NASA-AIAA-Analysis Design and Optimization of Non Cylindrical Fuselage for Blended Wing Body Vehicle

0American Institute of Aeronautics and Astronautics

AIAA 2002-5664Analysis Design and Optimization ofNon-cylindrical Fuselage forBlended-Wing-Body (BWB) Vehicle

V. Mukhopadhyay, J. Sobieszczanski-SobieskiNASA Langley, Hampton, VAI. Kosaka, G. Quinn and C. Charpentier,Vanderplaats R&D Inc., Colorado Springs, CO

9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization

September 4-6, 2002Atlanta, GA

For permission to copy or to republish, write to American Institute of Aeronautics and Astronautics,1801 Alexander Bell Drive, Suite 500, Reston VA 20191-4344


AIAA 2002-5664ANALYSIS, DESIGN AND OPTIMIZATION OF NON-CYLINDRICAL

FUSELAGE FOR BLENDED-WING-BODY (BWB) VEHICLE

V. Mukhopadhyay*, J. Sobieszczanski-Sobieski**NASA Langley Research Center, Hampton, VA

I. Kosaka, G. Quinn and C. Charpentier,Vanderplaats R&D Inc. Colorado Springs, CO

AbstractInitial results of an investigation towards finding anefficient non-cylindrical fuselage configuration for aconceptual blended-wing-body flight vehicle werepresented. A simplified 2-D beam column analysisand optimization was performed first. Then a set ofdetailed finite element models of deep sandwichpanel and ribbed shell construction concepts wereanalyzed and optimized. Generally these conceptswith flat surfaces were found to be structurallyinefficient to withstand internal pressure andresultant compressive loads simultaneously.Alternatively, a set of multi-bubble fuselageconfiguration concepts were developed for balancinginternal cabin pressure load efficiently, throughmembrane stress in inner-stiffened shell and inter-cabin walls. An outer-ribbed shell was designed toprevent buckling due to external resultantcompressive loads. Initial results from finiteelement analysis appear to be promising. Theseconcepts should be developed further to exploittheir inherent structurally efficiency.

Introduction In revolutionary Blended-Wing-Body (BWB) mega-transport concepts1,2 with non-cylindrical lifting-body fuselage and in conformal shaped propellanttanks of reusable launch vehicles3, the pressurizedstructure must be designed to resist internalpressure and compression due to overall bending.These loads combine in a nonlinear manner toinduce severe deformation, and high stresses, thatmight necessitate significant structural weightpenalty. In addition, resulting deformation ofaerodynamic surface could significantly affectperformance advantages provided by lifting body.This problem was investigated for Airbus typeelliptic-section composite fuselage as well as forBWB and X33 with special sandwich compositeskin and metal honeycomb core.1,3,5 • In previousBWB studies,6,7 effects of cabin shape, and volumewere investigated, from a baseline configurationusing an aerodynamic based optimization scheme,but structural design with internal pressure or

• Associate Fellow, **Fellow, AIAA

buckling issues were not addressed. In anotherconceptual structural analysis5, several promisingnon-cylindrical fuselage configurations wereidentified but no optimization study was conducted.

This paper presents additional sizing,analysis, design and optimization results towardsfinding an efficient non-cylindrical BWBconfiguration, considering both internal pressureand compressive load including buckling stability.Initially four idealized deep sandwich and ribbedshell configurations were analyzed and optimizedwith stress and buckling constraints. These panelsrepresented a critical upper surface panel section, asshown in Fig. 1.

S4S3

S2

S1

S5

Y(Span-wise)

X(Chordwise)

A B

C DA

C

B

D

Span-wiseVaulted

C

B

D

X

Y(Span-wise)

Z

Pressure

A

Span-wiseCatenary

Chord-wiseVaulted

Flat Panel

Curved Panel

HighCompression

Curved Panel

HighCompression

S4S3

S2

S1

S5

Y(Span-wise)

X(Chordwise)

A B

C DA

C

B

D

A

C

B

D

Span-wiseVaulted

C

B

D

X

Y(Span-wise)

Z

X

Y(Span-wise)

Z

Pressure

A

Span-wiseCatenary

Chord-wiseVaulted

Flat Panel

Curved Panel

HighCompression

Curved Panel

HighCompression

Fig. 1 Conceptual configurations of flat and curvedtop surface panel

In an alternative approach, several multi-bubblestiffened fuselage section concepts were developed.This special configuration resists internal pressureload through membrane stress balance, whileresisting bending and compression load with anouter stiffened ribbed shell. The multi-bubbleconcept was then refined further, to meet criticaldesign requirements with minimal weightincrement.

The knowledge gained in this conceptualdesign study would provide the designers withoptions to make BWB revolutionary concept bothstructurally feasible and aerodynamically efficient.This could also give BWB development acompetitive advantage over the Airbus8 A380 in the


lucrative 500-800 passenger long range travelmarkets.

2-D Beam-Column AnalysisSome initial sizing, stress and deflections wereestimated using analytical nonlinear beam-columnsolutions9 for a 2-D simply-supported beamrepresenting a simplified cabin roof that acts as asurface of a pressure vessel and as a compressedflange of a beam in bending. Maximum deflectionzmax, bending moment Mmax and stress max at midspan for simply-supported boundary condition aregiven by Eqs. (1-3).

zmax = 5pr.l 4

384EI

12(2sec − 2 − 2 )

5 4 (1)

Mmax =pr.l2

8+

5 pr.l 4

384 EI

12(2sec − 2 − 2 )

5 4 P(2)

max = Mmaxd

2I+ P

2Wt (3)

where Pcr = 2EI / l2 and =2

P

Pcr

l

t

tP P

prHere P denotes distributed axial compressive load,pr denotes transverse cabin pressure load, I denotesbending moment of inertia, E denotes Young'smodulus and l denotes column length as shown inthe sketch. Note that stresses and deflections fromEqs.(1-2) diverge as P approaches criticalcompressive buckling load Pcr. Let us assume

I=0.5tw(d-t)2, where d is beam depth, t is thicknessof top and bottom flange or face sheet and w is unitwidth. Initially let us assume face skin thicknesst=0.006 meter, beam depth d=0.15 meter, beamlength l=3.5 meter, transverse pressure pr=84830Pascals (12.3 pounds per square inch) and axialcompressive load P= 165,000 kg/meter. The facesheet material of the sandwich was assumed to bealuminum AL7075-T6 with Young's modulusE=7.1x1010 Pascals, allowable stressesFtu=5.24E+8 Pascals, Fty=4.55E+8Pascals andFcy=4.62E+8 Pascals.

The resulting buckling load ratio P/Pcrwas close to 0.4. The non-dimensional mid-spandeflection ratio Zmax/d, maximum compressivestress ratio max/Yield stress Fcy and maximumbending moment ratio Mmax/(prl2/8) variation with

P/Pcr are shown in Figs. 2a-c. Figs.2a,b indicatethat, for P/Pcr=0.4, mid-span deflection is about40% of beam depth, and maximum combinedcompressive stress max is about 80% of theallowable compressive yield stress Fcy.

0 0.1 0.2 0.3 0.4 0.50.2

0.3

0.4

0.5

Zmax P( )

d

P

Pcr

Max deflection/beam depth vs P/Pcr

0 0.1 0.2 0.3 0.4 0.50.2

0.4

0.6

0.8

σmax P( )

Fcy

P

Pcr

Maximum Stress/Yield Stress vs. P/Pcr

0 0.1 0.2 0.3 0.4 0.51

1.5

2

2.5

Mmax P( ) 8?

pr l2?

P

Pcr

MAXIMUM BENDING MOMENT/(pr.l 2/8) vs. P/Pcr

pagFigs. 2a-c. Mid-span deflection Zmax/beam depth,maximum compressive stress ratio max/Fcy andmaximum bending moment ratio Mmax/(pr.l2/8)variations with axial compressive load P/Pcr for anidealized simply-supported beam-column.

Fig.2c shows that for this beam-column,additional bending moment caused by beamdeflection is almost 40% of that due to transversepressure load alone. The top and bottom flange or


skin panel weighs about 36 kg/sq meter, and thehoneycomb core weighs 6.4 kg/sq.meter. A quickspreadsheet based weight optimization wasperformed with beam depth and skin thickness asdesign variables and P/Pcr < 0.66, Zmax/d < 1 and

max/Fcy < 1 as constraints. Results are presentedin Table 1. The unit weight ratio was reduced to 38kg/sq meter by increasing d to 0.026 meter andreducing t to 0.0045 meters.

This simple but conservative non-linearanalysis and optimization was used for sizing thethree dimensional concepts. This also illustrates theweight penalty and high stress problem associatedwith resisting normal pressure by bending stress. Inthis beam of length l, bending stress isproportional to (pr.l2)/(d.t) while in a cylindricalpressure vessel of radius R , resulting membranestress is proportional to (pr.R/t). Assuming R is ofsame order as l, the beam has much higher stressand is consequently much heavier. The problem isaggravated by the non-linear effect of compressiveload acting on the deflected beam or plate. So inorder to obtain an efficient structure, one mustincrease the bending stiffness using deep sandwichshell with light weight high-strength compositeskin and honeycomb core. This investigation isdescribed next.

Panel FEM AnalysisFour idealized top fuselage surface composite panelconfigurations were analyzed and optimized forminimum weight, under internal pressure andestimated compressive loads with both stress andbuckling constraints. These finite element analysesand optimization were done using a tool describedin Ref 10.

Fig. 1 shows possible location of thiscritical top surface panel on a BWB plan-form.These four panel configurations, namely, a) FlatHoneycomb sandwich panel: b) Flat Double skincross-ribbed panel c) Flat honeycomb panel withspan-wise catenary and d) Span-wise vaulted shellwith rod stiffeners are shown in Figs. 3a-3d,respectively. Estimates of design loads at 2.5gflight condition were obtained from previous BWBanalyses1,2. In addition to internal cabin pressureload of 84830 Pascals, these panels were subjectedto an estimated resultant span-wise compressiveload of 165,000 Kg/meter and a chord-wise tensileload of 12500 Kg/meter. An orthotropic graphite-epoxy composite material was used for the skin andaluminum honeycomb was used for the sandwichcore1,2,5 . Two sets of approximate boundaryconditions were used, as shown in Figs. 3a and 3drespectively. Rigid elements were used at someedges for compatibility. Edge elements at boundarywere excluded for stress constraint evaluation to

prevent local stresses from applied boundaryconditions from driving the design.

A

C

B

D

uz = 0

uz = 0ux = 0

uy = 0uz = 0

Free

Excluded regionfrom constraint

3a. Flat Honeycomb sandwich panel showing firstset of boundary conditions:

3b. Flat Double-skin cross ribbed panel

3c. Flat honeycomb panel with span-wise catenary

HA

C

B

D

uz = 0

uz = 0ux = 0

uz = 0

ux = 0

3d. Span-wise vaulted shell with bar stiffener,showing second set of boundary conditions.

Figs. 3a-3d. Four idealized panel configurations.

Flat Honeycomb sandwich panel :A baseline graphite-epoxy composite sandwich3.5x3.8 meter rectangular panel with 0.003 meterthick top and bottom skin and a honeycomb corewas first considered. The panel depth and skinthickness were treated as design variables. Thebaseline panel weight was about 15.3 kg/sq. meter.The constrained optimized weight with first set ofboundary conditions increased to 28.5 kg/sq. meter.With second set of boundary conditions, optimized


weight was close to 24.5 kg/sq. meter. A summaryof result is presented in Table 1.

Lower Bound for Rib Thickness

Negative Value IndicatesPanel Depth is Growing

Bottom Skin Thickness

Chordwise and SpanwiseRib Thickness

Design Cycle

Design Cycle

Panel Depth

Design Variables

Fig. 4 Design variable history from initial resultsof a flat double-skin ribbed panel optimization withonly stress constraints and pressure load.

Flat Double-skin ribbed panel:A baseline double-skin cross-ribbed panel of samedimension was also analyzed, as an alternative tothick honeycomb panel. The panel depth, web andskin thickness were treated as design variables. Thebaseline graphite epoxy ribbed panel weight wasabout 13.5 kg/sq. meter with14 chord-wise ribs and16 span-wise ribs at 0.25 meters interval. Based onsimple plate buckling analysis12-14, span-wise andchord-wise cross-rib spacing was determined toprevent local panel buckling. Fig. 4 shows initialresults of this double-skin ribbed paneloptimization with only internal pressure load andstress constraints. The optimizer tended to increasethe lower skin thickness and panel depth, whilereducing the span-wise and chord-wise ribthickness. This resulted in marginal reduction ofweight by about 18%.

However, with both stress and bucklingconstraints, under the estimated compressive load,the skin thickness increased significantly afteroptimization. Consequently, the weight (objectivefunction) of the optimized panel with first set ofboundary condition actually increases by over 240%as shown in Fig. 5. With second set of boundarycondition, and edge elements excluded, the resultswere somewhat reasonable. Optimized panel weightwas 25.6 kg/sq meters. The fine mesh FEM modelexhibited many lower local plate buckling modes,due to the manner in which the compressive loadswere applied at nodes, to represent the bending

loads approximately. Hence, a course mesh wasused to capture overall panel buckling modes foroptimization purposes.

Objective function

Maximum Constraint Violation (%)

Maximumconstraint

violation (%)

NormalizedWeight

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Design Cycle

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15Design Cycle

3.5

3.0

2.5

2.0

1.5

1.0

200

160

120

80

40

0

Fig. 5 Objective function and constraint violationhistory from initial results of a double-skin ribbedpanel optimization under both stress and bucklingconstraints with combined compressive andpressure loads.

Flat Honeycomb panel with catenary cable :A catenary cable support system with vertical rodconnections to the honeycomb panel was used toreduce deflection, much like a suspension bridge, asshown in Fig. 3c. However, optimization resultswere similar to the previous cases. Catenary cableswere marginally beneficial for reducing lower skinthickness assuming that the deflections and loadskeep the cable system in tension.

Span-wise vaulted shell with rod stiffener :This concept used a span-wise vaulted shell tocontain pressure efficiently. Three span-wise barelements were added for increasing bucklingstiffness, as shown in Fig. 3d. Spanwise vaultingalso increases stiffness to compressive load, thus itrequired less skin thickness but exhibited higherdeflections.

The optimization results and weightestimates shown in Table 1 were not surprising andwere consistent with the 2-D non-linear beam-column analysis from Eq.(1-3) and with earlierdesign results presented in Ref. 5. Thus it becameapparent that inner cylindrical segments of fuselagewere necessary in order to contain pressureefficiently through membrane stress. Themembrane in-plane forces at the fuselage junction


could be symmetrically balanced in tension usingthe inter-cabin wall, thus avoiding major bendingstresses at the junction. Thus, the outer super-structure at the top and bottom part of the fuselagecould be used to resist the span-wise bending load,yet retain aerodynamic shape and smoothness. Thisled to the design of a set of multi-bubble structuralconcept, as described next.

Conventional FuselageA number of stiffened aluminum fuselageconfigurations shown in Figs. 6-9 were initiallyanalyzed, for acceptable stress and deflection with127530 pascals (18.6 psi) internal pressure loadsonly. These finite element models were developedin-house and analyzed using a tool described in Ref.11. An idealized Airbus A380 elliptic-sectionfuselage and a baseline cylindrical section fuselagewith hoop stiffeners, shown in Figs 6-7, were firstanalyzed for comparison purposes.

Elliptic section fuselage :A 10 meters long section with 3 floors, as

shown in Fig. 6, was analyzed first, in order tocompare cylindrical versus elliptic section fuselagestrength characteristics under internal pressure. The8.5 meters high, 7m wide Airbus A380 typestiffened elliptic section, shown in Fig. 6, wasstiffened with 21 ring stiffeners, each 0.1 meterdeep at 0.5 meter interval. Thickness of skin andring stiffeners were assumed to be 0.003 meters.These values are generally typical for commercialtransport aircraft12,14. Maximum displacement fromthe FEM analysis was about 0.153 meters at topand bottom of the fuselage. The resulting nodalVon-Mises stresses at the shell element top surfaceare shown in Fig. 6. Average Von-mises stress onthe skin was of the order 3.5E+8 pascals which is2.1 times the ideal hoop stress pr.D/2t. Nobuckling analysis was done. FEM weight of thissection was 3828 kg with total floor area of 177 sq.meters.

Von-mises nodal stress,Pascals (0.000145 psi)

1.29 E+9

9.67 E+8

6.47 E+8

3.27 E+8

6.98 E+6

Fig. 6 A380 type 8.5mx7mstiffened elliptic sectionfuselage: Element Von-Mises stresses due to127530 Pascals (18.6 psi) internal pressure.

Von-mises nodal stress,Pascals

4.71 E+8

3.54 E+8

2.36 E+8

1.18 E+8

8.83 E+5

Fig. 7 Baseline stiffened cylindrical fuselage: 7.75meter s diameter: Nodal Von-Mises stress due to127530 pascals (18.6 psi) internal pressure.

Baseline cylindrical section fuselage :The cylindrical section with 7.75 meters diameter,shown in Fig. 7, had same circumference as theelliptic section. It was also stiffened with ringstiffeners, each 0.1 meter deep, at 0.5 metersinterval. Thickness of skin and ring stiffeners wasassumed to be 0.003 meters. This cylindricalsection fuselage was also subjected to 127530Pascals internal pressure. Maximum displacementswere of the order 0.035 meters. The resulting nodalVon-Mises stresses at the shell element top surfaceare shown in Fig. 7. Average Von-Mises stress onthe skin was of the order 2.6E+8 Pascals which isabout 1.5 times the ideal hoop stress given bypr.D/2t. No buckling analysis was done. FEMweight of this section was 3943 kg with total floorarea of 192 sq. meters. For this cylindrical section,FEM stresses were significantly lower, and hadhigher floor area, although net weight was slightlyhigher.

Multi-bubble FuselageBased on the lessons learned from these analyses, 3-floor load-balanced multi-bubble stiffened-shellpressure vessel concepts were developed. Diametersof the cylindrical segments were almost same as thecylindrical segment previously described. In thisdesign the two merging bubble-sections meet withthe inter-cabin vertical wall at an angle, so thatsurface in-plane membrane forces are in self-equilibrium12. Thus in an ideal case, the resultingmembrane stresses on the cylindrical section skinare balanced by tension in the inter-cabin walls.This geometrical arrangement could reduce unduebending at these joints, thereby preserving theadvantage of a cylindrical section fuselage, underinternal cabin pressure. This special geometryresults in 3-floor multi-aisle fuselage, each 5.8meters wide. In this and subsequent FEM models,


cylindrical skin segments were stiffened with 10 cmdeep ring stiffeners, that were modeled by beam3delements. These I beam stiffeners, with 5 cm wideflange, 10 cm deep web and 3mm thick flange andweb, were used at 0.5 meter chord-wise interval onall cylindrical surfaces, inter-cabin walls and floors.These values are generally typical for commercialtransport aircrafts12,14.

Four-bubble Fuselage:This force-balanced bubble concept was examinedfor double and triple bubble configurations and thenextended to a four-bubble 3-floor concept withadditional outer stiffened double panels, at top andbottom of the fuselage. These outer panels initiallyconsisted of two stiffened shells 25 cm apart andwere supported by the cylindrical inner fuselagesections at midpoint. These outer shells were notconnected to the inter-cabin vertical walls directly,as shown in Fig. 8, at top. The outer shell wasadded to provide bending and buckling stiffness tospan-wise bending loads that were not considered inthe double- and triple-bubble concepts. This modelwas subjected to the standard 84835 pascals internalcabin pressure as load case 1. For load case 2, topstiffened panels were subjected to 164350 kg/meterspan-wise compressive loads. Equal and oppositetensile loads were applied at bottom panels, torepresent an equivalent maximum estimatedbending moment.

Figure 8 shows element nodal Von-Mises stress attop due to 84835 Pascals internal cabin pressureand 164350 kg/meter span-wise compressive loadon top panel and equal tensile load at bottom panel.Maximum displacement was of the order 0.05meter. Skin thickness was assumed to be 0.003meters except for that of outer double wall whichwas 0.005 meters. Total weight of this section(8.25m high, 19.325m wide, 5m long) was about11000 kg. Buckling safety factor was not satisfiedfor assumed boundary condition. To increasebuckling stiffness, cross ribs were later added (Fig.8) to the outer double walls at 0.25 meterschordwise interval and 0.18 meters spanwiseinterval. FEM weight was 13100 kg with crossribs. Total floor area was 267 sq. meters. Bucklingsafety factor was about 1.0 for the compressiveload. However undesirable lower local buckingmodes of the cargo floor panel for reversed loadingwere present. Overall, this design was better butnot satisfactory.

2.50 E+8

1.88 E+8

1.24 E+8

6.22 E+7

0.0

Von-Miseselement stress, Pascals(0.000145 psi)

2.50 E+8

1.88 E+8

1.24 E+8

6.22 E+7

0.0

Von-Miseselement stress, Pascals(0.000145 psi)

Fig. 8 Four-bubble fuselage concept: Elementnodal Von-Mises stress at top due to 84835 pascals(12.3 psi) internal cabin pressure and 164350kg/meter (9200 lbs/in) span-wise compressive loadon top panel and equal tensile load at bottom panel.

Five-bubble double-wall fuselage: The five-bubble configuration, shown in Fig. 9was conceived and analyzed with internal designpressure loads, as well as with estimated equivalentcompressive loads on top panels (and equal tensileload on bottom panels) due to fuselage bending, inorder to obtain acceptable stress, deflection andbuckling stability safety factor. Based on platebuckling analysis13,14 the top and bottom doublewall depth was chosen as 0.15 meter with 0.003meter thick span-wise running ribs at 0.25 meterinterval. Radius of inner cabin vaulted ceiling werereduced from 3.875m to 3.75 meters. Radius of theouter cabin was calculated to be 3.248 meters inorder to get approximate membrane stressequilibrium at outboard joints. Additional span-wise running tie-rods were also used at the top andbottom of the cabin. Since only half the fuselagewas modeled, symmetric clamped boundaryconditions were assumed at the plane of symmetry.


8.68 meters

8.2 meters

3.75 R meters

3.25 Rmeters

Fig. 9 Five-bubble fuselage with ribbed outerdouble-wall: Force-balanced stiffened fuselageconcept

Von-Mises element stress, Pascals (0.000145 psi)

1.75 E+8

1.30 E+8

8.73 E+7

4.36 E+7

0.0

Von-Mises element stress, Pascals (0.000145 psi)

1.75 E+8

1.30 E+8

8.73 E+7

4.36 E+7

0.0

Fig. 10 Five-bubble fuselage with ribbed outer-wall: Element nodal Von-Mises stress distributionat top surface due to 84835 pascals internal cabinpressure and 164350 kg/meter span-wisecompressive load on top panel and equal tensileload at bottom panel.

Initial results of the redesigned multi-bubblefuselage appear to be interesting. Maximumdisplacements were of the order 0.018 meters at theouter cabin walls and inside vaulted ceiling mid-span. Figure 10 shows Von-mises stressdistribution at element nodes computed on topsurface due to combined internal cabin pressure andspan-wise compressive load on top panel and equaltensile load at bottom panel. These stresses werewell within allowable limits and about 25% lowerthan the four-bubble design with about 10%increase in unit weight/floor area. Buckling safetyfactor for pressure alone was –1.0, indicatingcylindrical shell buckling for a reversed pressuredirection. With this cross-ribbed outer wall design,

which was similar to those of the panel shown inFig. 3b, buckling safety factors with the designcompressive load were satisfactory. However, thefine mesh FEM model exhibited many lower localplate buckling modes, due to the manner in whichthe compressive forces were applied at nodes, torepresent bending loads approximately. Thevertical supports between outer double-wall andvertical cabin walls exhibited many lower localpanel buckling modes with buckling safety factorsstarting from 0.7 to 1.95 for the first 20 modes.The total weight of this half FEM model was about5176 kg with a floor area of 115 sq. meters.

Unit Weight Comparison

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10

Fuselage Concepts

lb/sq

ft f

loor

are

a

5-Bubble 17.2m

4-Bubble-19.3m

HH

C P

anel

3-Bubble-15.5m

2-Bubble-11.6m

Elliptic

Cylinder

Bay3 V

LRS

Bay3 V

HH

C

Bay3 F

HH

C

Relative Unit Weight Comparison

With Bucklingload

WithoutBucklingload

BWBBay 3

Fig.11 Relative FEM weight per unit floor area.

Unit Weight comparison It would be difficult to make a fair comparison ofdifferent concepts that were analyzed due to the factthat each concept was a different model of aparticular component of the fuselage with their ownrepresentative loading and boundary conditions, anddid not include wing structure or other superstructures. However, an initial attempt was made toestimate the fuselage component unit FEM weightper unit payload floor area and observe the trend.Summary of this comparison is shown in Fig. 11.

These relative unit weights were computedas ratio of total finite element weight of thestructure divided by floor areas inside the fuselagesection. First three concepts labeled BWB Bay–3weights of vaulted shell with heavy honeycomb(VHHC); flat sandwich shell with heavyhoneycomb core (FHHC); and vaulted ribbed shell(VLRS) also included side walls, front and rearpressurized spar of similar construction5. It shouldbe noted that these previous designs were notoptimized or analyzed for buckling stability,although sizing was done using 2-D nonlinearbeam-column analysis similar to that describedearlier in the paper.


For all the cylindrical, elliptic and 2-bubble and 3-bubble concepts, the total FEMweight was divided by floor area that included twopassenger floor and one cargo floor, in order toobtain the unit weight ratio. Unlike previous BWBbay-3 analysis, weights did not include pressurebulkhead. For the case heavy honeycomb corerectangular (HHC) panel described earlier in Fig.3a, FEM based weight was multiplied by 2 toaccount for bottom panel, floor, side walls orpressure bearing spar for an approximate equitablecomparison. This modified weight was simplydivided by panel area to get the unit weight ratioshown in the figure. These estimates appearconsistent with that of FHHC case studiedpreviously5. As a rule of thumb, FEM basedweights are generally 40-50% lower than an actualfabricated structure. However, this unit weightcomparison confirm two previously knownhypothesis, and provide some quantitative values,namely: 1) The multi-bubble non-cylindricalpressure vessel configurations appear to be twice asinefficient compared to cylindrical structure, and, 2)Proper integration of partially cylindrical surfacesin pressurized fuselage design could reduce theoverall weight by about 20-30% compared to usingall flat surfaces.

Conclusions A set of structural concepts for pressurized fuselageof blended-wing-body type flight vehicles werepresented. A multi-bubble fuselage configurationconcept was developed for balancing internal cabinpressure load efficiently, through balancedmembrane stress in inner cylindrical segment shellsand inter-cabin walls. In order to provide bucklingstability and carry span-wise bending loads,additional cross-ribbed outer shell structure appearto be quite effective. Thus, it was advantageous touse the inner cylindrical shells for pressurecontainment and let the outer shells resist overallbending. This decoupling may enable bothcomponents to stay in a membrane state of stress,with minimal bending. The duct-space betweeninner- and outer-shell could be used for a directventilation system with potential weight and powersavings. However, in case of a cabin pressure leakduring flight, the outer ribbed shell was strongenough to withstand operational cabin pressure,thus providing adequate redundancy. Additionalsafeguard in this regard could be provided byventing the duct space through pressure valves.Nevertheless, further studies for refinement andoptimization of these concepts are necessary, forgaining acceptance by the industry.

AcknowledgementThe authors wish to thank Dr. Dennis Bushnell forfunding this project through his ‘Creativity andInnovation’ Initiative. Thanks are also due to Drs.Robert Liebeck and Sean Wakayama of BoeingCompany and Dr. Gary Vanderplaats of VR&D Inc.for their insight and critique.

References 1Liebeck, R. H. "Configuration Control DocumentCCD-3: Blended Wing Body:" Final report UnderContract NAS1-20275 NASA Langley ResearchCenter, Oct. 1, 1997.2Liebeck, R. H., Page, M. A., and Rawdon, B. K.“Blended-Wing-Body Subsonic CommercialTransport.” AIAA Paper 98-0438, Jan. 1998.3Dorsey, J., et. al., 'Airframe Integration TradeStudies for a Reusable Launch Vehicle,' Paper No.247, Space Technology & Application Forum,Albuquerque, NM, Jan. 31-Feb. 4, 1999.4Hitch, H. P. Y., " Pressure Cabins Of EllipticCross Section," Aeronautical Journal, Vol. 92 No.916 Jun-Jul. 1988, pp. 207-223.5Mukhopadhyay, V., 'Structural Concepts Study ofNon-circular Fuselage Configurations,' Paper No.AIAA SAE WAC-67, World Aviation Congress,Los Angeles, Calif. Oct. 22-24, 1996.6Wakayama, S. and Kroo, I., “The Challenge andPromise of Blended-Wing-Body Optimization.”AIAA Paper 98-4736, Sept. 1998.7Smith, H., et al. “Blended Wing Body Airliner:Air Vehicle Design," Cranfield University, Webpage, http://www.wing.cranfield.ac.uk/ . 19998Morrocco, J. D. and Flottau, J., "Europe SeeksGlobal Leadership in Aeronautics," Aviation Weekand Space Technology, February 5, 2001, pp. 30-31.9Timoshenko, S. P. and Gere, J. M., "Theory ofElastic Stability, " McGraw Hill Book Co., NewYork, 1961, pp. 1-11.10GENESIS V6.0: Structural Analysis andOptimization, Vol. I Overview, Vol.2 Reference,Vanderplaats R&D Inc. January 2000.11COSMOS/M Basic FEA System User's Guide,Structural research and Analysis Corporation, SantaMonica, CA, 1993.12Bruhn,E. F., “Analysis and Design of Flightvehicle Structures,” Tri State Offset Co., 1965,pp.A16.1-A16.9 and pp.C11.29-C12.5113Young, Y. C.,”Roark’s Formulas for Stress andStrain, McGraw Hill Ed.6, 1989, pp.515-64314Niu, M. C. Y., "Airframe Structural Design,"Conmilit Press Ltd., Hong Kong, 1993, pp. 376-428.


Table 1. Summary of results from the 2-D beam column and 3-D panel finite element analysis and optimization.

Concept Initial optimizeddepth skin t P/Pcr wt/area depth skin P/Pcr wt/area max disp materialmeters meters meters kg/sq.m meters meters meters kg/sq.m meters

2D HC Beam 0.150 0.006 0.40 42.44 0.2642 0.0045 0.18 37.9 0.0300 ALFlat HC 0.137 0.003 0.50 15.3 0.2007 0.0046 0.66 24.1 0.0086 compFlat ribbed 0.152 0.003 0.50 13.5 0.1842 0.0058 0.66 25.6 0.0064 compFlat HC+Cat 0.167 0.003 0.50 15.4 0.2007 0.0046 0.71 24.2 0.0090 compVaulted HC 0.200 0.003 17 0.1702 0.0033 0.66 25.4 0.0112 comp

l

t

tP P

pr

A

C

B

D

uz = 0

uz = 0ux = 0

uy = 0uz = 0

Free

Excluded regionfrom constraint

HA

C

B

D

uz = 0

uz = 0ux = 0

uz = 0

ux = 0

NASA-AIAA-Analysis Design and Optimization of Non Cylindrical Fuselage for Blended Wing Body Vehicle

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