material
step modeling and analysis methodology is described in
propertiefosrdifferenptressurewserealsodiscusseadn,d
detail in Ref. 29, where results are given for inflatable
thebeammodewl asusedin amorecomplexstructure.
cylindrical beams.
Thepapedremonstrattheadtconventionfainliteelement
The lenticular film was modeled using NASTRAN
analysipsackagecosuldbeveryusefuilntheanalysiosf
quadrilateral plate elements, each of which were .001 in.
compleixnflatablsetructuresR.eferenc2e0describeasn
(1-mil) thick. Modulus, density, and Poisson's ratio as
investigatioonf thedynamicosf polyimidethin-film
used were provided by the film manufacturers. The CP-I
inflatecdylindersa,ndRefs.21-29discusrsecendtynamic
tests/analyasensdpotentiaalpplicationosfinflatablseolar film has E=300 ksi, v=0.34, and 9=0.0518 Ibm/in 3. An
concentrators. internal pressure of 0.03 in. H20 (.00108 psig) was
applied to the lenticular element.
Modeling of the catenaries was done using silicon rod
Description of Inflatable elements under a temperature load. The suggested
temperature-loading pretension method was verified by
Concentrator Investigated in the
comparing stress results to a rod with an applied force.
Current Study
The Aluminum-5052 test fixture was also modeled
using quadrilateral plate elements. The section of the
In Fig. 3, a prototype elliptical, off-axis paraboloid aluminum plate with 3600 holes was modeled by altering
4x6-meter inflatable concentrator manufactured by SRS the thickness accordingly to account for the adjusted
Technologies, Inc. is shown that consists of a pressurized density.
lenticular supported by an aluminum fixture. The The steel I-beam stands were modeled using beam
aluminum fixture will be supported by four I-beam stands elements and multipoint constraints. A modal test was
for testing in a horizontal configuration. The inflatable is performed on a stand that was supported on three feet.
attached to the fixture by 204 silicon catenaries. The The stands in the finite element model were cantileavered
lenticular has a 226-in. major axis and a 164.08-in minor but were created with modes and mode shapes equivalent
axis. This collector can function as a space-based antenna to that of the tested stand. Multipoint constraints were
for communications, surveillance, and radiometry, or as a used to define a plate-sectioned rigid body in the place
solar concentrator assembly for solar thermal propulsion where the stand would be secured to the aluminum fixture.
systems. The inflatable lenticular element is constructed Fig. 4. shows the integrated finite element model.
of NASA Langley Research Center's CP-1 which is .001 Several parameter studies were performed to help
in (1 mil) thick. Silicon-backed Kapton is the adhesive diagnose problems and to aid in understanding of the
used for joints in the inflatable structures. A reflective solutions. Mode shapes and frequencies were compared
coating on the inner lenticular CP-I film provides the while varying thickness, geometry, and material. Studies
means of collecting radio waves or solar energy. It is were also made on the effect of an induced strain or applied
noted that the particular application for the pressure. Drastic effects on mode shapes and frequencies
antenna/concentrator depends on the surface accuracy of the would appear by changing only the geometry from
reflective lenticular surface. Use as an optical system elliptical-shaped to paraboloid-shaped. The introduction of
would require greater surface accuracy than a solar curvature into the problem would not only affect system
concentrator for propulsion systems, for example. dynamics but also drastically increase computation time of
In the case of solar thermal propulsion applications the nonlinear static solution. It is interesting to point out
(Fig. 1), the collector assembly would locus sunlight into that the strain of the paraboloid geometry (while averaging
an absorber or secondary concentrator near the fixed ends about 0.03%) did have a varying value across the
of the struts. Solar energy stored in the absorber could be membrane due to the applied pressure. The flat elliptical
utilized to heat a propellant and generate thrust as model had an induced uniform strain of 0.03%. But when
described previously. a pressure was applied to the flat elliptical membrane
Inflatable structures in general are extremely giving a much greater and varying strain, the mode shapes
lightweight and the collector described in this paper is no were identical indicating that the mode shapes seem to be
exception. The thin-film inflatable part of the a function of geometry. The frequencies were not the
concentrator weighs approximately 3lb. same in this case. Ref. 30 shows that sag has played an
American Institute of Aeronautics and Astronautics
interestinrgolein cablesandcabk:trussesasshown. and then modeled in NASTRAN using this technique.
Fundamenntaalturaflrequencioefs,:ableswitha small Results of another finite element analysis for this test
amounotfsagcanbeasmuchas300%morethanthose were replicated. A strain of 0.2% due to dry shrinkage and
of a straighctable. Similarbehaviomr ayoccurin other effects was found by comparing the test data with
membranes. the model results.
Thegreatesdtifficultyencounteriendmodelingand A finite element model of the 4x6-meter inflatable
analysiwsasobtainincgonvergenocfethenonlineasrtatic membrane was modified (converted to a flat 2-D ellipse)
pressurizatiosnolutionin MSC/NASTRAN. This and re-analyzed in MSC/NASTRAN. In this analysis, the
difficultyisduetotheextremetlyhinpolyimidme aterial support stand and ring fixture were not included in the
ofwhichtheinflatablceomponenatrseconstruct(eIdmil model to allow a focus on the critical aspects of the
or1/1000ofoneinch).Theratios_)ffilmthicknestso modeling process and to allow comparison to closed form
overallgeometridcimensionssuchas lenticularaxes solutions. The pressure load was replaced by a uniform
appeatro bethecriticalparameteirns thenonlinear temperature-induced strain. The catenaries were also
pressurizatiaonnalysisF. orexampleit, wasfoundthat removed and the perimeter of the ellipse was fixed in all
increasintghefilm thicknestso 1__milsor 1/100in. directions. Hamidzadeh's closed-form solution had the
resulteidnsolutiontshatconvergeedasilyT. hereasofnor following conditions: flat elliptical membrane, zero
thisphenomenaopnpeartosbethatextremetlyhinfilms displacement on the boundary, uniform strain, and CP-I
tendto havelargedisplacemenatnsdlargestiffness properties. A nonlinear static analysis followed by a
changewshenpressurleoadingis _pplied.Obviously, modal 'restart' was performed for this model as well.
increasetdhicknessreducesthe magnitudeof these The results are summarized in Table 2. The closed
changesA.notheirssuein modecl,mvergenwcaesfine- form solution compared well with the NASTRAN
tuningtheNASTRANparamete'_rdiag'. A valueof solution. The mode shapes were identical and the
'kdiagh' elpsconvergenbcyeinitiallyaddinagsmalvl alue frequencies were on target. Slight differences in the
tothestiffnesms atrixdiagonatelrmsandthenis later frequencies can be attributed to approximate values for the
removedW. iththisassistancthee,r,w_"asconvergenocfe Mathieu functions in the closed form solutions and slight
iterationsearlyon thatnormallywouldhavetrouble geometric discrepancies in the NASTRAN model. A
converging.Thevalueof 'kdi_g'wascontinually polynomial expansion for the Mathieu functions and
decreasuendtil successivreesultswouldhavesimilar modified Mathieu functions were used in calculating
solutionsindicatinngonecessafriyirtherchangein the natural frequencies. The geometric dimensions in the
parameter. NASTRAN model were slightly different then the design
After all the difficulties encounte-ed in this modeling dimensions because the geometry followed that of the
and analysis effort, it was satisfying to obtain reasonable fabricated prototype.
results. The first natural frequency o__the integrated model
was 7.87 Hz, and the mode shape was characterized by an
Summary
up-and-down bobbing of the inflatable through the ring
fixture as shown in Fig. 5. With the: exception of the 4tn
mode, the first seven modes exhibit rigid-body type modes Modeling of a large 4x6-m thin-film inflatable
due to the 204 catenaries that connec_ the inflatable to the concentrator structure has been accomplished.
fixture. Another example of these r_gid-body type modes Comparisons with modal tests will be made at a later
is shown in Fig. 6. These types of modes have time. This work is significant because of (!) general
frequencies not equal to zero but d_splay motion in the difficulty in accurately representing the nonlinear material
directions of rigid body modes. A breathing mode of the and geometric characteristics of these structures, (2) the
entire inflatable occurs at 9.82 Hz, which is the 4th mode. large size of this thin-film structure, and most
The next system mode excluding the -igid-body type mode importantly, (3) the accomplishment of a modeling
(mode 8) occurs at 13.44 Hz characterized as a 2_-order methodology that realistically represents the internal
breathing mode with node line aloJ_g major axis of the pressure loading and the stiffness properties of the thin
inflatable. Table 1 shows some modes of the entire films in a modal solution.
system. Some interesting curvature effects on the mode It was shown that many workarounds were required to
shape are apparent in mode 9(13.98 Hz), Fig. 7. Coupled obtain convergence of the nonlinear static pressurization
support structure and inflatable structure modes were seen procedure in MSC/NASTRAN. In this regard,
for the first time at 26.15 Hz (mode :_0)shown in Fig. 8. MSC/NASTRAN was found to have limitations in its
nonlinear analysis capability, particularly for large thin-
film structures of the type investigated in this paper. The
Comparison of Finite Element Results to use of ABAQUS or other finite element packages should
Closed-Form Solutions also be considered for inflatable structures.
The suggested method of applying a uniform strain to
the membrane or a pretension to the _:atenaries is by using Acknowledgments
a change in temperature. This method was verified by
comparing a catenary in strain to a catenary with an SRS Technologies is acknowledged for design and
applied force. A 17.5-inch diameter membrane was tested construction of the 4x6-m structure. Jennie McGee
American Institute of Aeronautics and Astronautics
providegdeometraicndparametienrformationneedefodr
16. Webber, J.P.H., "Deflections of Inflated
modelinogfthestructure.
Cylindrical Cantilever Beams Subjected to Bending and
JohnLassitearndRoberEtngberogfMarshaSllpace
Torsion", Aeronautical Journal 86(858), pp. 306-312,
FlightCenter'Sstructur&alDynamicTsestingGroup
1982.
provideidmportanmtodatlesdt ata.
17. Main, J.A., Peterson, S.W., and Strauss, A.M.,
"Load-Deflection Behavior of Space-Based Inflatable
Fabric Beams", Journal of Aerospace Engineering, 7(4),
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Figure 3. Vertically Supported 4x6-Meter Inflatable
Concentrator with Aluminum Ring Fixture
Figure 1. Concept for Solar Orbita Transfer Vehicle
Utilizing Inflatable Solar Concentrators
Figure 4. Finite Element Model Representation of
Inflatable Collector and Supporting Structure
Figure 2. Space Solar Power C_ncept Based on
Inflatable Structures
Figure 5. Fundamental Mode Shape Obtained in Finite
Element Analysis (7.87 Hz)
5
American Institute of Aeronautics and Astronautics
Figure6.Rigid-BodTyypeModeShapOebtaineind
Figure 8. Coupling Between Support Structure and
FiniteElemenAtnalysi(sMode5,10.34Hz)
Inflatable at Mode 30 (26.15 Hz)
Mode Freq
Mode Freq
Mode Closed Form NASTRAN
Number(Hz) Node Lines Number (Hz) Node Lines
Number Freq. (Hz) Freq. (Hz) Node Lines
1 7.87
z-trans 7 I1.18 z-rot
1 4.1 4.2
2 8.51 x-trans 8 13.44 2 5.9 6.2 "_
3 8.58 _,-trans 9 13.98 7.0 7.3
4 9.82 _'_' 10 16.52 7.5 8.3
5 10.34 y-rot 11 16.54 8.2 9.0
Table 2. Modes Predicted Using Finite Element @
6 10.95 x-rot 12 18.48
Analysis and Closed Form Solutions for Flat Ellipse
x
Table 1. Frequency Results for Finite Element @
Analysis of Concentrator and Support x
Figure 7. Mode 9 (13.98 Hz) Showing Geometric
Curvature Effects on Mode Shape
6
American Institute of Aeronautics and Astronautics