Sdm 2000
H. Millwater, K. Griffin, D. WielandSouthwest Research Institute
A. West, H. Smith, M. HollyThe Boeing Co.
R. HolzwarthAir Force Research Laboratory
Probabilistic Analysis of an Advanced Fighter/Attack Aircraft Composite Wing
Structure
Sdm 2000
RTM Composites
Fiber Placed/Steered
HSM Aluminum
HIP’d Titanium Castings
Aluminum Sh Metal
Titanium Machining
Cocured Composite Dorsal AssyWith Fiberplaced Skins
Peripheral MembersCompatible With
Existing Structure
Titanium HIPCastings
RTM Carbon/Glass Hybrid SparsCobonded To Fibersteered LowerWing Skin
Sinewave Stiffened RTM SparsIncorporate Three DimensionalWoven Inserts
Assess the benefits of applying probabilistic design technology to a state-of-the-art composite wing design
Objective
Sdm 2000
RTM Composites
Fiber Placed/Steered
HSM Aluminum
HIP’d Titanium Castings
Aluminum Sh Metal
Titanium Machining
Cocured Composite Dorsal AssyWith Fiberplaced Skins
Peripheral MembersCompatible With
Existing Structure
Titanium HIPCastings
RTM Carbon/Glass Hybrid SparsCobonded To Fibersteered LowerWing Skin
Sinewave Stiffened RTM SparsIncorporate Three DimensionalWoven Inserts
Aircraft structure is a composite wing designed under an advanced lightweight aircraft structures development program.
•Represents state-of-the-art in aircraft design•Has high quality computational models available•Has experimental component test data available
Background
Sdm 2000
Structural Example
RTM Composites
Fiber Placed/Steered
HSM Aluminum
HIP’d Titanium Castings
Aluminum Sh Metal
Titanium Machining
Cocured Composite Dorsal AssyWith Fiberplaced Skins
Peripheral MembersCompatible With
Existing Structure
Titanium HIPCastings
RTM Carbon/Glass Hybrid SparsCobonded To Fibersteered LowerWing Skin
Sinewave Stiffened RTM SparsIncorporate Three DimensionalWoven Inserts
Sdm 2000
Purpose: compute probability distribution of failure load and compare with experimental results– Two test temperatures: -65 F and 75 F– Three specimens at each temperature– Pull-off load increased until failure
Edges Remain Connected
Evident Failure Surrounding Nugget
Comparison with Test Structures
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Computational Model
Skin Ply 1Skin Ply 2
.
.
.Skin Ply n
Left Flange Ply 1Left Flange Ply 2
.
.
.Left Flange Ply n
Right Flange Ply 1Right Flange Ply 2
.
.
.Right Flange Ply nr
hbl
hbr
lsl lfl lfr lsr
ta
P
M
NuggetAdhesive
Nonlinear composite analysis using BLADEM/THELMA (Boeing) Probabilistic analysis computed using NESSUS (SwRI)
Sdm 2000
Random Variable Statistics
Composite Tape COV(%) Distribution*Modulus of Elasticity (E1) 3.2 TNORMModulus of Elasticity (E2) 2.0 TNORMShear Modulus (G12) 5.0 TNORMPoisson’s Ratio (Nu12) 11.9 TNORMPly Thickness 10.0 TNORMTensile Strength (S3) 7.8 TNORMShear Strength (T) 8.7 TNORM
Composite ClothModulus of Elasticity (E1) 6.9 TNORMModulus of Elasticity (E2) 5.0 TNORMShear Modulus (G12) 5.4 TNORMPoisson’s Ratio (Nu12) 41.5 LOGNORMALThickness 1.5 TNORMTensile Strength (S3) 4.6 TNORMShear Strength (T) 8.4 TNORM
AdhesiveInitial Shear Modulus (G) 12.8 TNORMTau Ultimate (τulτ) 9.1 TNORMGam m a Ulτim aτe (Gulτ) 22.9 TNORMNuggeτ Radius (NR) 3.0 TNORMPly Thickness 10.0 TNORMInτerlam inarShear Sτrengτh (T) 3.8 TNORM
TNORM = Truncated Normal Dist. at 3 s
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Failure Model
Structure is assumed failed when failure index >= 1.0
( ) ( )TS
FI 2
2
23
2
31
2
3
3 ττσ ++= ⎟⎟⎠
⎞⎜⎜⎝⎛
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
-6 -5 -4 -3 -2 -1 0 1 21.0
Prob. ofFailure
S3, T - Material Strengths
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Experimental ComputationalCOV (%) 2.15 8.02
Failure due to pull-off load (75 degrees; 3 test structures)
Comparison of Computational and Experimental Results
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Probabilistic Sensitivity Factors (75)
Variable dprob/dmean Normalized (%) dprob/dstdev Normalized(%)
Cloth E1 -1.57E-10 0.97 -7.08E-11 0.11Cloth E2 6.56E-11 0.15 -1.25E-11 0.00Cloth G12 2.60E-10 0.01 -1.25E-11 0.00Cloth Nu12 1.08E-03 0.00 -1.40E-04 0.00Cloth Thick -0.2081 3.12 -4.51E-02 0.01Tape E1 1.22E-10 2.14 -3.88E-11 0.03Tape E2 3.52E-10 0.08 -1.60E-11 0.00Tape G12 -1.36E-09 0.36 -1.44E-10 0.00Tape NU12 2.19E-04 0.00 -7.01E-06 0.00Tape Thick 1.577 50.72 -3.382 55.62Adhesive Goct -7.92E-09 1.46 -6.93E-09 1.54Adhesive Tau-ult -2.22E-08 0.01 -7.13E-10 0.00Adhesive Gam-ult 3.34E-04 0.00 -1.24E-05 0.00Adhesive Thickness -1.72E-02 0.00 -7.94E-04 0.00Nugget Radius 7.27E-02 26.35 -8.91E-02 5.92Cloth Ten strength 7.62E-07 7.72 -1.16E-06 14.16Cloth Shear Str. 3.77E-07 6.92 -6.45E-07 22.61Tape Ten Str. -1.41E-16 0.00 -7.16E-11 0.00Tape Shear Str. -9.18E-17 0.00 -4.89E-11 0.00Adhesive Shear Str. -3.51E-16 0.00 -1.61E-10 0.00
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Comparison of Computational and Experimental Results
Failure locations and mean failure load agree. Amount of variation in pull-off load is several times that from test Expected reason:
• Computational results were developed using material property data collected over several years.
• Test structures were manufactured as one structure then sectioned.
• Variations in material properties and geometries likely to be significantly less than that used in computation.
• Computational results expected to be more accurate of fleet.
• Use of test results as indicative of fleet may be unconservative.
Sdm 2000
Skin Ply 1Skin Ply 2
.
.
.Skin Ply n
Left Flange Ply 1Left Flange Ply 2
.
.
.Left Flange Ply n
Right Flange Ply 1Right Flange Ply 2
.
.
.Right Flange Ply nr
hbl
hbr
lsl lfl lfr lsr
ta
P
M
NuggetAdhesive
Failure: pull-off load in bonded joint of spar/wing Severe down bending load (ultimate load) 20 independent random variables - material properties Geometrically Nonlinear NASTRAN analysis of wing - local analysis of composite joint Failure probability and sensitivities computed
Probabilistic Analysis of a Composite Wing
Spar 3 Location of Load Extraction
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WING-BLADE ANALYSIS Methodogy
NASTRANNon-linear Global
ALAFS Model
BLADEMDetailed Blade
Model
BLADEM_POSTExtraction of FailureIndex from Results
BLADEM_PREPreprocessor to Create BLADEM Input File
Force Post-ProcessorExtract Free-Body Forces
for Sub-model Region
Prob. Distrib.
lsl lfl lfr lsr
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Material property
inputPatran Nastran PatranNon-linear
bdfNon-linear
op2
Nastran Linearbdf
Linearop2PatranFreebody
exeFreebody
data
Blademinput
Bladem/Thelma
ThelmaResults
NESSUS
NESSUS
1
2 3
7
4
9
6
8
5
Computational Procedure
Link NESSUS, PATRAN, NASTRAN, THELMA
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Structural Deformation At Nominal Values
Post-buckled Wing Skin
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Joint STRESSES
Highly stressed region
lsl lfl lfr lsr
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Random Variables
Mat’l Variable COV(%) DistributionTape Modulus of elasticity - E1 (tension &
compression)1.3 TNORM
Tape Modulus of elasticity - E2 (tension &compression)
4.5 TNORM
Tape Modulus of elasticity - E3 (= E2)Tape Shear modulus - G12 (tension &
compression)2.7 TNORM
Tape Shear modulus - G23 (tension &compression) = E2/(2*(1+Nu23))
Tape Shear modulus – G13 (tension &compression) = G12 = G31
Tape Poisson’s ratio – Nu12 5.1 TNORMTape Poisson’s ratio – Nu23 = 0.3Tape Poisson’s ratio – Nu31 (=E2*Nu12/E1)Cloth Modulus of elasticity - E1 5.8 TNORMCloth Modulus of elasticity - E2 6.2 TNORMCloth Modulus of elasticity - E3 6.2 TNORMCloth Shear modulus - G12 1.8 TNORMCloth Shear modulus - G23 2.2 TNORMCloth Shear modulus - G31 (=G23)Cloth Poisson’s ratio – Nu12 62.5 LOGNORMA
LCloth Poisson’s ratio – Nu23 7.3 TNORM
Tape 2 Modulus of elasticity - E1 (Cloth Nu31 =E3*Nu23/E1 Tape 2)
2.7 TNORM
Adhesive Modulus of elasticity – E 9.1 TNORMAdhesive Shear modulus – G 9.1 TNORM
Tape Tensile Strength 6.1 TNORMTape Shear Strength 4.7 TNORMCloth Tensile Strength 6.9 TNORMCloth Shear Strength 8.2 TNORM
Sdm 2000
System Reliability Results
]
[] [][
1
11
ePlyNRightFlangePlyRightFlang
PlyNLeftFlangePlyLeftFlangeSkinPlyNSkinPlyadhesivenugget
FF
FFFFFFPionin any regfailurePbladeP
∪
∪∪∪∪∪∪==
LLL
Consider failure of the joint as failure in any location or ply, i.e., adhesive, nugget, flanges or skin
Results indicate failure governed entirely by failure in 1st ply of left flange.
Sdm 2000
Probabilistic Sensitivity Results
Random Variable dprob/dmean Normal-ized (%) dprob/dstdev Normal-ized (%)
Tape E1 -1.77E-08 1 -3.35E-10 0Tape E2 -1.21E-07 0 -2.07E-09 0Tape G12 -7.47E-07 1 -1.17E-08 0Tape Nu12 -7.52E-01 0 -1.13E-02 0Cloth E1 -1.02E-007 2 -3.76E-009 0Cloth E2 2.76E-07 17 -2.85E-08 5Cloth E3 4.13E-07 1 -6.47E-09 0Cloth G12 1.23E-07 0 -2.89E-09 0Cloth G23 1.50E-06 4 -2.96E-08 0Cloth Nu12 0.2874 0 -0.1046 0Cloth Nu23 2.45E-01 0 -4.70E-03 0Cloth Nu31 -9.37E-10 0 -1.55E-10 0Adhesive E 1.46E-07 0 -6.36E-09 0Adhesive G 6.21E-06 0 -1.56E-07 0Tape Tensile Strength 2.21E-12 0 -1.64E-06 0
Tape Shear Strength 9.96E-14 0 -1.12E-07 0
Cloth Tensile Strength -8.15E-04 74 -1.88E-04 95
Cloth Shear Strength -2.17E-07 0 -8.77E-08 0
*
*
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Probability of Failure was too high from original design
Several redesigns were explored deterministically– Effective redesigns were:
» Increase nugget radius (from prob. sensitivities)» Remove ply from right flange» Soften E2 modulus of cloth (from prob. sensitivities)
Probabilistic Redesign
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Probabilistic Redesign
Probability Density Function after Redesign
Pf ~ 10-30
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Probabilistic Redesign Conclusions
A many order of magnitude improvement in safety was obtained with a small amount of effort
Probabilistic sensitivity factors indicated 2 of the 3 elements to change - nugget radius and E2 of the cloth
– The effect of E2 would have been difficult to ascertain without the sensitivity analysis
Exploratory analyses were performed determinstically (quickly) to indicate a promising design
Sdm 2000
Summary and Conclusions
Computed distribution of probability of failure loads were compared with test results. Failure region and mean failure load agree. Computed scatter was several times that of test. Expected reason - test structures do not exhibit realistic amount of variation that would be seen in fleet. Computational results expected to be more representative of fleet. Use of test results as indicative of fleet may be unconservative.Test procedures may need to be modified in order to represent better the variation seen in production.
Test Structures
Sdm 2000
Summary and Conclusions
Probabilistic analysis of a state-of-the-art composite wing is practical using standard probabilistic and structural analysis tools. Probability of failure of a post-buckled wing/joint subjected to a severe down bending load was determined
– Combined probabilistic analysis (NESSUS) with geometrically nonlinear NASTRAN analysis with local composite THELMA analysis
Wing/Joint Analysis
Sdm 2000
Summary and Conclusions
Wing/joint structure was redesigned by modifying three variables: nugget radius, removing ply from right flange and reducing E2 material property.Probabilistic sensitivities give valuable insight into the redesign. Redesigned structure’s probability of failure was reduced by many orders of magnitude