Buckling Design Studies of Inverted, Oblate Bulkheads for a Propellant Tank

13 Pages·2002·1.1 MB·English

by  Smeltzer, Stanley S., III

AIAA 2002-1525
BUCKLING DESIGN STUDIES OF INVERTED,
OBLATE BULKHEADS FOR A PROPELLANT TANK
Stanley S. Smeltzer III*
NASA Langley Research Center
Hampton, VA 23681-2199
and
Lynn M. Bowman*
Lockheed Martin Engineering and Sciences Corporation
Hampton, VA 23681-2199
E Young's modulus of elasticity(psi.)
Abstract G shear modulus (psi.)
normal vector
An investigation of the deformation and buckling
P internal tank pressure (psi.)
characteristics of a composite, oblate bulkhead that has
r tank radius (in.)
an inverted geometry and is subjected to pressure-only
s arc length
loading is presented for three bulkhead geometries and
z tank longitudinal axis
thicknesses. The effects of a stiffening support ring at
the bulkhead to cylinder interface are also evaluated.
Introduction
Buckling analyses conducted using the axisymmetric
shell code BOSOR4 are discussed for several bulkhead The past decade has provided numerous studies
configurations. These results are analytically verified that have identified various reusable launch vehicle
using results from the Structural Analysis of General (RLV) configurations 1-3as well as strategies intended to
Shells (STAGS) code for a selected bulkhead optimize their performance, a-6 An important
configuration. component in each one of these vehicle optimization
The buckling characterization of an inverted, oblate strategies isthe willingness to trade increased structural
bulkhead requires careful attention as small changes in component weight for an overall reduction in vehicle
bulkhead parameters can have a significant effect on the weight or vehicle performance. All of these endeavors
critical buckling load. Comparison of BOSOR4 and have been conducted with one goal in mind: to develop
STAGS results provided a very good correlation a RLV capable of providing cost-eftbctive ($1000/lbm)
between the two analysis methods. In addition, the access to low-earth-orbit by reducing launch and
analysis code BOSOR4 was found to be an efficient operations costs. One of the important areas related to
sizing tool that is useful during the preliminary design the development of a future reusable launch vehicle is
stage of a practical shell structure. Together, these two the capability for accurately predicting optimum vehicle
aspects should give the design engineer confidence in weight based on a variety of component configurations;
sizing these stability critical structures. Additional such as tanks, intertanks, or thrust structures.
characterization is warranted, especially for a The current strategy for the RLV program appears
composite tank structure, since only one bulkhead to be centered about a vertical-takeoff, horizontal
configuration was examined closely. landing, single-stage-to-orbit, winged-body derivative
that uses rocket propulsion. This being the case,
Primary Symbols conventional launch vehicle loading will be relied upon
for designing major structural components, such as
ellipsoidal major axis (in.)
tanks. Improvements in structural efficiency for these
ellipsoidal minor axis (in.)
*Aerospace Engineer, Mechanics and Durability Branch. Member, AIAA and ASME.
Aeronautical Engineer.
Copyright © 2001 by the American Institute of Aeronautics and Astronautics, Inc. No copyright isasserted in the United States under Title 17,
U.S. Code. The U.S. Government has aroyalty-free license to exercise allrights under the copyright claimed herein for Governmental Purposes.
All other rights are reserved bythe copyright owner.
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componenatrsetypicallyobtainetdhrouggheometric literaturtehataddresstehsedesigna,nalysios,ruseof
changetosstructuroertheuseofadvancemdaterials.oblateh,emiellipsoidbaullkheadfosrlaunchvehicle
Geometrcichangeasreusedto deriveanoptimum applicationAsd.ditionallayl,loftheprevioursesearch
balancebetweenincreasecdomponenwteightand hasfocuseodnbulkheadosfvariousshapethsatare
improvedsystemperformancew,hile material madeofametallicmaterial.Thusa, needexiststo
substitutionosfferimprovedstrengthandelastic characteritzheebehavioorf oblateh,emiellipsoidal
modululso,wedrensitya,ndmoredesirabcleoefficientsbulkheadtshatareinvertedm, adeof composite
ofthermaelxpansiaonndconductivity. materialsa,ndhaverepresentatilvaeunchvehicle
Akeycomponeinntthedesigonfapropellatnatnk geometaryndloadincgonditions.
is theresponsceharacterizatioofnthebulkheads. Theexistinlgiteraturreelatedtothebehavioorf
StudieosfpreviouRsLVconfiguratiohnasveutilized invertedbulkheadissprimarilyconcernewdiththe
conformatalnksandoblatebulkhea7d'8sto reduce bucklingandcollapsoefthesestructureinsamode
overallvehicleweightandto improvesystem referretdobyCoron9aas"domereversal."Allthe
performancIne.theworkbySiskandWu,theshapes earlybucklinginvestigationwsereperformedon
of the bulkheadrsangedfromhemispherictaol bulkheacdonfiguratiotnhsathadasphericraaldiusof
hemiellipsoidinagleometaryndwereattachetodthe curvatufroertheshelsl egmenintsvolvedA. classical
cylindricaplortionofthetankin a mannetrhatis investigatiboynBudians1k°ycharacterizaenddsolved
conventionfaolrpropellantatnksoflaunchvehicles. theaxisymmetcriocllapsoefclampesdphericsahlells,
Thatis,thecenteorfcurvaturfoerthebulkheadwsas while HutchinsHonidentifiedthe unstableand
locateidnsidethetankvolume.Adifferenbtulkhead imperfectionsensitivebehaviorof post-buckled
geomettrhyatismorecommotnothepressuvreessel sphericaslhells. Severaelxperimentsatludie1s2-15
industrryeversethsedirectioonftheradiuosfcurvature investigatetdhe bucklingbehaviorof spherical,
sothatthebulkheahdasaninvertesdhapelik,ethaton hemisphericaanld,torisphericbaullkheasdusbjectetod
thebottomofanaluminubmeveragcaen.Thistypeof hydrostaptircessurGe.alletl_y6etal.,Blachut 17-19et al.,
bulkheagdeometrhye,reaftreerferretdoasinvertedis,
and Lu2°have more recently performed numerical and
showninFigure1alongwithconventionbaullkhead
experimental studies to determine the effects of
geometry. imperfections and local features on the buckling of
Aninvertebdulkheagdeometirsyimportafnotrthe
spherical shells. One other notable area of research
vehicleoptimizationstrategysincean inverted
related to the buckling of inverted bulkheads is the
bulkheapdrovideasdditionfaelaturetosthepropellant
work on dynamic buckling of oblate and prolate domes
designthatarenotavailablefroma conventional
by Ross2_,et al.
bulkheadA. fewadvantagoefsferedbyaninverted
The investigations by Corona and Ross et al. are
bulkheadth,atprovideanopportuniftoyrreducing
the only ones that characterized the buckling behavior
weightduringthevehicleoptimizatioanr,e1) a
of oblate, hemiellipsoidal bulkheads. Corona
capabilitfyornestingadjacentatnks,2) additional
performed an experimental study of a low profile,
volumfeorhardwabreetweetannksandintertankasn,d
hemiellipsoidal bulkhead configuration that included a
3) thecapabilitfyorimprovintghefabricatioannd
nonlinear axisymmetric analysis. Although a buckled
performancoef interfacjeoints. Forexamplea,n
mode shape for the bulkhead was not given, the
invertedbulkheadgeometryoffers potential
experimental results determined that the failure mode
improvemetnottsheperformanocfeadhesivebloynded
for the bulkhead occurred as a rapid collapse followed
jointsatthebulkheatodcylindeinrterfac(ei.e.Y, -joint)
by apartial reversal of the dome upon reaching the limit
becaustheeinternaplressulroeadinogfthetankcreates
point. In the work by Ross et al., the primary objective
adeformebdulkheasdhaptehatresultisnout-of-plane
of the investigation was to determine the buckling
compressaiotnthejoint. Thusp,eesl tressethsatcan
pressures and mode shapes for an array of prolate and
leadtoprematujroeintfailurearesuppressbeydthe
oblate bulkheads due to pressure and a vibratory
out-of-plancoempressriveesponsfreomthebulkhead,
excitation of the shell wall. However, a brief
whichleadstoimprovejodintperformancHeo.wever,
description of the static buckling response and critical
tocapitalizoenthesaedvantagaethsorougkhnowledge
pressure for each of the bulkhead shapes was given.
oftheresponsoefaninvertebdulkheaisdparamount.
The objective ofthe present paper is to state results
Althougahsignificanptortionofliteratureexistsfrom
from an analytical investigation to determine the
theindustriaplressurveessealndpipingcommunity
deformation and buckling characteristics of a
relatedto the bucklingbehaviorof externally
composite, oblate bulkhead that has an inverted
pressurizsepdhericatol,rispherichael,misphericaanld,
geometry and is subjected to pressure-only loading. In
hemiellipsoidbaullkheadsth,ereis no available
the remainder of the paper, a description of the overall
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tankconfiguratioanndloadinga, summaroyf the
Description of Bulkhead Modelin_ and Analyses
differentytpesofanalyseussedintheinvestigatioann,d
adiscussioofntheresultasregiven. Two different types of analysis codes were used to
perform the analyses of the inverted bulkheads
evaluated during the present investigation. The first set
Bulkhead Configuration and Loading
of analyses was conducted using the BOSOR423
The configuration of the bulkhead that was analysis code that was developed for analyzing
considered in the present study corresponds to a scaled axisymmetric shell structures using a finite difference
propellant tank for a launch vehicle. Specifically, the solution algorithm. BOSOR4 is capable of stress,
tank geometry and pressure were scaled to represent a stability, and vibration analyses of segmented, ring-
typical full-sized cryogenic tank for a reusable launch stiffened, branched shells of revolution and prismatic
vehicle. The tank and inverted bulkhead geometry are shells. For this investigation, two options within the
depicted in Figure 1along with the applied loading of BOSOR4 code were used to evaluate the bulkhead
only internal pressure. The tank internal pressure (P) models: the "quasi-linear" analysis option and the
was 216 psi. while the right circular cylindrical portion nonlinear analysis option. The "quasi-linear" option
of the tank as well as the inverted bulkhead had a radial uses nonlinear theory for the prebuckling analysis and
diameter (2a) of 36 inches. The shape of the bulkhead calculates the bifurcation buckling load for a range of
varied from a hemispherical to hemiellipsoidal circumferential wave numbers using a fixed load
geometry; in addition, a detailed account of the condition. The nonlinear option uses the same
different bulkhead shapes used in this investigation is nonlinear theory for the prebuckling analysis, but
given in the section: Description of Bulkhead calculates the stability determinant for a given
Modeling and Analyses. The material properties for the circumferential wave number as the load is
tank were representative of a non-autoclave cured, incremented. Once a change in sign for the stability
carbon fiber reinforced plastic (CFRP) composite determinant is obtained, the critical buckling load
material system with a qnasi-isotropic laminate corresponding to that wave number is obtained using
configuration. This laminate configuration was used to the nonlinear prebuckling analysis.
represent the shell wall for both the cylinder and The second set of analyses was conducted using
bulkhead structures for each of the analyses and did not the STAGS 24(Structural Analysis of General Shells)
include the effects of material or geometrical nonlinear shell analysis program. STAGS is a finite
imperfections. As discussed by Hilburger and element code designed for the static and dynamic
Starnes 22,the effects of initial geometric imperfections analysis of general shells. In addition, STAGS can
may have a significant influence on the buckling perform an eigenvalue analysis for buckling and
response of shells; however, there was no attempt made vibration based upon a linear or nonlinear stress state.
in the present investigation to quantify the effects due The program uses both the modified and full Newton
to geometric imperfections. The in-plane material methods for its nonlinear solution algorithms, and
properties for the bulkhead and cylinder used in this accounts for large rotations in a shell wall by using a
investigation are given in Table 1. co-rotation algorithm at the element level. In a
The applied loading for this investigation was nonlinear analysis, STAGS performs an initial linear
limited to the effect of internal tank pressure only. The solution and then load or arc-length increments are
effects of mechanical loading due to factors such as the automatically adjusted based upon the nonlinear
weight of components stacked above the tank, bending response. The load and arc-length path-parameter
loads due to wind loading, or head pressure from the strategy, also known as the Riks pseudo arc-length
acceleration of the propellant fluid were outside the path-following method isused to continue past the limit
scope of the present investigation. Although points of a nonlinear response. In this strategy, the
mechanical loading is important to the overall design of incrementally applied loading parameter is replaced by
a propellant tank, the present study was primarily an arc-length along the solution path, which is then
concerned with determining the buckling behavior of used as the independent loading parameter.
different bulkhead configurations with simple boundary A survey of the features for each code revealed the
effects and loading. Similarly, thermal loading was not benefit of BOSOR4 as a relatively quick and efficient
explicitly included in the analyses; however, changes in tool for conducting trade studies of axisymmetric shell
material stiffness due to the cryogenic fluid were structures while the STAGS code offered capabilities
accounted for by using material properties that were for performing and displaying detailed investigations
determined at 423°F. into the buckling behavior of all shell structures. The
benefits of using the BOSOR4 code were fast and
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American Institute of Aeronautics and Astronautics
efficientetchniqufeosrmodelintghestructuraen,alysis withthismodeulsingBOSORw4,hichcorrespontodas
methodthsatincludendonlineaarnalysrisoutinesa,nd full-factorial (3 3) design. Furthermore, linear and
analysriosutinetshatrequirevderylittlecomputteimr e
nonlinear BOSOR4 analyses of this model were
to providea solution.In everycaset,heactual
conducted using the optimum bulkhead configuration
computerurn-timewasnevelrongetrhanfourhours
that was chosen from the design study.
usingasingleprocessSorunSpaUrcltra30machine.
The cylindrical section of the tank and the
Thisimportanfteatureof theBOSORc4odethat
bulkhead were each modeled using one BOSOR4 shell
providesdhort-duratisoonlutiotnimesforthemodels
segment that consisted of 97 mesh points. The vector
analyzeisdduetotheeliminatioonfthecircumferential
normal to the curvilinear shell segments denoted by
dependenicnetheshellequationthsatreducetdhe
displays the direction of the shell thickness. The
equationfrsompartiadl ifferentiaelquationtosone-
length of the cylindrical shell, segment two, varied in
dimensionaolr,dinarydifferentiaelquations.One
length depending on the bulkhead shape, but was a
drawbacokftheaxisymmetprircoblemdefinitiownas
constant fifteen inches beyond the apex of the bulkhead
thatdataplotsgenerateudsingBOSOR4were
for each model. The thickness of segment two was a
curvilinearerpresentatioonfstheshellcross-section,
constant 0.0676 inches for the entire length except for
whichlackedtheabilitytoproducecolorbanded,
the last six inches where the cylinder intersects the
contouprlots. In contrastS,TAGSmodelswere
bulkhead at node 97. At that location, a 4-inch-long
consideramblyorecompletxogeneratoef,feresdimilar
bnilt-up region with a 0.125-inch thickness is modeled
nonlineasrolutiornoutinesa,ndrequireadgreadt eal
at the edge of the cylinder with a 2-inch-long transition
morecomputetrimeto obtaina solution. The
between the two cylinder thicknesses. As previously
advantagoefusingSTAGSwasagreatevrarietyof
stated, the bulkhead maintained a constant thickness
solutiornoutineasb, ilitytomodenlonsymmetrsichaelll
along the entire meridian. Additionally, the geometry
loading and behavior,and superiorvisual
of the support ring was not explicitly modeled using
representatioofnosutpudtata.
shell segments, but was accounted for by using a
The objectivefsor conductintghe BOSOR4
discrete ring option within BOSOR4. Using the
analysewseretoperformapreliminarayssessmoefnt
discrete ring option, the ring stiffness and torsional
severablulkheacdonfiguratiothnastwouldpotentially
rigidity for each ring case was included in the model at
affectthebucklinrgesponsoefthebulkheasdtructure
node 97. The boundary conditions for the bulkhead
anddeterminaesinglebulkheacdonfiguratiofnor
segment, segment one, were a symmetry condition at
furthesrtudy.Threebulkheasdhapeasndthicknesses,
the center of the bulkhead, node one, and free along the
andtheeffecot fthreesizesofsupportinrigngsatthe
edge of the bulkhead. The cylindrical shell, segment
bulkheatdo cylinderinterfacewereevaluatetdo
two, was tied to the bulkhead at node 97 using the
determinaecceptabpleerformanucnedertheinternal
discrete ring and a cylinder symmetry condition at node
pressulroeadingT.hethreebulkheasdhapecshosefnor
one which was employed to hold the axial displacement
thestudywerea hemisphericbaullkheaadndtwo
and meridional rotation to zero while leaving the
hemiellipsoidbaullkheadwsithmajortominor(a:b)
circumferential and radial displacements free.
axisratiosgiveninTable2.Thethreesheltlhicknesses
The STAGS analyses were performed using two
chosefnorevaluatioanlongwiththreesizesofsupport full bulkhead models that were created in
ringsarealsoshown.Furthermotrhee,thicknesosf MSC/PATRAN. The first model did not include a
eachbulkheawdasconstaanltongtheentiremeridiainn
cylindrical tank section and was referred to as the
allcases.Onceallthecaseswereevaluatetdh,e
bulkhead-only model while the second model included
selectioonfasinglebulkheacdonfiguratiwonasmade
a cylindrical tank section similar to the BOSOR4
asa functionof severaplrogrammactiocnstraints.models and was referred to as the tank-bulkhead model.
Althougahlltheparameteurssedtoselecthteoptimum
The bulkhead configuration that was used for all the
configuratiofonranRLVderivativaereunavailable,
STAGS analyses was determined from the BOSOR4
thebulkheatdhicknesrsin,gsizea,nddomegeometry
design study that will be discussed in detail later. The
wereprimarilychosebnasedona combinatioonf
bulkhead-only model and the tank-bulkhead model both
minimumtankweighatndlengthwhilemaintainianng
used the 2:1 hemiellipsoidal bulkhead configuration and
adequamtearginofsafety.
did not include a support ring.
A descriptioonftheinvertetdankgeomettrhyat
The bulkhead-only model had 3120 elements and
wasmodeleudsingBOSORa4ndthecorresponding
approximately 18,886 degrees of freedom. The
modealreshowinnFigure2.Thismodewlasusedto refinement of the finite element mesh of the bulkhead
performadesigsntudyusingthebulkheapdarameters
was limited by the aspect ratios of the triangular
giveninTable2. Twenty-sevceansewsereevaluatedelements located in the center of the bulkhead. The
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boundacryonditioncosnsisteodftheedgeregionofthe
After a short inspection of all three figures, it is evident
bulkheaddefinedin a localcylindricacloordinate
that a significant change in the buckling response
systemin whichthenodadl egreeosffreedomwere
occurred between the hemispherical bulkhead and the
clampedin thecircumferentaianldaxialdirection
shallower hemiellipsoidal bulkheads. The buckled
similatrotheBOSORm4odeclonditionTs.hepurpose
mode shape shown in Figure 4 for the hemispherical
of thetank-bulkhemadodewl astoinvestigatthee
bulkhead has a single, short half-wave along the
influencoefthecylindricatlankboundaroyntothe
meridian that appears to occur very close to the edge of
responsoeftheinvertebdulkheadT.hetank-bulkhead
the bulkhead with no attenuation, and corresponds to a
modeclonsisteodftheinvertebdulkheacdonnectteoda
circumferential wave number of twenty. In contrast,
cylindricatalnkwallsegmenTt.heinvertebdulkhead
the mode shapes for the two hemiellipsoidal bulkheads
andcylindricatlankwall hadthesamematerial
in Figures 5 and 6 have three half-waves along the
propertiesH.owevetrh,ecylindricatalnkwallhada
meridian that appear to occur closest to the center ofthe
thicknesosf .50-inchenseartheouteredgeof the
bulkhead and slowly attenuate towards the edge. Also,
invertebdulkheaadndthentaperetdoanominawlall
the number of circumferential waves that correspond to
thicknesosf.30-inchefosralengthof18-incheTs.he
the mode shapes for the 1.414:1 and 2:1 hemiellipsoidal
tankmodeclonsisteodf 5520elementasnd33,286
bulkheads are one and zero, respectively. These results
degreeosffreedomT.heboundacryonditionfosrboth
for the hemiellipsoidal and hemispherical bulkheads
modelsremainetdhesameforboththelinearand
correspond to the same bifurcation buckling mode
nonlinearSTAGSbucklinganalysesthat were
shapes detailed in the investigation by Ross, et al.
conductedIn. additiona,neigenvaluaenalysiwsas
Examining the data from the "quasi-linear"
conducteadtseveranlonlinealoradlevelsforeach
BOSOR4 results in Figure 3 shows a nonlinear
model.
relationship between decreasing bulkhead thickness and
a corresponding decrease in the critical buckling
Results and Discussion pressure for each individual bulkhead geometry. This
nonlinear relationship is evident for both the
A summary of the BOSOR4 results for selected
hemispherical (1:1) bulkhead geometry and the 1.414:1
cases using the "quasi-linear" option is given in Figure
hemiellipsoidal bulkhead geometry as the slope of the
3. These results only represent a small subset of all the
piecewise linear curves increase from the 0.25-inch
results that were determined during the design study,
thickness to the 0.125-inch thickness. In addition, the
but are deemed sufficient to illustrate the behavioral
2:1 bulkhead incurred a 56% decrease in the critical
trends. The operating pressure normalized with respect
bifurcation buckling pressure for a corresponding 30%
to the critical pressure for bifurcation buckling is
reduction in the bulkhead thickness. Also, a similar
plotted here as a function of the bulkhead thickness for
nonlinear relationship appears to exist between changes
various ratios of the bulkhead major to minor axis.
in bulkhead geometry and a corresponding change in
Although the parameters for these cases were
the critical buckling pressure at a constant thickness.
representative of bulkheads with variable geometry and
That is, as the bulkhead becomes shallower the critical
thickness, a fixed value of 3.0 in.2for the discrete ring
buckling load decreases more rapidly. For example, a
was used. The reason for choosing a discrete ring area
29% reduction in height exists from a 1.414:1 bulkhead
of 3.0 in.2was two-fold. First, the effect of the discrete
to a 2:1 bulkhead; however, at the 0.175-inch thickness
ring on the critical pressure for bifurcation buckling
the critical buckling pressure decreased by 50% for the
was minimal for two of the three bulkhead geometries.
same configuration.
Also, solutions for the bulkhead with the shallowest
The effect of the discrete ring on the ratios of
geometry, i.e. the 2:1 (a:b) bulkhead, experienced
critical buckling pressure was moderate for the
convergence problems for the majority of cases due to
hemispherical bulkhead, and very small for the
the instability of the bulkhead. Two cases that
hemiellipsoidal bulkheads. In the case of the
converged to a solution had a discrete ring size of 3.0
hemispherical bulkhead with a bulkhead thickness of
in.2and were therefore chosen for presentation here.
0.125-inch thickness, the critical buckling pressure
The mode shape corresponding to the critical
decreased by less than 1% between the 3.0 in.2and 1.0
bifurcation buckling load using nonlinear prebuckling
in.2 discrete ring cases; however, a 22% decrease
strains is given for the hemispherical, 1.414:1
occurred from the case with a discrete ring of 1.0in.2to
hemiellipsoidal, and 2:1 hemiellipsoidal bulkhead
the case with no ring. The effect the support ring
geometries in Figures 4,5, and 6, respectively. In
displayed on the critical buckling pressures for the
addition, each bulkhead displayed in Figures 4-6 had a
hemiellipsoidal bulkheads was almost negligible;
discrete ring area of 3.0 in.2and was 0.175-inches thick.
however, as mentioned earlier in the cases for the 2:1
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American Institute of Aeronautics and Astronautics
bulkheagdeometryth,e3.0in.2ringprovidedthe
smaller wave pattern some distance outward from the
necessasrtyiffnestsothemodetloallowBOSORt4o
first centralized wave along ameridian. Also, the mode
identiftyhecriticablucklinpgressurFe.urtheervidence
shape obtained using STAGS closely resembled the
ofthedifferenetffectsthesupporrtinghadonthe
bifftrcation buckling mode shape from BOSOR4 that
bucklinbgehavioforreachbulkheacdanbefoundin
was given in Figure 6 for the bulkhead with a shell
theircharacterisbtiuccklingresponsesA. snoted thickness of 0.175 inch and the same bulkhead
earlietrh,ehemispherbicuallkheahdadabucklemdode
geometry. The nonlinear solution for the bulkhead-only
shaptehatwaspredominanctolynfinetdotheedgeof
case required an initial analysis and three additional
thebulkhead.Thereforeth,atbulkheagdeometry
restart runs. The nonlinear analysis converged to a
appearetodbemuchmoresensitivteo changeins
critical load factor of 1.742 or critical buckling pressure
stiffnessin the regionnearthe bulkheadedge.
of 377 psi. A very good agreement between the
Whereatsh,ehemiellipsoidbaullkheadhsadbuckled
nonlinear BOSOR4 results for the optimum
modeshapetshatappearetodoccurmainlynearthe
configuration and the STAGS analyses was also shown
centeorfthebulkheawdhichmadethemrelatively
with approximately 8% difference between the two
insensititvoechangeinsstiffnesastthebulkheaeddge.
solutions. The nonlinear response, as shown in Figure
A choiceofbulkheasdhapeth,icknesasn,dring
8, was almost identical to the linear solution except the
sizewasselectebdaseodnthe"quasi-lineraers"ultfsor
second wave appeared to have slightly larger amplitude.
furtherevaluatiounsingBOSORa4ndSTAGS.As The results of the tank-bulkhead model are shown
describeedarlier,theconfiguratiownasprimarily
in Figure 9 as the linear buckling analysis produced a
chosebnaseodnthedesiretodeterminaeminimum
critical buckling pressure of 399 psi for this model.
heighatndweighetfficientatnkthatmettheapplicable
These results indicate that for the linear analysis the
marginsof safetyandwouldprovideanoptimum
influence of the boundary edge conditions appeared
vehicledesign.Thisresulteidnthechoiceofa2:1
negligible. However, the nonlinear analysis converged
hemiellipsoidbaullkheadshapewith a 0.21-inch
to a critical load factor of 1.631 or critical buckling
thicknesasndno supportring as the optimum
pressure of 353 psi. Figure 10 shows the nonlinear
configuratioUn.singBOSORa4d,ditionaanl alyseosf
response of the inverted tank-bulkhead model. The
thisconfiguratiownereperformeudsingboththe
nonlinear critical buckling pressure of the tank-
"quasi-lineaorp"tionandthenonlineaarnalysoisption.
bulkhead model was approximately 13% lower than the
Theeigenvaluceorresponditnogthe
"qnasi-linear" linear solution. These results indicate that the boundary
bifurcation buckling analysis was 1.825 and the critical constraint of the tank wall had some influence in
load factor for the nonlinear analysis of the chosen lowering the critical pressure of the bulkhead.
configuration was 1.602. The critical load factor from
the nonlinear analysis was obtained just prior to the Concludin_ Remarks
BOSOR4 code indicating axisymmetric collapse of the
The BOSOR4 analysis code is an efficient sizing
bulkhead that was similar to that found by Corona.
tool that is useful during the preliminary design phase
Thus, the convergence problems identified in some of
of a practical shell structure such as an inverted
the earlier cases using the 2:1 bulkhead were due to the
bulkhead for a propellant tank. Comparison of the
selection of bulkhead thicknesses that were incapable of
results between BOSOR4 and STAGS revealed a very
supporting the applied pressure load except for in a
good correlation between the two analysis methods. By
post-buckled configuration.
selecting three important bulkhead parameters, a
The linear buckling analysis from a linear prestress
reasonable amount of insight into the buckling response
solution using STAGS was determined for the
of the shell was obtained. Although the list of
bulkhead-only model by running an eigenvalue analysis
parameters and range of values are not comprehensive
at the operating pressure of 216 psi. A critical buckling
in this investigation, the amount of computer time that
pressure of 403 psi. was determined for the bulkhead
would be necessary to obtain the results for a
only model, which corresponds to a critical load factor
comprehensive preliminary design study for a vehicle
of 1.864 times the 216 psi. operating pressure. An
would not be unreasonable.
excellent agreement between the "qnasi-linear"
An inverted bulkhead geometry is an important
BOSOR4 results that were discussed earlier, but not
feature of a comprehensive tank optimization strategy
presented, and the linear STAGS results was shown
that can provide the design engineer with an additional
with approximately 2% difference between the two
configuration for minimizing vehicle weight. The
solutions. The corresponding mode shape, as shown in
results presented here have confirmed previous work in
Figure 7, consisted of one axisymmetric wave that was
this area by Corona and Ross, et al. while providing
localized in the center of the bulkhead and a much
6
American Institute of Aeronautics and Astronautics
additionainlformatioonnavarietyofconfigurations
Programs and Technologies Conference,
andboundareyffectsforhemiellipsoidbaullkheads. Huntsville, AL, September 21-23, 1993.
Howevears,mentioneedarlietrh,eeffectosfgeometric
imperfectioonnsthebehavioorfthestructuriensthis 4. Braun, R.D., Powell, R.W., Lepsch, R.A., and
studywerenotquantifieadndmayhaveasubstantial Stanley, D.O., "Multidisciplinary Optimization
impacotntheresults.Overalal, sufficienletvelof Strategies for Launch Vehicle Design," AIAA
correlatiohnasbeendemonstrabteedtweethnecurrent Paper No. 94-4341, 5th
analysitsoolsto providethedesignengineewrith AIAA/NASA/USAF/ISSMO Symposium on
enougchonfidenctoeusebulkheadthsatarestability Multidisciplinary Analysis and Optimization,
critical. Panama City Beach, FL, September 7-9, 1994.
Thebucklincgharacterizaotifoanninverteodb, late
5.
bulkhearedquirecsarefualttentioanssmalclhangeins Engelund, W.C., Stanley, D.O., McMillin, M.L.,
bulkheapdarametecrasnhavealargeeffectonthe and Unal, R., "Aerodynamic Configuration Design
Using Response Surface Methodology Analysis,"
criticablucklinlgoad.Forexamplteh,ebulkheawdith
AIAA Paper No. 93-3967, AIAA Aircraft Design,
majorto minoraxisratioof 2.0incurreda 56%
Systems, and Operations Meeting, Monterey, CA,
decreaisnethecriticablifftrcatiobnucklinpgressufroer
August 11-13, 1993.
a correspondin3g0%reductionin the bulkhead
thickness. Finally,sinceonly one bulkhead 6.
Finckenor, J.and Bevill, M., "CORSSTOL:
configurationwas examinedclosely, fftrther
Cylinder Optimization of Rings, Skin, and
characterizatisiownarrantedA.reasofconcertnhat
Stringers with Tolerance Sensitivity," NASA TP-
mayprovidesignificanitnsightaretheeffectof
3551, May 1995.
laminatceonstructioontherthanquasi-isotropaicn,d
theeffectofusinga tailoredthicknesosr stiffness 7.
Sisk, D.B., "Low Profile Bulkheads for Launch
profile. Vehicle Propellant Tanks An Optimum System
Solution," AIAA Paper No. 93-4223, AIAA Space
Acknowledgements Programs and Technologies Conference and
Exhibit, Huntsville, AL, September 21-23, 1993.
We would like to express our appreciation and
gratitude to Dave Bushnell of LMSC for his guidance 8. Wu, K. C.and Lepsch, R. A., "Nontangent,
and suggestions for modeling and executing solution Developed Contour Bulkheads for a Wing-Body
techniques using BOSOR4. We would also like to Single Stage Launch Vehicle," AIAA Paper No.
thank Richard Young and Mark Hilburger of NASA 99-0835, 37thAIAA Aerospace Sciences Meeting
Langley Research Center for their valuable technical and Exhibit, Reno, NV, January 11-14, 1999.
discussions that provided additional insight into the
buckling of shell structures. 9. Corona E., "Dome Reversal ofMetal Beverage
Containers," J. of Pressure Vessel Tech., 120-4,
References November 1998, pp. 456-461.
1. Freeman, D.C., Wilhite, A.W., and Taley, T.A., 10. Budiansky, B., "Buckling of Clamped Shallow
"Advanced Manned Launch System Study Status," Symmetrical Shells," Proc. of lUTAM symposium
IAF Paper No. 91-193, 42ndCongress of the on the Theory ofThin Elastic Shells, Delft, The
International Astronautical Federation, Montreal, Netherlands, 1959, pp. 64-94.
Canada, 1991.
11. Hutchinson, J.W., "Imperfections Sensitivity of
2. Wurster, K.E., Rowell, L.F., and Peach, L.L., "The Externally Pressurized Spherical Shells," J. of
Next Generation Manned Launch System A Applied Mechanics, 89, 1967, pp. 49-55.
Complex Decision," AIAA Paper No. 93-4160,
AIAA Space Programs and Technologies 12. Kaplan, A. and Fung, Y.C., "A Nonlinear Theory
Conference, Huntsville, AL, September 21-23, of Bending and Buckling of Thin Elastic Shallow
1993. Spherical Shells," NACA TN-3212, 1954.
3. Eldred, C.H., Powell, R.W., and Stanley, D.O., 13. Homewood, R.C., Brine, A.C., and Johnson, A.E.,
"Single Stage Rocket Options for Future Launch "Experimental Investigation of the Buckling
Vehicles," AIAA Paper No. 93-4162, AIAA Space Instability of Monocoque Shells," Proc. of the
7
American Institute of Aeronautics and Astronautics
Society for Experimental Stress Analysis, 18, 1961,
pp. 88-96. 20. Lu, Z., "Imperfection Sensitivity of Elastic and
Elastic-Plastic Torispherical Pressure Vessel
14. Jones, E.O., "The Effects of External Pressure on Heads," Thin-Walled Structures', 23, 1995, pp. 21-
Thin-Shell Pressure Vessel Heads," ASME J. of 39.
Engineering for Industry, 84, 1962, pp. 205-219.
21. Ross, C.T.F. and Johns, T., "Dynamic Buckling of
15. Huang, N.C., "Unsymmetrical Buckling of Thin Thin-Walled Domes Under External Water
Shallow Spherical Shells," J. ofApplied Pressure," Res Mechanica, 28, 1989, pp. 113-137.
Mechanics, 31, 1964, pp. 447-457.
22. Hilburger, M. H. and Starnes, J. H., Jr., "High-
16. Galletly, G.D., Blachut, J., and Kruzelecki, J., fidelity Analysis of Compression-loaded
"Plastic Buckling of Imperfect Hemispherical Composite Shells," AIAA Paper No. 2001-1394,
Shells Subjected to External Pressure," Proc. of the Proceedings of the 42nd
Institution ofMechanical Engineers', 201-C3, 1987, AIAA/ASME/ASCE/AHS/ASC Structures,
pp. 153-170. Structural Dynamics, and Materials Conference,
Seattle, WA, 2001.
17. Blachut, J., Galletly, G.D., and Moreton, D.N.,
"Buckling of Near-Perfect Steel Torispherical and 23. Bushnell, D., "Stress, Stability, and Vibration of
Hemispherical Shells Subjected to External Complex Branched Shells of Revolution
Pressure,"AIAA J., 28, 1990, pp. 1971-1975. Analysis and User's Manual for BOSOR4," NASA
CR-2116, October 1972.
18. Blachut, J.and Galletly, G.D., "Clamped
Torispherical Shells Under External Pressure 24. Rankin, C.C., Brogan, F.A., Loden, W.A., and
Some New Results," J. Strain Analysis, 23, 1988, Cabiness, H.D., "STAGS User Manual," Lockheed
pp. 9-24. Martin Missiles and Space Co., Palo Alto, CA,
October 1998.
19. Blachut, J,"Buckling of Sharp Knuckle
Torispheres Under External Pressure," Thin-Walled
Structures, 30, 1998, pp. 55-77.
Table 1. In-plane laminate material properties for the cylinder and bulkhead shell walls at 423°F
Young's Modulus of Elasticity (Exand Ev), Msi 8.77
Shear Modulus (Gxv), Msi 3.76
Poisson's Ratio (Vxv) 0.299
Table 2. Minimum, intermediate, and maximum values used to define the bulkhead configurations for the
BOSOR4 analyses
Bulkhead shape Bulkhead thickness Ring area
(a/b) (in.) (in.2)
1.00 0.125, 0.175, 0.250 0.00, 1.00, 3.00
1.414 0.125, 0.175, 0.250 0.00, 1.00, 3.00
2.00 0.125, 0.175, 0.250 0.00, 1.00, 3.00
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American Institute of Aeronautics and Astronautics
\T/
Conventional
bulkhead
P Inverted
bulkhead
Figure 1.Cross-section of a propellant tank with conventional and inverted bulkhead geometries.
A
Node 97
z I
I
I
Inverted /_
Node 1 Segment 2
I
i Segment 1 s
Cylinder
I
wall
Tank internal ! •
pressure I r Node 1
I
I
a) Description of the cylinder and inverted b) Model displaying nodes along the reference
bulkhead geometry surfaces
Figure 2. Structural definition for BOSOR4 analyses.
9
American Institute of Aeronautics and Astronautics
1.0
a/b = 2.0
a/b = 1.414
" l
0.8
Poper
%
0.6
a/b = 1.0 _
- .%
0.4
0.2 ---.-__.._._
---_____
, I , I , I , I , I , I
0
0.1 0.125 0.15 0.175 0.2 0.225 0.25
Bulkhead thickness (in.)
Figure 3. Ratio of operating pressure to critical buckling pressure results from the BOSOR4 models as a
function ofbulkhead thickness for aring area of 3.0.
20
Deformed bulkhead
15 geometry
Axial 10
station wall
(in.) 5
0
-5
-10
0 5 10 15 20 25 30
Radius (in.)
Figure 4. Bulkhead mode shape from BOSOR4 linear analysis corresponding to the critical buckling
pressure of 980 psi. with ahemispherical geometry and 0.175-inch shell thickness.
10
American Institute of Aeronautics and Astronautics