Airship Structural Analysis - info.aiaa.org · Lin Liao Aeronautical Engineer, PhD Worldwide Aeros...

Airship Structural AnalysisAirship Structural Analysis

Lin LiaoAeronautical Engineer, PhD

Worldwide Aeros Corp., Montebello, CA

1The Eighth Annual AIAA Southern California Aerospace Systems and Technology (ASAT) Conference

Santa Ana, CA, May 21, 2011

Overview

Introduction

Overview

Introduction

Analysis of airshipsRigid body motion analysisRigid body motion analysis

Static bending moment

Aerodynamic bending moment

Envelope stress analysis

Stress analysis of empennage attachment

Cable_truss structures

Summaryy



Introduction

Non‐rigid airships

Introduction

Non rigid airshipsEmpirical experiences

“Airship Design”, “Airship Technology”

Finite Element modeling

NASTRAN,ABAQUS

Rigid airships Bulkhead construction

No FEA model of rigid airships



Vertical & Longitudinal DirectionsVertical & Longitudinal Directions

The Eighth Annual AIAA Southern California Aerospace Systems and Technology (ASAT) ConferenceSanta Ana, CA, May 21, 2011

4

Lateral DirectionLateral Direction


5

( )static air heliumL Vρ ρ= −

Vertical & Longitudinal Directions

Calculation of lift, drag, and pitching moment

Vertical & Longitudinal Directions

2 / 3D LL C V q=2 / 3

DD C V q= y MyM C Vq=

[( / ) ( / ) ]cos cosT emp emp emp emp empL S q dC d dC dα α δ δ θ α= +

Sum of forces and moments in vertical & longitudinal directions



( )static air heliumL Vρ ρ= −

Lateral Direction

Sum of forces and moments in lateral direction

Lateral Direction



Flight Maneuver ConditionsFlight Maneuver ConditionsCondition Speed Weight Attitude Load Factor and

Acceleration1 Level Flight V W Horizontal n n n =0;χ ø=01 Level Flight VH Wt Horizontal nx ,ny,nz=0;χ,ø=0

2 Level Flight Reverse Thrust N/A N/A N/A N/A

3 Nose Down VH Wo Θ=+30° ny =0;nz>0;χ, ø=04 Nose Up V W Θ= 30° n =0;n <0;χ ø=04 Nose Up VH Wo Θ=-30 ny =0;nz<0;χ, ø=05 Descent & Pull-Up VH Wt Θ<0 ny =0;nz>0;χ,ø=06 Turn Entry VSH Wo Horizontal ny ≠0;ø>07 Turn & Reverse VSH Wo Horizontal ny ≠0;ø<08 Di E t V W H i t l 0 <0 08 Dive Entry VH Wo Horizontal ny =0;χ<0;ø=09 Climb Entry VH Wo Horizontal ny =0;χ>0;ø=010 Turn & Climb VH Wo Horizontal χ>0;ø>011 Turn & Dive VH Wo Horizontal χ<0;ø>012 Turn VSH Wo Horizontal nx ,nz=0;ny<0;χ,ψ=013 Turn Recovery VSH Wo Horizontal nx ,nz=0;ny<0;χ,ψ=014 Turn Rec. & Climb VH Wo Horizontal ny<0;χ>015 Turn Rec. & Dive VH Wo Horizontal ny<0;χ<0


8

o

16 Light Flight VH Wmin Θ<0 ny=0; nz>0; ø=0

Calculation of Static Bending Moment

The envelope is divided into longitudinal segments.Distribution of buoyancy force is obtained by multiplying the segment

Calculation of Static Bending Moment

Distribution of buoyancy force is obtained by multiplying the segmentvolume by the Helium (96% purity as specified by ADC) unit lift. Thebuoyancy forces is given the (+) sign.

The segment envelope weight is obtained in proportion to the segmentsurface area, and given the (-) sign to denote weight downward.

The components (nose cone, helium, etc.) are placed in their nearestsegment, and given the (-) sign.

The segment load F is obtained by summing up the above forces andweights.

The envelope shear at each segment, S, is obtained by summing the aboveF f th t th t h h i d t i dF from the nose up to the segment where shear is determined.

The envelope bending moment at each segment, M, is obtained bysumming the above S multiplied by the segment length, from the nose up tothe segment where bending moment is determined



the segment where bending moment is determined.

Static Bending MomentStatic Bending Moment

10 00012,00014,000

b]

02,0004,0006,0008,000

10,000

ding

Mom

ent [

ft-lb

Case 1Envelope: 30%Car: 55%

-4,000-2,000

00% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%B

end

Distance Aft of Nose (Percent of Airship Length)Envelope Bending Moment due to Weight & Buoyancy

4 5006,5008,500

10,50012,500

men

t [ft

-lb]

Case 2Envelope: 36%

-3,500-1,500

5002,5004,500

0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%Ben

ding

Mom

Di t Aft f N (P t f Ai hi L th)

pCar: 50%


10

Distance Aft of Nose (Percent of Airship Length)

Envelope Bending Moment due to Weight & Buoyancy

Static Bending MomentStatic Bending Moment

10 50012,500

2,5004,5006,5008,500

10,500

Mom

ent [

ft-lb

]

Case 3Envelope: 37%Car: 48%

-3,500-1,500

5000% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%

Ben

ding

M

Distance Aft of Nose (Percent of Airship Length)Figure 5. Envelope Bending Moment due to Weight & Buoyancy

Static bending moment increases from zero to maximum along thelongitudinal length of airships and then decreases to negative maximum.M i t ti b di t d ith th i f lMaximum static bending moment decreases with the increase of envelopeweight.


11

Aerodynamic Bending Moment

( ) ( )[ ] 25.002.0max 5.05624.04/129.0 LVolVLDLM ⋅⋅⋅⋅⋅−⋅⋅−+⋅= ∞μρ

Aerodynamic Bending Moment

Aerodyanmic Bending Moment vs Diameter

Gust 1, Gust 2, and Gust 3: 20 ft/s, 25 ft/s, 30 ft/s

360

410

460

t (10

3 lb

-ft)

210

260

310

ng M

omen

t

gust 1gust 2gust 3

160

48 49 50 51 52 53 54 55 56 57Ben

din

Max Diameter (ft)


12

Variation of Aerodynamic Bending Moment with respect to Diameter

Aerodynamic Bending MomentAerodynamic Bending Moment

410

460

b-ft

)

Aerodyanmic Bending Moment vs Length

310

360

410

omen

t (10

3 lb

gust 1

160

210

260

210 220 230 240 250 260 270 280 290 300Ben

ding

Mo gust 2

gust 3

210 220 230 240 250 260 270 280 290 300B

Length (ft)

Variation of Aerodynamic Bending Moment with respect to Length


13

Envelope Stress AnalysisEnvelope Stress Analysis

Envelope stresses due to internal pressure & bending moment

2PR P

tσ ⋅

= max3 2m

M y M R MI R t R t

σπ π

⋅ ⋅= ± = ± = ±

⋅

2

2m P

R P MR

σ σ σ ⋅= + = = 2m yield

MR t

σ σ σ= = ≤

Pressurized airships and rigid airships


14

2m P t R tπ ⋅ 2m yieldR tπ ⋅

Stress Analysis of Empennage AttachmentStress Analysis of Empennage Attachment



Cable truss StructuresCable_truss Structures

Restraints: fixed Nodes1, 4, and 5Applied loads:Fx =1000 lbs at Nodes 9, 10, 11, 12

bl i lbCable pretension: 100 lbs

Cable tension in the deformed configuration

Cable C1 C2 C3 C4 C5 C6 C7 C8 C9T i (lb ) 156 96 43 07 113 38 86 79 200 95 0 7 79 192 92 43 72Tension (lbs) 156.96 43.07 113.38 86.79 200.95 0 7.79 192.92 43.72

Cable C10 C11 C12 C13 C14 C15 C16 C17 C18Tension (lbs) 156.17 82.68 116.89 95.04 104.26 263.12 0 235.79 0




Restraints: fixed Nodes1-5, 9-13Restraints: fixed Nodes1 5, 9 13Applied loads: Fz =400 lbs at Nodes 7, 8, 15, 16Cable pretension: 100lbs

Th D i C fi iThree Design Configurations:Design A: no cables are usedDesign B: six cables are includedDesign C: 14 cables (Each of four truss members is replaced by two cables)


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Design C: 14 cables (Each of four truss members is replaced by two cables)


Node 7 Node 8A B C A B C

Displacements in the deformed configuration

UX (1E-3) -2.4040 -2.0239 0.2537 -0.9174 -0.7827 -0.0552UY (1E-4) 0.0018 3.1681 3.0836 0.0024 2.3054 2.3075UZ (1E-3) 5.3029 4.1754 2.1358 3.4412 2.6296 2.7121U (1E-3) 5 8223 4 6509 2 1728 3 5613 2 7533 2 7225


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UT (1E-3) 5.8223 4.6509 2.1728 3.5613 2.7533 2.7225


Design Node 5 Node 6Ux Uy Uz Ut Ux Uy Uz Ut

A (all) 2 8882 0 6030 4 3362 5 2448 2 5297 0 36406 2 5316 3 5973

Displacements in the deformed configuration

A (all) -2.8882 0.6030 -4.3362 5.2448 -2.5297 0.36406 -2.5316 3.5973B(1/2) -1.0161 0.4342 -1.5344 1.8909 -0.5751 0.1376 -0.5817 0.8295

C(1/2/3/4) -2.8342 0.1595 -4.2621 5.1209 -2.5728 -0.01747 -2.5788 3.6428D(5/6) -0.3899 -0.05827 -0.5891 0.7088 -0.3134 -0.1107 -0.3155 0.4583E(9/10) -0.4838 0.09942 -0.7368 0.8870 -0.2231 -0.07710 -0.2292 0.3290


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F(7/8/9/10) -0.4878 0.06495 -0.7428 0.8910 -0.2172 -0.1181 -0.2233 0.3331

Summary

Rigid body motion analysis has been utilized to study a variety of flightmaneuver conditions of airships.

Summary

maneuver conditions of airships.

Static bending moment and aerodynamic bending moment are calculated.Aerodynamic bending moment increases with the increase of airship lengthand increases with the decrease of equivalent max diameter for the samevolume and prismatic coefficients. Airship envelope stress is expressed as afunction of bending moment and internal pressure.

Finite element model of empennage attachment of airships is presented.

C bl t i h i ifi tl i t t ith t i d blCable tension changes significantly in contrast with pretension and cablescould completely lose tension. Optimal cable pretension and configurationare helpful for the minimization of structural deformation.



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