Probabilistic Analysis of an Advanced
Fighter/Attack Aircraft Composite Wing
Structure
H. Millwater, K. Griffin, D. Wieland
Southwest Research Institute
A. West, H. Smith, M. Holly
The Boeing Co.
R. Holzwarth
Air Force Research Laboratory
Sdm 2000
Objective
Assess the benefits of applying probabilistic design
technology to a state-of-the-art composite wing design
Sdm 2000
Background
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
Sdm 2000
Structural Example
Cocured Composite Dorsal Assy
With Fiberplaced Skins
Peripheral Members
Compatible With
Existing Structure
RTM Composites
Sinewave Stiffened RTM Spars
Incorporate Three Dimensional
Woven Inserts
RTM Carbon/Glass Hybrid Spars
Cobonded To Fibersteered Lower
Wing Skin
Fiber Placed/Steered
HSM Aluminum
HIP’d Titanium Castings
Titanium HIP
Castings
Aluminum Sh Metal
Titanium Machining
Sdm 2000
Comparison with Test Structures

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
Sdm 2000
Computational Model

Nonlinear composite analysis using BLADEM/THELMA (Boeing)

Probabilistic analysis computed using NESSUS (SwRI)
P
M
Skin Ply 1
Skin Ply 2
.
.
.
Skin Ply n
hbl
Left Flange Ply 1
Left Flange Ply 2
.
.
.
Left Flange Ply n
Nugget
Right Flange Ply 1
Right Flange Ply 2
.
.
.
Right Flange Ply n
r
hbr
Adhesive
ta
lsl
lfl
lfr
lsr
Sdm 2000
Random Variable Statistics
Composite Tape
Modulus of Elasticity (E1)
Modulus of Elasticity (E2)
Shear Modulus (G12)
Poisson’s Ratio (Nu12)
Ply Thickness
Tensile Strength (S3)
Shear Strength (T)
Composite Cloth
Modulus of Elasticity (E1)
Modulus of Elasticity (E2)
Shear Modulus (G12)
Poisson’s Ratio (Nu12)
Thickness
Tensile Strength (S3)
Shear Strength (T)
Adhesive
Initial Shear Modulus (G)
Tau Ultimate (ult)
Gamma Ultimate (ult)
Nugget Radius (NR)
Ply Thickness
Interlaminar
Shear Strength (T)
COV(%)
3.2
2.0
5.0
11.9
10.0
7.8
8.7
Distribution*
TNORM
TNORM
TNORM
TNORM
TNORM
TNORM
TNORM
6.9
5.0
5.4
41.5
1.5
4.6
8.4
TNORM
TNORM
TNORM
LOGNORMAL
TNORM
TNORM
TNORM
12.8
9.1
22.9
3.0
10.0
TNORM
TNORM
TNORM
TNORM
TNORM
3.8
TNORM
TNORM = Truncated Normal Dist. at  3 
Sdm 2000
Failure Model

Structure is assumed failed when failure index >= 1.0
  3    
  
T
 S3 
2
FI 
2
2
31
23

2
S3, T - Material
Strengths
0
.
4
5
0
.
4
0
.
3
5
0
.
3
0
.
2
5
0
.
2
0
.
1
5
0
.
1
P
r
o
b
.
o
f
F
a
i
l
u
r
e
0
.
0
5
0
65 43 2 1
0
1 2
1
.
0
Sdm 2000
Comparison of Computational and
Experimental Results
Failure due to pull-off load
(75 degrees; 3 test structures)

COV (%)
Experimental Computational
2.15
8.02
Sdm 2000
Probabilistic Sensitivity Factors (75)
Variable
Cloth E1
Cloth E2
Cloth G12
Cloth Nu12
Cloth Thick
Tape E1
Tape E2
Tape G12
Tape NU12
Tape Thick
Adhesive Goct
Adhesive Tau-ult
Adhesive Gam-ult
Adhesive Thickness
Nugget Radius
Cloth Ten strength
Cloth Shear Str.
Tape Ten Str.
Tape Shear Str.
Adhesive Shear Str.
dprob/dmean
-1.57E-10
6.56E-11
2.60E-10
1.08E-03
-0.2081
1.22E-10
3.52E-10
-1.36E-09
2.19E-04
1.577
-7.92E-09
-2.22E-08
3.34E-04
-1.72E-02
7.27E-02
7.62E-07
3.77E-07
-1.41E-16
-9.18E-17
-3.51E-16
Normalized (%)
0.97
0.15
0.01
0.00
3.12
2.14
0.08
0.36
0.00
50.72
1.46
0.01
0.00
0.00
26.35
7.72
6.92
0.00
0.00
0.00
dprob/dstdev
-7.08E-11
-1.25E-11
-1.25E-11
-1.40E-04
-4.51E-02
-3.88E-11
-1.60E-11
-1.44E-10
-7.01E-06
-3.382
-6.93E-09
-7.13E-10
-1.24E-05
-7.94E-04
-8.91E-02
-1.16E-06
-6.45E-07
-7.16E-11
-4.89E-11
-1.61E-10
Normalized
(%)
0.11
0.00
0.00
0.00
0.01
0.03
0.00
0.00
0.00
55.62
1.54
0.00
0.00
0.00
5.92
14.16
22.61
0.00
0.00
0.00
Sdm 2000
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
Probabilistic Analysis of a Composite Wing
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

P
Spar 3
Location of Load Extraction
M
Skin Ply 1
Skin Ply 2
.
.
.
Skin Ply n
hbl
Left Flange Ply 1
Left Flange Ply 2
.
.
.
Left Flange Ply n
Nugget
Right Flange Ply 1
Right Flange Ply 2
.
.
.
Right Flange Ply n
r
hbr
Adhesive
ta
lsl
lfl
lfr
lsr
Sdm 2000
WING-BLADE ANALYSIS Methodogy
NASTRAN
BLADEM_POST
Non-linear Global
ALAFS Model
Extraction of Failure
Index from Results
Force Post-Processor
Prob. Distrib.
BLADEM
Extract Free-Body Forces
for Sub-model Region
Detailed Blade
Model
sl
l
lfl
fr
l
sr
l
BLADEM_PRE
Preprocessor to Create
BLADEM Input File
Sdm 2000
Computational Procedure
Link
NESSUS, PATRAN, NASTRAN, THELMA
NESSUS 1
2
Material
property
input
3
Non-linear
bdf
Patran
4
Non-linear
op2
Nastran
6
7
Freebody
exe
Freebody
data
Bladem
input
Bladem /
Thelma
5
Linear
op2
Patran
8
Patran
Nastran
Linear
bdf
9
Thelma
Results
NESSUS
Sdm 2000
Structural Deformation At
Nominal Values
Post-buckled Wing Skin
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Joint STRESSES
lsl
lfl
lfr
lsr
Highly stressed region
Sdm 2000
Random Variables
Mat’l
Tape
Tape
Tape
Tape
Tape
Tape
Tape
Tape
Tape
Cloth
Cloth
Cloth
Cloth
Cloth
Cloth
Cloth
Cloth
Tape 2
Adhesive
Adhesive
Tape
Tape
Cloth
Cloth
Variable
Modulus of elasticity - E1 (tension &
compression)
Modulus of elasticity - E2 (tension &
compression)
Modulus of elasticity - E3 (= E2)
Shear modulus - G12 (tension &
compression)
Shear modulus - G23 (tension &
compression) = E2/(2*(1+Nu23))
Shear modulus – G13 (tension &
compression) = G12 = G31
Poisson’s ratio – Nu12
Poisson’s ratio – Nu23 = 0.3
Poisson’s ratio – Nu31 (=E2*Nu12/E1)
Modulus of elasticity - E1
Modulus of elasticity - E2
Modulus of elasticity - E3
Shear modulus - G12
Shear modulus - G23
Shear modulus - G31 (=G23)
Poisson’s ratio – Nu12
Poisson’s ratio – Nu23
Modulus of elasticity - E1 (Cloth Nu31 =
E3*Nu23/E1 Tape 2)
Modulus of elasticity – E
Shear modulus – G
Tensile Strength
Shear Strength
Tensile Strength
Shear Strength
COV(%)
1.3
Distribution
TNORM
4.5
TNORM
2.7
TNORM
5.1
TNORM
5.8
6.2
6.2
1.8
2.2
TNORM
TNORM
TNORM
TNORM
TNORM
62.5
7.3
2.7
9.1
9.1
6.1
4.7
6.9
8.2
LOGNORMA
L
TNORM
TNORM
TNORM
TNORM
TNORM
TNORM
TNORM
TNORM
Sdm 2000
System Reliability Results
Consider failure of the joint as failure in any location or
ply, i.e., adhesive, nugget, flanges or skin

P[blade]  P[ failure in any region] 
P[ Fnugget  Fadhesive  FSkinPly1   FSkinPlyN  FLeftFlangePly1   FLeftFlangePlyN 
FRightFlangePly1   FRightFlangePlyN ]
Results indicate failure governed entirely by failure in
1st ply of left flange.

Sdm 2000
Probabilistic Sensitivity Results
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R
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%
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/
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p
) d
%
(
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N
1
E
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p
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T
8
0
E
7
7
.
1
-
1
0
1
E
5
3
.
3
-
0
2
E
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p
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T
7
0
E
1
2
.
1
-
0
9
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7
0
.
2
-
0
2
1
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p
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7
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2
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3
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9
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3
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C
6
0
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0
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1
4
8
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6
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2
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4
7
8
2
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0
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6
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3
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1
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2
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3
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0
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1
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1
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9
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5
5
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-
0
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4
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9
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6
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.
6
-
0
G
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A
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1
2
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6
0
7
0
E
6
5
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1
-
0
h
t
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n
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S
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T
e
p
a
T
2
1
E
1
2
.
2
0
6
0
E
4
6
.
1
-
0
h
t
g
n
e
r
t
S
r
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h
S
e
p
a
T
4
1
E
6
9
.
9
0
7
0
E
2
1
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1
-
0
h
t
g
n
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t
S
e
l
i
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T
h
t
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C
4
0
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5
1
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8
-
4
7
4
0
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8
8
.
1
-
5
9
h
t
g
n
e
r
t
S
r
a
e
h
S
h
t
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l
C
7
0
E
7
1
.
2
-
0
8
0
E
7
7
.
8
-
0
Sdm 2000
Probabilistic Redesign


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)
Sdm 2000
Probabilistic Redesign
Pf ~ 10-30
Probability Density Function after Redesign
Sdm 2000
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
Test Structures
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.

Sdm 2000
Summary and Conclusions
Wing/Joint Analysis
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
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

Sdm 2000