The Effect of Asymmetric Mechanical and Thermal Loading on Membrane Wrinkling

12 Pages·2002·2.9 MB·English

by  Blandino, Joseph R.

AIAA 2002-1371
The
Effect of Asymmetric Mechanical and Thermal Loading on Membrane Wrinkling
Joseph R. Blandino*
James Madison University
John D. Johnston**
NASA Goddard Spaceflight Center
Jonathan J. Miles*.**
James Madison University
Urmil K. Dharamsi ....
James Madison University
Abstract Previous Studies
Large, tensioned membranes are being considered for Membrane structures such as solar sails and sunshieids
future gossamer spacecraft systems. Examples include are near-term application of gossamer spacecraft
sunshields, solar sails, and membrane optics. In many technology. In both cases a relatively fiat, reflective
cases a relatively flat membrane with minimal _ membrane surface is desired. Achieving a flat
wrinkling is desired. Developing methods to predict membrane surface, is difficult because tensioned
and measure membrane wrinkling is important to the membranes will typically undergo wrinkling. The
future development of gossamer spacecraft. Numerical wrinkling occurs because membranes have negligible
and experimental data are presented for a 0.5 m square, bending stiffness and cannot support compressive
tensioned membrane. The membrane is subjected to loads. A comprehensive overview of membrane
symmetric and asymmetric mechanical loading. Data wrinkling is presented by Jenkins and Leonard. 1The
are also presented for a symmetrically loaded compressive loads may be due to either mechanical or
membrane subjected to spot heating in the center. The thermal loading. There have been several studies that
numerical model shows good agreement with the have investigated thermal-mechanical effects on
experiment for wrinkle angle data. There is also membranes. Chiu et. al.2presented an analytical study
reasonable agreement for the wrinkled area for both of wrinkling .of a polymer membrane subjected to
isothermal and elevated temperature tests. combined thermal and mechanical loads. This work was
not related to spacecraft, but instead was studying the
Introduction effect of spot heating on transparency films. The work
Membrane structures typically exhibit nonlinear is relevant to this study because the membrane was
behavior when loaded. Since a membrane structure tensioned and subjected to localized heating at the
center of the membrane. Jenkins et. al.3 studied the
cannot support compressive stresses, local buckling or
wrinkling often occurs. At ambient temperature the effect of heating on the wrinkling behavior of a round
wrinkle pattern is dependent upon both the membrane optical membrane. This investigation presents a
and loading geometry. At elevated temperature the detailed analysis as well as data from a preliminary
experiment. Blandino et al.4 presented experimental
wrinkle pattem may also be a function of the material
properties and the residual stress state of the membrane. data on the wrinkling near the comer of a
The coefficient of thermal expansion will cause the symmetrically tensioned square membrane. Although
data was presented for several isothermal cases, the
material to expand, while heating may relieve any.
residual stress from the membrane that was created details of an experimental apparatus capable of elevated
temperature testing and preliminary data for a heated
during manufacturing. Quantifying the wrinkling
behavior of a membrane poses many challenges, both membrane were also presented.
experimentally and analytically. The purpose of this
This paper builds upon previous work by the authors 5
paper is to present both experimental and computational
data quantifying the wrinkling behavior of a square quantifying the wrinkling of a square membrane
membrane subjected to symmetric and asymmetric subjected to symmetric isothermal loading. A detailed
analysis of the wrinkled region and wrinkle angles will
mechanical loading as well as non-uniform thermal
loading. be compared with experimental results for both
isothermal asymmetric mechanical loading as well as
combined symmetric mechanical and asymmetric
*Assistant Professor, Department of Integrated Science and
Technology, Member AIAA. thermal loading.
**Aerospace Engineer, Member AIAA.
**'Associate Professor, Department of Integrated Science and
Technology.
.... Undergraduate Research Assistant, Department of Integrated
Science and Technology.
Copyright © 2002 by Joseph R. Blandino.
Published by the American Institute of American Institute of Aeronautics and Astronautics
Aeronautics and Astronautics, Inc. with
permission.
Experiment Design Test Series
Many of the elements that make up the experimental Two series of tests were run, one under isothermal
apparatus have been described previously. 4,5 This conditions and another at elevated temperatures. The
section will provide a brief overview of the test
isothermal tests were repeated with two different
specimen, heating system, instrumentation, and load
membranes. This allowed direct comparison between
cases.
wrinkle regions from case to case on a single membrane
and comparison of wrinkle regions between
Test Specimen
membranes. The test sequence began with a 2.45 N
Two test specimens were used for this study. One for load applied. The loading remained unchanged for
each series of tests. Both were a 0.5 m (19.68 in) approximately 15-30 minutes while measurements were
square, 2.54 x 10.2 mm (0.001 in) thick Kapton ® taken of the membrane. At the completion of a test case
membranes. The membranes have a 1x 10.3mm (3.94 additional mass was added to the left-side comer and
x 10-5 in) vapor deposited aluminum coatine on one
the.sequence started again until measurements were
side. The test articles were cut from a roll of-material.
recorded for each load case. The actual loads applied to
The cut section was chosen to be free of either the comers are shown in Table 1 For the elevated
significant material wrinkles or creases. The comers
temperature tests the membrane was loaded
were reinforced with 0.12 mm (0.005 in) thick symmetrically with 2.45N.
transparency film on both sides. Mechanical loads were
applied at discrete points at the corners of the Membrane Surface Profile Measurements
membrane via Kevlar ®threads. Kevlar ® threads were
Photogrammetry was used to determine the surface
also used to anchor the comers opposite the loads to the profile of the loaded membrane. This method has been
test frame. Each membrane was oriented in the load
demonstrated on membrane structures by the authors
frame such that the manufacturing direction for the
and others. 5'6A symmetric pattern of target spots was
rolled material was along the x-axis. The test specimen projected onto the non-aluminized side of the
mounted in the load frame is shown in Fig. 1(a). Details membrane using a high intensity light projector and
on the load frame are provided in Refs. 4 and 5.
slide. The surface profile is found by accurately
determining the location of the center of each target in
Mechanical Loading
each image and triangulating. For membrane 1two sets
Mechanical loads were applied by hanging masses from of images were taken for each load case. The first set of
the ends of the Kevlar ®threads. This design provided a
images had targets projected over entire membrane,
constant force at all four of the membrane corners.
while the second had targets projected only in the
Once the membrane was loaded, the Kevlar ® threads
quadrant of the membrane near the left comer. The
were checked to ensure that they were square with the
second membrane had images taken with targets
test frame. Excess thread at the top and fight side were
projected over the entire membrane only. For images
pulled taut and securely fastened to the test frame so
taken of the entire membrane the target diameter was
that the membrane could not slip. Prior to hanging the
approximately 3mm with targets approximately 3 mm
manufacturer's value for each mass was verified using on center. For images of just the area of the membrane
an electronic balance.
near the left comer the target diameter was
approximately 2 mm and the targets were
Thermal Loading
approximately 2 mm on center. The two sets of images
Thermal loads were applied to the membrane using a provided two levels of detail of the membrane surface
radiant heater. The radiant heater was a flexible heater profile.
attached to a 76.2 mm diameter brass disk with a
Silicone RTV designed for use at temperatures up to Two images were taken with identical, calibrated,
200 °C. The face of the disk facing the membrane was digital cameras mounted approximately
painted black. The heater is designed to operate at 610 mm from the membrane surface. The baseline
Voltages up to 115V and was attached to a variac sothat between the two cameras was approximately 580 mm.
voltages ranging from 0 to 115V could be applied. The The cameras had a 2048 X 1536 pixel resolution. A
heater was located in the center of the front face of the frame with several targets surrounded the-membrane.
membrane. For the elevated temperature tests this was These 12.5 mm diameter targets were used to scale the
the uncoated side of the membrane. This was done by images and orient the axes. The frame with respect to
mounting theheater on a 3.1 mm diameter ceramic rod, the membrane was shown in Fig. l(a). The targets on
the top of which was inserted into a hole drilled in the
the frame are also used within the program to determine
brass disk. The bottom of the rod .was inserted into an camera rotations and the angle between the camera and
aluminum mounting that attached to the test frame. A the image.
picture of the heater is shown in Fig. 1(b).
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American Institute of Aeronautics and Astronautics
It is importanttonotethatto a certainextentthe
accuracoyfresultsobtaineudsingphotogrammeatrrey below the imager to control stray thermal emissions, a
dependeonnt thetargestizeandtargedtensityE.ach necessary step given the low temperatures and
targemt ushtaveasufficienntumbeorfpixelstoallow ernittance associated with the membrane. A stream of
accuratdeeterminatioonf thecentery,etthetarget 100 images was integrated to produce a single image
densitymustbelargeenoughto havea sufficient with lower noise associated with each pixel. The
numbeorfdatapointstoresolvedetailsinthewrinkle Agema system does not adjust for emittance spectrally,
patternsF.orimagintgheentiremembranweiththe3.1 but rather invokes a singlel averaged value. Several flat
megapixecal meraussedforthisstudytheminimtim black dots were painted on the membrane and then it
targestizeisapproximate1l.y8mm.Thedesiretdarget was heated under the same conditions as during the test.
sizefor highestaccuraciys approximate7lymm. Given that the black spots would emit nearly like a
Unfortunateilfy,7mmdiametetarrgetswereusedfor blackbody, we were able to back out an estimated
thisprojectthetargetdensitywouldhavebeentoo average emissivity value by comparison of the images
coursteoresolvaenywrinkledetails. collected before and after the spots were applied. This
The projector and
results in a repeatable emissivity value of 0.115. This
slide format used were not capable of projecting 1.8
was assumed constant across the entire membrane
mm targets across the entire membrane. If only a
quadrant of the membrane is imaged the minimum
Experimental Results
target size becomes approximately 1.0 mm and the
The goal of this research was to quantify the wrinkled
ideal target size is approximately 3.5 mm. The method
region of a square membrane subjected to asymmetric
for determining ideal target sizes is given in Ref. 7.
mechanical loading as well as non-uniform thermal
Details such as wrinkle amplitude and wrinkle angle are
loading. This section presents experimental data for the
best determined using images of only a membrane
isothermal mechanical loading as well as elevated
quadrant while wrinkled region can be determined from
temperature tests.
images of the entire membrane. Another factor
affecting the accuracy of the membrane profile is target
Isothermal Mechanical Loading
illumination. As discussed previously accuracy depends
Contour plots of the left comer of membrane 1for both
on determining the center of a target in two images.
load cases are presented in Fig. 2(a)-(b). Figure 2(a)
Thus it is desirable to have uniform illumination across
shows the wrinkle patterns for membrane 1subjected to
the membrane surface. Projecting targets, even on the
a symmetric 2.45 N load. Figure 2(b) shows the same
non-aluminized side of the membrane, produced glare
membrane subjected to an asymmetric 2.45 N x 7.36 N
and non-uniform contrast across the membrane.
load. Note that the load is applied at X=0,Y=0 in these
Therefore the membrane was coated with a thin layer of
plots. In both plots the contour lines show 0.05 mm
a talc-based developer solution. The solution dried
changes in surface amplitude. Figure 3shows some bad
white and adhered but did not bond to the membrane
pixel data near the X-axis but several wrinkles are
surface. The coating provided a non-reflective surface
clearly visible in both Fig. 2. A program was written in
to project targets onto the membrane. •
LabVIEW that determined the X and Y coordinates of
the wrinkle peaks and valleys at various cross sections.
Membrane Surface Tern erature Measurements
The program then used this data to determine the angle
The temperature profile of the heated membrane was
of the peaks and valleys with respect to the X-axis.
acquired using an Agema 870 Thermovision ®infrared
Table 2 provides data on the angles with respect to the
scanning imager. The imager head uses a TE-cooled
X-axis for peaks and valleys for both load cases.
HgCdTe detector and is sensitive in the 8-12gm
waveband. The image produced comprises 144 x 144
The wrinkle amplitudes from membrane 1 are
pixels and is interlaced 4:1, with each line refreshed 6-
compared for both load cases in Fig. 3. The wrinkle
1/4 times per second. Image processing was amplitude for the symmetric case is similar to that
accomplished using a dedicated software package that
reported by the authors in Ref. 5. Figure 3(a) shows a
accepts an estimated averaged target emissivity value
cross section of the membrane plotted from data taken
and ambient and atmospheric temperatures that are
along a line from X=100 mrn to Y=100 mm. Figure
incorporated into the conversion algorithm that converts
3(b)_ shows a cross section of the membrane plotted
raw radiosity data into temperatures. We recognize that from data taken along a line from X=150mm to
the aluminum coated membrane surface exhibits a
Y-150mm. Diagonal cross sections are chosen because
particularly low spectral emittance profile. In order to
they are approximately perpendicular to the wrinkling.
maximize spatial resolution the imager was placed one Figure 3 shows that as the loading ratio is increased
meter from the rear of the membrane, the shortest
there is a slight decrease in the wrinkle amplitude and
distance that would allow for the entire temperature the wrinkle wavelength. '
profile to be in view. A canopy was placed above and
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American Institute of Aeronautics and Astronautics
Figures4-5comparetshetwodifferentmembranes
usingphotogrammeretrsyultfsortheentiremembrane.Nonlinear analysis techniques are required in order to
Figure 4 comparesthe symmetricallyloaded accurately account for geometric nonlinearities, load
membranewsh,ileFig.5comparethsetwomembranesstiffening, and wrinkling effects in the analysis of
subjectetdoasymmetrloicadingC.omparisocnasnalso membrane structures. The present analysis is
bemadebetweetnhetwofiguresforsimilarmembranesperformed using the commercially available finite
subjectetoddifferenlotads.Itisimportantotnotef,or element analysis program ABAQUS. 8 A nonlinear
thereasondsiscusseindtheexperimednetsignsection, static analysis with membrane wrinkling effects
thatthesefigureswillnotshowallthewrinklepsresent accounted for through the use of a user defined material
inthemembranseurfaceprofile.Whatthesefigures (UMAT) subroutine is used to predict the structural
will show is relativelylarge amplitudel,arge response of the membrane. The formulation utilized
wavelengtwhrinklesT. heyareusefulfor making here was developed by Adler 9based on work by Miller
and Hedgepeth. _°In this approach, membrane element
generasltatemenatsboutthewrinkledregionofthe
membraneF.igure4 showsthatthe wrinklingis material properties are iteratively modified during the
primarilyconfinedtoaregionwithin200mmofthe analysis to account for the effects of wrinkling and
cornersW.rinklingisappareonnt eachmembranneear slackness. The analysis procedure is as follows. First, a
allfourcomersF.igure5showsthatastheloadratio finite element model of the structure is generated using
increasefrsom1"1to1:3thewrinkledregionislarger membrane elements that are asslgned the wrinkling
nearthecomersof increaseldoading(thecorners material model. Next, a nonlinear static analysis of the
X=0,Y=0andX=500,Y=500T).hewrinkledregion structure is performed during which the state of each
nearthesecomersis largerthanthat for the element (taut, slack, or wrinkled) is determined. A
symmetricallolyadedmembraneTsh.ewrinkledregion combined stress-strain criteria is used in the UMAT to
occurwsithin250mmofthecomers. determine the element states. Following the elements
state determination, the stiffness matrix of each element
Elevated Temperature Tests. is updated as follows. If the element state is taut, the
stiffness matrix is unaltered. If the element state is
To study the effect of thermal loading on membrane
slack, the stiffness matrix is set equal to zero. If the
wrinkling membrane 2 was loaded symmetrically with
element state is wrinkled, the stiffness matrix is
2.45 N loads and a spot heater was used to apply anon-
modified according to Stein-Hedgepeth wrinkling
uniform thermal load to the center of the membrane.
theory._l Stein_Hedgepet h wrinkling theory predicts
Thetemperature distribution near the center of the
that the stress state in a Wrinkled region of a membrane
membrane is shown in Fig. 6. The figure shows that the
is uni-axial (positive major principal stress and zero
temperature drops off rapidly away from the heated
minor principal stress) and wrinkles form in straight
area. The maximum temperature was approximately
lines along the direction of the major principal stresses
355 K. The temperature near the edges of the
(load transfer in the wrinkled region is along these
membrane was approximately 293 K. Figure 7 shows a
lines). Note that the theory predicts average strains and
comparison between the surface profiles for the heated
displacements (not individual wri_akle details such as
and unheated membranes. Contour lines are shown
amplitude and wavelength) in the wrinkled region.
every 0.05 mm. The most distinctive feature, shown in
Further details regarding the UMAT developed by
Fig. 7(b) is the depression in the membrane in the
Adler can be found in Ref. 12. This analysis procedure
heated area. This depression is 4-5 times larger in
was previously used by the authors to predict the
amplitude than the largest wrinkles near the edges.
wrinkling behavior of a square membrane subject to
Slight changes are also visible in the wrinkled region comer loads. 5
between the heated and unheated membranes. The
•wrinkled region, particularly near the left corner,
In the current paper, this work will be extended to
appears less distinct on the heated membrane.
consider combined mechanical and thermal loading. A
sequentially coupled thermal stress analysis is
Analysis of Experiments
performed to predict the response of the membrane to
An analysis was performed to predict the membrane
combined mechanical and thermal loading. A steady-
wrinkling behavior studied in the laboratory
state heat transfer is first performed using a heat
experiments. The following sections discuss the
transfer model to predict the temperature distribution in
technique used to analyze the wrinkled membrane,
the membrane. Next, a nonlinear static structural
details of the finite element model, and predictions for
analysis is performed in two steps. In the first Step the
the membrane structural response under symmetric
mechanical preloads are applied to the structure. In the
mechanical, asymmetric mechanical, and combined
second step the thermal loads are applied by prescribing
symmetric mechanical and thermal loading.
the temperature results from the heat transfer analysis.
Analysis Technique
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American Institute of Aeronautics and Astronautics
F_jnite Element Model
The finite element model of the laboratory experiment corresponding to the increase in horizontal preload. The
includes representations of the membrane, corner minor principal stress plot, Fig. 10(b), predicts that the
reinforcements, and Kevlar threads. The membrane is region of near-zero minor principal stresses expands.
modeled using ABAQUS M3D4 and M3D3 membrane The wrinkle region, Fig. 11(b), is seen to expand in the
left and right comers and to now include a band across
elements which are assigned the wrinkling material
model. The corners are modeled with ABAQUS S3R the center of the membrane. In case 3 the membrane is
subjected to symmetric mechanical loading of 2.45 N.
shell elements, and the Kevlar threads are represented
The membrane has a non-uniform temperature
using ABAQUS B31 beam elements. The boundary
conditions are applied at the ends of the Kevlar threads distribution, Fig. 8(c). This temperature distribution
attached to the test fixture. The ends of the top and left corresponds to the spot heating laboratory experiment
that resulted in a 'bulls-eye' temperature distribution
threads are constrained in all three translational degrees
of freedom, while the fight and bottom threads are with a maximum temperature of 355 K at the center of
constrained in the two translational degrees of freedom the membrane. The plot of the major principal stresses,
normal to the loading direction. The mechanical loads Fig. 9(c), shows a significant change in the stress
distribution compared to load case 1.The center of the
are applied as concentrated loads at the ends of the fight
and bottom Kevlar threads. Thermal loads are applied membrane now has a large region of near-zero major
as predefined temperatures at the grid points. The principal stresses. The minor principal stress plot, Fig.
initial temperature of all grids is taken to be 293 K. 10(c), also shows major changes compared to load case
1. The region of near-zero minor principal stresses now
A__naiyticalPredictions encompasses all of the membrane except for four oval-
The structural response of the membrane was analyzed shaped regions near the four comers. Figure 11(c)
for three cases" (1) symmetric mechanical loading at shows that there are both wrinkled and slack regions
room temperature, (2) asymmetrical mechanical present in the membrane. The slack region is roughly
preloading at room temperature, and (3) combined smqeumarberanei.n shape and is located in the center of the
symmetric mechanical and thermal loading. Table 3
summarizes the maximum stress and the stress at the
Discussion
center of the membrane for each of the load cases.
Figure 8 presents plots of the temperature distributions Predictions from the finite element analysis were
in the membrane for each of the load cases. Figures 9- compared with results from the laboratory experiments.
11 present plots of analytical predictions for the major The analysis is useful in predicting wrinkle regions and
principal stresses, minor principal stresses and wrinkle direction, however it does not predict wrinkle
wrinkled/slack regions, respectively for each of the load details such as amplitude and wavelength. Figure 12
cases. These wrinkle/slack region plots were generated compares the wrinkle angle data from Table 2 with the
by outputting the element integration point states from predicted values from the analysis. The comparison is
the final step of the analysis. made between the predicted major principal stress
directions and the measured wrinkle angles (for both
In case 1 the membrane is subjected to symmetric the troughs and crests of the wrinkles). Both the angular
mechanical loading of 2.45 N. The membrane has a measurements are taken from the x-axis as defined in
uniform temperature of 293 K, Fig. 8(a), i.e. the Fig. 1. Recall that Stein-Hedgepeth theory predicts that
wrinkles form instraight lines along the direction of the
membrane is at room temperature. The plot of the major
principal stresses, Fig. 9(a), shows that there are stress major principal stresses, thus the measured wrinkle
concentrations at the comers of the membrane where angles are expected to fall along the predicted major
principal stress angles. Figure 12(a) shows a
the mechanical loads are applied. The minor principal
stress plot, Fig. 10(a), predicts that there is a region of comparison for the symmetrically loaded membrane,
near-zero minor principal stress around the comers and while Fig. 12(b) compares the asymmetrically loaded
outside edges of the membrane. The wrinkle region, membrane. In both cases there is good agreement
Fig. 11(a), is seen to extend from the corners around the between the predicted and measured wrinkle angles.
edges of the membrane corresponding to the region of This data also agrees with data presented by the authors
zero minor principal stresses. In case 2 the membrane is in Ref. 4. Comparing Figs. 4 and 1l(a) show that the
subjected to asymmetric mechanical loading of 2.45 N analysis under-predicts the size of the wrinkled area for
in the vertical direction and 7.35 N in the vertical the symmetrically loaded membrane. The experiments
direction. As with load case 1, the membrane has a show that the wrinkled region extends approximately
uniform temperature of 293 K, Fig. 8(b). The plot of the 200 mm from each comer. The analysis shows
major principal stresses, Fig. 9(b), shows that the wrinkling within approximately 125 mm from each
stresses in the horizontal direction have increased comer. The agreement between experiments and
analysis is better for the asymmetric load case.
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American Institute of Aeronautics and Astronautics
ComparinFgigs.5andll(b) forthe2.45Nx7.36N
Acknowledgement
loadcaseshowsthattheanalysipsredictsthatthe
Thisresearchhasbeensupporteidn partby NASA
wrinkledregionsnearthetopandbottomof the
GoddarSdpacFelighCt enteGr ranNt AG5-10701.
membranweill shrinkandthewrinklingwill extend
acrostshemembranfreomtheleftandrightcorners. References
Althoughtheexperimendtsonotshowthewrinkling
1. Jenkins,C.H.andLeonardJ,.W.,"Nonlinear
extendinagcrostshemembrantheedatashowthatthe
DynamicResponsoefMembranesS:tateoftheArt,"
wrinkledregionsat the top andbottomof the
AppliedMechanicRseviewsA, mericanSocietyof
membrandeoshrinkinsizeT. heexperimenatlssoshow
MechanicEalngineerVs,ol.44,No.7,
thatthewrinkledareanearthecomersextendosutto July 1991 pp.
319-328.
approximate2l5y0mm.Thedatapresentehdereandin
Ref.5verifythatthenumericatelchniquiseviablefor 2. Chiu, H.C., Benson, R.C., Fiscella, M.D., and Bums,
useoverarangeofisothermlaoladcases. S.J., "Mechanical and Thermal Wrinkling of Polymer
Membranes". Journal of Applied Mechanics, Vol. 61,
March 1994, pp. 67-70.
Theexperimentadlataalsoshowthatthe analysis
techniquies usefulforpredictingcombinetdhermal- 3. Jenkins, C.H., Fitzgerald, D.M., Liu, X., "Wri nK""ung
of an Inflatable Membrane with Thermo-Elastic
structurablehaviorT.heanalysipsredicteadrelatively
largeslackareaneatrhecenteorfthemembranaeswas Boundary Conditions," 41stAIAA StructureS, Structural
showinnFig.11(c).Theexperimenrteaslultsshownin Dynamics, and Materials Conference, Atlanta, GA,
Paper No. AIAA-2000-1727, April 2000.
Fig.7(b)showalargeamplituddeepressiownithinthe
heatedareoaf themembrantheatroughlycorresponds4. Blandino, J.R., Johnston, J.D., Miles, J.J., Soplop,
J.S., "Thin-Film Membrane Wrinkling due to Thermal
tothelocationofthepredictesdlackregionA.lthough
theresultnseedtobeverifiedandthetestsperformeind and Mechanical Loads," 42_a AIAA Structures,
undervacuumconditiontsoeliminatceonvectiotnh,e Structural Dynamics and Materials Conference,
comparisonbetweenexperimenatnd analysisis Seattle, WA, Paper No. AIAA-2001-1345, April 2001.
promisingT.heslackregiondevelopdsuetOover- 5. Blandino, J.R., Johnston, J.D., and Dharamsi,• U.K.,
"Comer Wrinkling of a Square Membrane due to
expansioonf thecenteorfthemembran(weherethe
Symmetric Mechanical Loads, " submitted to Journal
thermally-inducsetrdainsarethegreatescto)mparetod
of Spacecraft and Rockets, July 200 i.
theouteredgesP.reviousstudiebsytheauthorshave
shownthatthestresseasndwrinkleregionpredictefodr 6. Pappa, •R.S., Giersch, L.R. and Quagliaroli,
thecaseof symmetricmechanicaloladinganda •J.M.,"Photogrammetry of a 5m Inflatable Space
uniformelevatetdemperatumreembranaerethesame Antenna with Consumer Digital Cameras," NASA TM-
2000-210627. Dec. 2000, pp. 16.
asthosepredictefdoramechanicloaal donly(i.e.room
temperaturaen)alysis.Thisis dueto the'constant 7. Photomodeler User Manual, Version 4.0, EOS
Systems, Inc. Vancover, B.C., Canada. 2002.
force' preloadingschemewhichis intendedto
accommodattheermalexpansion/contracotifonthe 8. ABAQUS /Standard User's Manual, Version 6.1,
membraneIn.terestingltyh,eresultosfthisstudyshow Hibbitt, Karlsson, & Sorensen, Inc., Pawtucket, RI,
20O0.
thattheconstanftorcepreloadingschemeis less
effectivein thepresencoefnon-uniformtemperature9. Adler, A.L., Mikulas, M.M., and Hedgepethi J.M.,
distributions.In generali,t is expectetdhatlarge "Static and Dynamic Analysis of Partially Wrinkled
membransetructurefsor spaceapplicationssuchas Membrane Structures," 41`tAIAA Structures, Structural
sunshielwdsillnothaveuniformtemperaturaensd,thus Dynamics, and Materials Conference, Atlanta, GA,
carefual ttentionshouldbegiventothesethermal- Paper No. AIAA-2000-1810, April 2000.
structural•effects. 10. Miller, R.K. and Hedgepeth, J.M., "An Algorithm
for Finite Element Analysis of Partly Wrinkled
Summary Membrane Structures," AIAA Journal, Vol. 20, No. 12,
December 1982, pp. 1761-176
Thispapehrasdescribeadcombineedxperimenatanld
analyticastludyofmembranwerinklingforthecaseosf 11. Stein, M. and Hedgepeth, J.M., "Analysis of Partly
symmetricandasymmetricisothermaml echanicalWrinkled Membranes". NASA TN D-813, 1961.
12. Adler, A.L., "Finite Element Approaches for Static
loadingandcombinesdymmetrimcechaniclaolading
and Dynamic Analysis of Partially Wrinkled Membrane
andnon-uniformthermalloadingA. comparisoonf
experimenrtaelsultsandanalyticaplredictionfsorthe Structures," PhD Thesis, Department of Aerospace
wrinkledirectionsandwrinkleregionsshowsfair Engineering, University of Colorado, Boulder, CO,
2000.
agreement.
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American Institute of Aeronautics and Astronautics
Figure 1- Membrane mounted in test frame: (a) back-side of membrane isshown and (b) front side of
membrane with heater.
I 1 I ! I
• • i
20 i
x.o=_(_) '" _ = 5'0 _o 15o 2_o 2_o
• X-Distance (ram)
Figure 2: Contour of Membrane I subjected to (a) symmetric loads and (b) asymmetric loads. Note that the
plots have been scaled such that the xand y axes are similar.
O_=l=_¢=_ ml_onl_Cut(ram)
Figure 3: Amplitude data taken from crosssections of thewrinkled membrane: (a) data along a diagonal line
from X=100 mm to ¥=100 mm and (b) data along adiagonal line from X=150 mm toI'=150 ram.
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American Institute of Aeronautics and Astronautics
i
Fwiitghre4""Wrinkled regions of two symmetricall Yloaded membr anes: (a) membran-e_,_It_)symmetric..a..lly loaded
2"45 N f°ices ind (i) mlmblane i symmetrically loaded with 2.45 N forces.
X-Distance (mm)
Figure 5: Wrinkled regions of two asymmetrically loaded membranes: (a) membrane I asymmetrically
loaded with 2.45 N and 7.36 N Forces and (b) membrane 2asymmetrically loaded with 2,45 N and 7.36 N
Forces.
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American Institute of Aeronautics and Astronautics
Figure6:
Measured temperature distribution near the center of the heated membrane.
4
45
4(}
3
30
2O
0 5O 100 150 2OO 25O 3OO 350 400 450 0 _ 1(_0 _ i t f
X-Distance (ram) 150 200 250 300 350 400 450
X-Distance (ram)
Figure 7: Wrinkle regions for symmetrically loaded unheated and heated membranes: (a) symmetrically
loaded membrane prior to heatingand (b) symmetrically loaded membrane subjected to heating in center.
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American Institute of Aeronautics and Astronautics
Ii !
Figure 8: Temperature distributions for (a) load case 1, (b) load case 2, and (c) load case 3.
I
Figure 9- Major principal stresses in membrane: (a) load case 1, (b) load case 2, and (c) load case 3.
i_!_i_ii_i! _i_! _z.i:i
_gure 10: Minor principal stresses in membrane: (a) load case 1, (b) load case 2, and (c) load case 3.
........ _ _ .... _!i!0.:...,._..:.._..._i_:___÷_i__
Floiagdurecase11-3.Wrinkled (white) and slack (red) regions in membrane: (a) load case 1 (b) load case 2, and (c)
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American Institute of Aeronautics and Astronautics