Advanced composite technology offers potentials for sizable improvements in many areas: weight savings, maintainability, durability, and reliability. However, there are a number of inhibitors to these improvements. One of the biggest inhibitors is the imposition of traditional metallic approaches to design of composite structure. This is especially detrimental in composites because new materials technology demands new design approaches. Of particular importance are the decisions made regarding structural criteria. Significant changes cannot be implemented without careful consideration and exploration. This new approach is to implement changes on a controlled, verifiable basis. Probabilistic design is the methodology and the process to accomplish this. Its foundation is to base design criteria and objectives on reliability targets instead of arbitrary factors carried over from metallic structural history. The background is discussed of probabilistic design and the results are presented of a side-by-side comparison to generic aircraft structure designed the 'old' way and the 'new'. Activities are also defined that need to be undertaken to evolve available approaches to probabilistic design followed by summary and recommendations

Gray, P. M.

Riskalla, M. G.

English

NASA Technical Reports Server

D_
N95- 28443
PROBABILISTIC DESIGN
OF
ADVANCED COMPOSITE STRUCTURE
P. M. GRAY
M. G. RISKALLA
LTVAEROSPACE AND DEFENSE
AIRCt_T DIVISION
/
/ DALLAS, TEXAS/
/
/
ABSTRACT
Advanced composite technology offers potentials for sizable improvements
in many areas: weight savings, maintainability, durability, and reliability.
However, there ere a number of inhibitors to these improvements. One of the
biggest inhibitors is the imposition of traditional metallic approaches to
design of composite structure. This is especially detrimental in composites
because new materials technology demands new design approaches. Of paEticular
importance are the decisions made regarding structural criteria. Significant
changes cannot be implemented without careful consideration and exploration.
This new approach is to implement changes on a controlled, verifiable basis.
Probabilistic design is the methodology and the process to accomplish this.
Its foundation is to base design criteria and objectives on reliability tar_s
instead of arbitrary factors carried over from metallic structural h_story." "
This paper discusses the background of probabilistic design and presents
the results of a slde-by-side comparison to generic aircraft structure designed
the Wold" way and the "new". Activities are also defined that need to be
undertaken to evolve available approaches to probabilistic design followed by
smmuary and recommendations.
INTRODUCTION
Current aerospace design procedure disregards the fact that component
dimensions, environment (temperature and aging}, manufacturing quality, and
even the externally applied loads pertaining to aircraft structure are
statistical in nature as opposed to deterministic, or single-valued variables.
That is, these variables fall within a spectrum of possible values, and no
specific value should be singled out as representing a reliable solution for a
mechanical equation. Conventional solutions to design equations generally
result in an uncertainty between prediction versus performance; this
uncertainty is hidden under a blanket of safety factors. A more rational
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solution to this reality is to strive for a predeteralned reliability goal.
This will require more knowledge about the nature of design inputs. The
ultimate goal is to change the design _th from: "...if it can happen at a11,
design to it," to "...design to an acceptable probability of failure,
accounting for the likelihood and consequences of occurrence."
_ Cm_posite materials are known to _ Susceptible to two enviromuntal
actors: elevated temperature and moisture. They are also sensitive to flaws
that Can originate during the manufacturing process or in operational usage.
The conventional design approach adopted by gnveraaent and industry does not
recognize the variable nature of design manufacturing and operational input
data. Current procedures force the engineer to design aircraft structure for
worst-case scenarios adhering to contractually defined margins of ufety with
no knowledge of reliablllty _rfozmance. This is the traditional deterministic
approach. In effect, it forces a weight increase with an unknown reliability
that must be tolerated for every part regardless of the probability of
encountering adverse conditions.
Ccuqgosite part design is governed by compounded conservatism illustrated
by the following criteria:
o Worst case loading X safety factor (1.5) (_')
o Worst case temperature
o Worst case molsture
o Worst case damage, undetected
The effect of combining these conservative structural criteria is to
continually drive down the allowab!e stresses. This has reduced weight savings
to the extent that composites are notizealAzlngthepayoffs originally
forecast. This current approach is illustrated in Figure 1. Significant
changes must occur in the design approach to future military and space programs
to take full advantage of composite material perfomance and to he able to more
accurately manage risk.
DETERMINISTIC VS_PROBABILISTIC DESIGN
Figure 2 p_sentsa _ison of the two (2) _ferent approaches. The
deterai_/stic philosophy utilises worst case design_ameters to produce
structural components which are overly conservative and heavy. The
deterministic approaches possess positive margins to withstand glvenmaxlmum
load, but there also are inherent, unknown reliabilities at the given load
levels.
An intez_madiate approach is to apply a portion of probabilistic design but
still retain the limit to ultimate factor. This type of risk analysis augments
the structural design engineer' 8 current capabilities and allows him to
quantify the structural reliability of the aircraft structure. Previous risk
analyses have shown that by accounting for the stochasticnature of design
parameters _ identifying the z_skdrlvezs, one can produce reliability based
structures which maet the operational requirements.
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The probabilistic approach is to utilize the deslgn data characterized by
statistical distributions to identify/optimize the risk drivers to produce
minimum weight structures for which the reliabilit_ been specified.
PROBABILISTIC DESIGN
Probabilistic design is a finely integrated process as shown schematically
in Figure 3. The approach is to define/develop the functional relationships of
the operations within the boxes, then build the relationships between them,
thus integrating the entire process. In this way, when a factor in one
operation changes, its effect can be determined on the others. The most
important evaluation is the effect on failure probability.
A flowchart of the LTV-AD Probabilistic Design model is shown in Figure 4.
This model consists of four major activities, namely the design process,
material production, manufacturing, and operations. Output from the design
process is the expected operating stress distribution resulting from the flight
spectra. The remaining three activities provide the material strength
distribution, determined through Monte Carlo simulation of random variables
representing random variation of incoming material strength, manufacturing
defects, and operational factors. Probability of failure occurs when the
stress exceeds the strength. This is calculated by a double integral of the
stress and the strength probability density functions to determine the
probability that "stress exceeds strength."
The basic probabiliatic design concept, as shown below, looks into the
probability distributions of both material strength and operating stress.
Because failure is a local phenomenon, division of a cceq_onent into nodes can
be done to represent all the locations at which failure is posslble to occur.
In general, the distributions are assumed to be identical at all the nodes.
Step 7 assumes that material strengths at the nodes are independent from each
other. As in step 8, if the calculated probabiity of _ailure does not agree
with the pre-defined and acceptable level, sensitivity analysis resulting from
changes in distribution(s) will provide invaluable information on needed
changes in the design.
Step No.
i..Establish allowable failure rate.
2. Establish the number of nodes where failure is possible.
3. Determine probability distribution for loads.
P(x s < x s) - F(x s)
4. Determine the operating stress probability density function fs(X).
5. Determine probability distribution for strength.
1
P<Y.<y.) !y.l
_t
Determine the material strength probability density function fM(y ).
525
7. Calculate failure probability P.
- J is(X) [i-[l f.(y)dy]"]dxPf
x y>x
8. If P_ is not in agreement with the established failure rate, then
_t_y 2 or 3.
Probabilistic analysis requires that the random variables be statistically
characterized. Statistical design databases, in general, do not exist.
In order to conduct a probabilistic design exercise one must characterize
many parameters, including the following:
(I) Incoming material mechanical properties
(2) External loads anticipated during the life of the article.
(3) Manufacturing processes and their effect on material strength.
(4) Environmental effect on strength.
(5) Enviror_ental history during operational usage.
(6) Flaw locations, severity, probability of occurrence and effect on
strength.
Quality of incoming ccmpositematerlal is crucial to final product
quality. To assure incom/ngmsterial meets specifications, testing procedures
and measured value limits must be established to sufficiently discri_nate
bet_n inferior and specified material. These criteria must be agreed upon by
producer and consumer. Each wants to minimize their risk. The producer's risk
is the probability of rejecting good material and the consumer's risk is the
probability of accepting inferior material.
PROBABILISTIC DESIGN APPLICATION AND EVALUATION
In order to calculate potential weight savings from a probabilistic
design, a simplified two-cell box beam was selected to represent aircraft wing
and tail structure. Most of the usual design concerns and requirements
inherent in military aircraft programs can be simulated in multicell,
ipressure-loaded box beams. Two independent design approaches were implemented:
the traditional deterministic method and probabilistic design.
The generic ?on_osi_e,-two-cell, three-spar wingbox used in this exercise
is presented in F_gure 5,!_-The w_ngbox is fixed (i.e., cantilevered) at the
root (Y-0.0). Design ultimate pressures of I0.0 and 5.0 psi are applied to the
forward and aft cell lower skins, respectively, in the upward (+z) direction.
The ultimate pressures were used only for the deterministic analysis.
Gecmstric details of the wingbox are presented in Figure 6, and the wingbox
section thicknesses are presented in Figure 7. TwO categories of
526
i :
aircraft were evaluated in this program, a Class A (attack) aircraft and a
Class Bx. (bomber) alrcraft. Both spectra were derl_ed from Mil-A-08866B (s)
and are _hown in Figure 8'
The composite wingbox was optimized for minimum weight using both the
deterministic and probabilistic design approaches. Buckling and damage
tolerance criteria were major factors in the sizing. The wing weight reduction
as a function of probability of failure is presented in Figure 9. The
reliability target determines the amount of weight savings. Two criteria were
applied:
(I) The probability of failure for an aircraft's single flight should be
1 x 10" or less.
(2) The expected number of aircraft lost by structural failure in the
lifetime of the fleet should be less than one.
Probabilistic design showed a possible weight savings of 13% when using a
fighter load spectrum, and a weight savings of 20% when using a bomber load
spectrum.
Deterministic/Probabilistic Equivalence
Incorporated in the methodology is the ability to relate probabilistic
design to the factor-of-safety used in deterministic design. The issue is to
determine the benefits to the aircraft if probabilistic advantages were
converted to increased performance rather than weight savings. Figure i0 shows
how much gain is available in maneuver load factor using probabilistic design
assuming the weight of the two design approaches is the same. The fighter
aircraft can sustain a 62 percent increase in "g" level (i.e., 16.2 vs. 10.0
g's) indicating the significant increase in maneuverability.
S_IARY/RECO2f4ENDATIONS
Probabilistic Design is a powerful alternative to today's approach for
composite design. It will require the development of sophisticated techniques
in probability and statistics and characterization of statistical data for
engineering variables just now becoming available. However, it is gaining
momentum as more people become aware of its presence and benefits.
"One Time Only" designs that cannot be tested to failure (such as missiles
and flight vehicle systems) are best designed by probabilistic methods where
the additional analysis complexity is justified from a safety or economic
standpoint. Likewise, in situations where a design is put into production
before it can be tested, probabilistic design would be the best way to predict
service life. In addition, probabilistic design is the best way to minimize
the weight of a component, and so should be used to $_ign critical parts for
lightwelght applicatlons such as aerospace vehicles." "
As the demand grows for more accurate, sophisticated designs, the
requirement for probabilistic design methodology will become more and more a
necessity. The incorporation of Probabilistic Design, while quite challenging
technically, will net significant payoffs in the form of improvement in vehicle
performance accompanied by a reduction in operating costs. To be in a position
527
to approach a new design/program from a probabilistic standpoint, additional
studies need to be perfonwd including:
- Probabillstic Design Philosophy/Methodology
- Risk analysis of current aircraft structure
- F_ghter/boe_eE probabilistic design study
- Development of statistical data bases required for probabilistic design
- Total quality mana_t relating to material performance (i.e.,
Reliability-based material acceptance criteria)
- Probabilistic Design of Advanced Primary/Secondary Aircraft Structure
- Qualification/certification methodology.
The application of Probabilistlc Design tonew and emerging aerospace
systems will result in minimum weight structures which have reliability as the
heart of the design and not Just a "fall-out" from a designed-in capability to
withstand a given load.
REFERENCES
1. AFP 800-7, "USAF R&M 2000 Process", 1 January 1989.
2. Muller, G. E. and Schm/d, C. J., "Factor of Safety - USAF Design Practice",
Technical Report AFFDL-TR-78-8, April 1978.
3. MIL-A-008866B, "Military Specification: Airplane Strength and Rigidity
Reliability Requirements, Repeated Loads, and Fatigue", 22 August 1975.
4. Lincoln, J. W. and Snead, J. M., " the X-30 Structural Integrity Program:
The Challenge Ahead".
528
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i-(n
o
m
U.
m
O
,1, 1O.
(n
0
FIGURE 1.
, ,, _ 100
90
10
0
DETERMINISTIC REDUCTION FACTORS VS.
PROBABILISTIC WEIGHT SAVINGS
DETERMINISTIC
(UMiT TO MARGIN
ULTIMATE OF
FACTOR) • HEAVY SAFETY
• MAT'L 8TR ,l_
DESIGN • LOAD _1
VARIABLES . TEMP ,n
MAT'L 8"rR A
RISK
LOAD A • DERNITION MANAGE.
TEMP A OF ruSK MENTMFG TOL A PROBABILISTIC DRIVERS
(PROB. OF
F_LURE_ ON
uMrr TO
• MAT'L STR A
• LOAD A
• TEMP A RF.NJS11C
• LIGHTER MEASURE
• RELIABILITY OF
QUANTIFIED RISK
FIGURE 2. PROBABlUSTIC VS. DETERMINISTIC DESIGN
529
I u-.NOUI QWdJTY
I.--H _ I
¢mTImlA llA'rlIRIAL
IIAlilqJ mZl[
I--"H " H - H - Hm ,_.i.,OW,I IILI_ .Ul,41.'nB
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llln' _
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(I) IKIILDRELAllONDIP _ BOXB
(1) 'WI'IN ONEIOX (_Ultli_, NTERItl IIIP,liGTON Ol1,111_
IITATIC H Iq.]GHTOPERATIO_
PI_DEAIULJ_FAILUFm PROBAIlUJTYFAILURE
SINGLE
FLEET
FIGURE 3. FULL PROBABILISTIC ANALYSIS
i _ I _TEm" I I'_FA=U_I
:, LOAII_ i =* _ HOLE _ !
i
I,BIZINGI'GEOMETRY I" mmTemL .uUm_TeoEeecxs"1
_ DEFECTS I
='_ I STRENGTH _.OtlnrOFTOLERANCE 1
_TEBAL WAVINESS I
ALLOWABLES
t 1 1
1
OPERATING MATERIAL
i STREN .__ STRENGTH
-I
' OPERATIONS J
,r-oo
) BIRD STRIKE
• TEMPERATURE
) MOISTURE
FIGU_4. _BABILISTIC _N
53O
STRUCTURAL FEATURES
TENSION SKIN
COMPRESSION SKIN
SPARS
RIBS
FASTENERS (JOINTS)
DAMAGE CRITERIA _/_ _ "*'72 IN.
COMBINED LOADS _ __ r_--_ "_.
VAR,ABLEPLVOR,ENTAT,ON,.0,.-"__ _"'f_
_1_.
"'"- NOT TO SCALE
Y
FIGURE 5. GENERIC COMPOSITE WINGBOX
i
SECTION B-8
36 IN,
I
I
FIGURE 6.
SECTION A-A SCALE _ 1:;_
WING BOX CONSTRUCTION
A
t
531
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i
LU
Z
¢,)
X
I--
Z
0
I-
r,.)
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x
0
m
(.'1
Z
}:
i,.:
W
r_
532
EXPECTED NUMBER OF A/C LOSSE$_IN FLEET LIFETIME
I 10
i .
1E_)3
, /_ 1E,_
I
: 1E-00 f
_ 1E-11
/ GOAL
_FR F_ET SIZE i 500 A/C
i A_C_AFTTV_;
--0-- FIGHTER]
, -_- BOMBERi
l&l 0 5 10 15 20 211 30
PERCENT WEIGHT REDUCTION FOR ENTIRE WlNGBOX
SINGLE lWL_ PROBABILITY OF FAILURE
I 1E-02
/
I -4- nOHTE.I
,o , _ I -'*'- BOUee_l
1E-17 ' _ I a
0 5 10 15 20 25 30
PERCENT WEIGHT REDUCTION FOR ENTIRE WINGBOX
FIGURE 9. COMPOSITE WINGBOX WEIGHT
REDUCTION BENEFITS
I.U
-.j
..i
Ik
O
>.
m
m
O
Q.
d
uJ
i
10 .7
10 .9
10"11
10"13
i
10 "15 __._.___
10.17!_/Ik''
100 110
i ! i i
_ i .i i
i/ i i
/ i i _* i 1"°';"" I i
_ .,. ,I lit i i I
ili
120 130 140 150 150 170 180 190 200 210
PERCENT LOAD FACTOR, n z
FIGURE 10. DETERMINISTIC/PROBABILISTIC EQUIVALENCE
533
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Probabilistic design of advanced composite structure

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