NASA Technical Reports Server (NTRS) 20010058885: Coupled Aerodynamic and Structural Sensitivity Analysis of a High-Speed Civil Transport

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by  NASA Technical Reports Server (NTRS)

t
AIAA-2001-1431
COUPLED AERODYNAMIC AND STRUCTUAL SENSITIVITY ANALYSIS OF A HIGH-SPEED CIVIL
TRANSPORT
B. H. Mason*
Analytical and Computational Methods Branch
and
J.L. Walsh*
Multidisciplinary Optimization Branch
NASA Langley Research Center
Hampton, VA 23681-2 t99
Abstract Wc Cruise weight
An objective of the High Performance Computing wM Maneuver weight
and Communication Program at the NASA Langley Kc Stiffness matrix (cruise shape)
Research Center is to demonstrate multidisciplinary Ko Stiffness matrix (unloaded shape)
shape and sizing optimization of a complete aerospace LF Inertial load factor (g's)
vehicle configuration by using high-fidelity, finite-
element structural analysis and computational fluid Introduction
dynamics aerodynamic analysis. In a previous study, a One of the objectives of the High Performance
multi-disciplinary analysis system for a high-speed civil Computing and Communication Program (HPCCP) at
transport was formulated to integrate a set of existing NASA Langley Research Center (LaRC) has been to
discipline analysis codes, some of them promote the use of advanced computing techniques to
computationally intensive. This paper is an extension rapidly solve the problem of multidisciplinary
of the previous study, in which the sensitivity analysis optimization of aerospace vehicles. In 1992, the
for the coupled aerodynamic and structural analysis HPCCP Computational Aerosciences (CAS) team at
problem is formulated and implemented. Uncoupled LaRC began a multidisciplinary analysis and
stress sensitivities computed with a constant load vector optimization software project. Initially, the focus of the
in a commercial finite element analysis code are CAS project was on the software integration system
compared to coupled aeroelastic sensitivities computed used to integrate fast analysis on a simplified design
by finite differences. The computational expense of application. The sample application for this project was
these sensitivity calculation methods is discussed. a High Speed Civil Transport (HSCT). Over the years,
progressively more complex engineering analyses have
Nomenclature been incorporated. In 1997, the sample application
ac Aerodynamic cruise load vector shifted to a more realistic model and higher fidelity
am Aerodynamic maneuver (converged) load vector analyses and is referred to as the HSCT4.0 application.
fa Augmented structural load vector The analysis formulation and preliminary results from
fc Structural cruise load vector the HSCT4.0 application were presented in Refs. 1and
fM Structural maneuver (converged) load vector 2, respectively. However, sensitivity analysis was not
So Unloaded shape vector performed in Refs. 1and 2.
Sc Cruise shape vector As discussed in Refs. 1 and 2, analytical
s_t Maneuver (converged) shape vector sensitivities can be obtained from most of the analysis
era Stress vector (due to augmented loads) codes by using automatic differentiation tools.
Uo Displacement (unloaded to cruise shape) vector However, Ref. 1 discussed the one major stumbling
Ua Augmented displacement vector block in formulating the sensitivity analysis--obtaining
Uc Cruise displacement vector sensitivity derivatives of the converged aeroelastic
uM Maneuver (converged) displacement vector loads and using those derivatives in a commercial finite
v Independent design variables element code. The aerodynamic pressures and
•Aerospace Engineer, Member AIAA
' Senior Research Engineer, Senior Member AIAA
Copyright ©2001 by the American Institute of Aeronautics and Astronautics, Inc. No copyright isasserted in the United States under Title 17, U.S. Code. The US.
Government hits arob,airy-free license to exercise all rights under the copyright claimed herein for Governmental Purposes. All other rights are reserved by the
copyright owner.
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structural deformations in the wing shape are mutually include engines. The GENESIS ®t° finite element
dependent. Because of this coupling between analysis code (a product of VR&D, Inc.) uses the
aerodynamic and structural responses, the sensitivity of 40,000 degree-of-freedom (DOF) FEM for
the aeroelastic loads is difficult to compute. displacement and stress response calculations. In this
Researchers use one of two methods to compute these FEM, the engines are modeled as masses on beam
aeroelastic sensitivity derivatives. For the first method, elements. Seven laterally symmetric load conditions
researchers assume that the aeroelastic loads are are used-- one cruise load condition and six maneuver
constant and then use exiting methods to obtain conditions (three at +2.5g and three at -l.0g). Note that
sensitivity derivatives. In the second method, the taxi condition used in Refs. 1and 2 is not used in
researchers assume the loads vary and use finite the present work.
differences to obtain sensitivity derivatives. There has
been some research __ using the global sensitivity
equations (GSE 6) to account for the coupling of
aerodynamics and structures. In Refs. 4 and 5, the GSE
were applied to simplified HSCT models to compute
derivatives of aerodynamic coefficients. In this paper,
the effects of the coupled aeroelastic loads on the
Fig. 1. HSCT4.1 linear aerodynamic model.
computation of stress sensitivities will be examined.
In Refs. 1and 2, the HSCT4.0 analysis consisted of
an integrated set of discipline codes and interface
codes. These codes were implemented in a CORBA-
Java computing environment known as CJOPT 7. The
present research does not use the CJOPT system;
instead, the discipline codes and interface codes are
implemented in the Phoenix Integration, Inc.'s
Fig. 2. ttSCT4.1 finite element model.
ModelCenter ®8. Implementation of the codes in
ModelCenter ®is not discussed in this paper. The work
Qptimization Problem Description
presented in the current paper is referred to as the
The objective function of the HSCT4.1
HSCT4.1 application.
optimization problem is to minimize the aircraft gross
In the HSCT4.1 application, the coupling of the
takeoff weight (GTOW) subject to stress constraints.
aeroelastic loads in the stress derivatives is important
The HSCT4.1 application has 271 design variables for
because both shape and structural design variables are
optimization--244 structural thickness variables and 27
used in the sensitivity analysis. The present paper will
shape variables. To limit the number of independent
quantify the effect of aeroelastic coupling on stresses.
structural design variables, the optimization model is
Coupled stress sensitivities obtained by finite difference
divided into 61 design variable zones. Each zone
techniques (with loads varying) are compared with un-
consists of several finite elements. Thirty-nine zones
coupled stress sensitivities obtained from a commercial
are located on the fuselage, and twenty-two zones are
finite element code (with loads held constant).
located on the wing (half are on the upper surface and
First, an overview of the model and analysis wilt
the other half are on the lower surface). Within each
be presented. Next, the coupled and uncoupled stress
zone, four structural design variables are used. These
sensitivity analysis formulation will be presented.
structural design variables consist of three ply-thickness
Finally, sample results for both the coupled and
variables (a 0°fiber variable, a 45° fiber variable, and a
uncoupled stress sensitivities are compared for both
90°fiber variable with a dependent -45° fiber variable
shape and structural design variables.
set equal to the 45° variable) and a core thickness
variable. The 0° and 90° ply orientations at various
Overview
locations on the model and the composite laminate
stacking sequences are shown in Fig. 3.
HSCT 4.1 Model
The 27 shape design variables are divided into two
The HSCT4.1 application uses the same linear
sets. The first set contains 9 planform design variables-
aerodynamic and finite element models as the HSCT4.0
the root chord, the outboard break chord, the tip chord,
application described in Refs. 1 and 2. The linear
the distance from the semispan to the outboard break,
aerodynamics grid and the finite element model used
the leading edge sweep of the inboard wing panel, the
for HSCT4.1 are shown in Figs. 1and 2, respectively.
leading edge sweep of the outboard wing panel, the
An aerodynamic surface grid of approximately 1100
total projected area of the wing, the fuselage nose
grid points is used in the linear aerodynamics code
length, and the fuselage tail length. The second set
(USSAERO) 9. The aerodynamic model does not
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consistosfthreesetsofsixvariabletshatcontrotlhe
The HSCT 4.1 Analysis process is started from the
cambetrh,icknesasn,dsheaorfthewingairfoil.
top of the data flow (Fig. 4) where the design variable
values are prescribed. First, the Geometry process is
used to derive updated geometric grids and FEM
,_Outboard Wing section properties from the design variables. Next, the
90_ Fuselage _..../j" _ __ Weights process uses the derived FEM grid and section
o _ t----k_
properties to calculate detailed weights and the center
of gravity (c.g.) locations for specified flight conditions.
....... _ 90_ _ A Inboard Wing Theoretical FEM weights are computed for each node
from the FEM data. A reference as-built weight
mooalawmg 0/'-__ _ x t increment is added to the theoretical FEM weight at
each node to produce the as-built weight.
Face Sheet Next the Rigid Trim process is executed for the
cruise condition to determine the configuration angle of
attack and the tail deflection angle that combine to yield
a lift equal to the weight, with no net pitching moment.
I 90° The linear aerodynamics code is used to compute the
Face T core trimmed aerodynamic pressures on the cruise shape
aerodynamic grid. These pressures are then transferred
45° from the aerodynamic grid points to the FEM nodal
o:°,
forces in the z-direction. Inertial forces (nodal weights
Fig. 3. Ply orientations and composite laminate times g-factor) are added to the aerodynamic forces to
stacking sequence. create the structural load vector. This structural load
vector is used by the Displacements process to compute
HSCT4. ! Analysis Process the unloaded shape of the aircraft (see Appendix A for
As discussed in Refs. 1 and 2, the HSCT4.0 further details). These cruise displacements are saved
analysis is formulated as a sequence of processes in the as a reference set for the Loads Convergence process.
data flow diagrams, as shown in Fig. 4. The HSCT4.1 In the Loads Convergence process, aeroelastic trim
analysis is focused on the difficult aerodynamic- calculations are performed for the six noncruise toad
structures analysis-coupling problem and uses the conditions, to produce the aeroelastically converged
analysis processes shown by shaded circles in Fig. 4. loads on the aircraft (see Appendix B for further
By convention, this paper uses italics for process names details). Forces representing cabin pressure are added
from Fig. 4. to these converged loads and are multiplied by a factor
of safety (1.5). These augmented loads are used in the
Stress & Buckling process to compute stress and buck-
ling constraints for all elements contained in the 61
design zones on the fuselage and wing. Buckling
constraints are not considered in this paper.
HSCT4.1 Sensitivity Analysis Formulation
In this section, sensitivities (first order derivatives
with respect to the design variables) are formulated for
the objective function (GTOW) and the stress con-
straints. First, the weight sensitivities are formulated
analytically. Then the stress sensitivities for both the
coupled and uncoupled methods are formulated.
Weight Sensitivity Formulation
In the HSCT4.1 system, structural weight sensi-
tivities are computed analytically from the finite
element dimensions and material properties using chain
rule differentiation. Non-structural weights (fuel,
payload, and non-modeled structures) are assumed to be
constant (i.e. non-structural sensitivities are zero).
Only shell elements are sized by the structural
Fig. 4. Analysis' Process. design variables. Because the weight of each of these
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elementissa linearfunctionofthestructuradlesign
variabletsh,eweighstensitivitfyorthoseelemenwtsith dua ] r _-1dKc
-_v;_.cou_,_ = - [KcJ --_7-vUA (8)
respectto astructuradlesignvariableis simplythe
elemenatreamultipliebdythenumbeorfpliesandthe The relationship between structural design vari-
densitoyfthatply. ables and the stiffness matrix can be set up as direct
Elemenwt eightsensitivitiewsithrespectto the input to GENESIS ®. The Geometry process was used
shapdeesignvariableasrecomputebdychainruledif- to generate relationships between the nodes of the stiff-
ferentiatioonftheequationdsefiningthedimensionosf
ness matrix and the shape design variables as another
theelemen(ltengthforbeamsa,reaforshellsa,ndvol- set of GENESIS ® input. Therefore, the uncoupled
umeforsolidelementsT).he
Geometry process is used sensitivity term (Equation 8) can be computed directly
to compute the derivatives of the node locations with using the sensitivity analysis capability in GENESIS ®.
respect to the shape design variables. Element weights The coupled sensitivity term (Equation 7) is similar
and weight sensitivities are extrapolated to the finite to the displacement calculation equation (Equation 4).
element nodes by the weight code. The element weight Therefore, GENESIS ® can be used to compute the
sensitivities are totaled to obtain the GTOW sensitivity. coupled sensitivity term in the displacement sensitivity
equation from a linear static finite element displace-
Stress Sensitivity Formulation ment analysis using the load sensitivities as a nodal
Structural stresses, Oa, are functions of the force vector. One complication of this method is that
displacements. Therefore, the stresses and stress the sensitivities with respect to each design variable
sensitivity derivatives (dOrA(cid:0)dr) are defined as follows: must be defined as a separate load case (i.e. one load
case is required per design variable). Another compli-
OA = Oa(llA) (l)
cation is the fact that the augmented load sensitivity
dora - Ocra dltA (2) (dfa Idv) must be computed outside of GENESIS ®.
dv _ua dv
The augmented loads (1_) are computed from the
The relationship between the stresses and the displace- converged maneuver loads (fM), the factor of safety
ments are defined in GENESIS®; therefore, it is only
(1.5) and the cabin pressures (constant); therefore the
necessary to study the displacement derivatives derivatives of the augmented loads are:
(duA/dV). Linear static structural displacements at
dfa - 1.5 dfu (9)
converged maneuver conditions (UA) are computed
dv dv
within GENESIS ®from the stiffness matrix (Kc) and
In the Loads Convergence process, the maneuver
the augmented loads (fa) using Equations 3 and 4.
loads (fM) and maneuver displacements (UM) are
Kc UA = fA (3)
mutually dependent. The nature of this dependency is
uA = [Kc]lfa (4) discussed in Appendix B, and is represented in
Derivatives of UA with respect to the design variable Equations 10 and I1:
,,. = uM(_rM,v) (m)
vector (v) are obtained by differentiating Equation 3:
fu = fM6'U 'v) (11)
K dua + dKc Ua - dfa (5)
c dv T dv Because of the coupling offM and Uu, computation
of dfMIdv is complicated and beyond the scope of this
Rearranging Equation 5 gives:
paper. The total stress sensitivity derivative (dcraldv) is
dudvA _ [Kc_ 1dfdAv r[Kcj1-1 -d-X-_ C ua (6) obtained by substituting &_aldv from Equation 6 into
Equation 2. For the uncoupled stress sensitivity
In Equation 6, the displacement derivative is composed derivative, dualdv from Equation 8are used in Equation
of two terms. One term requires the force derivative, 2 instead. In the next section, results are presented for
which is derived from the coupled aerodynamic and analytically computed uncoupled stress sensitivities.
structural analyses, and is referred to as the coupled Coupling effects are shown by parametric stress
sensitivity term in Equation 7. analyses in the next section.
HSCT4.1 Weight and Stress Results
dv
Coupled Analysis results were presented in Ref. 2. To
The other term requires the stiffness matrix derivative, validate the HSCT4.1 Analysis process, loads
which is determined from structural terms only, and is convergence displacements and stress results from Ref.
referred to as the uncoupled sensitivity term, Equation 2 for the baseline configuration were compared with
8. HSCT4.1 results. The results from the two analyses
agreed with each other. In Ref. 2, ten iterations were
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usedinthe
Loads Convergence process. Therefore, all 1.00015
results in this paper used ten iterations in the Loads
Convergence process. Both parametrically- and
analytically-computed GTOW and stress results are 1.00005
presented in this section. ] 11..0000001000
Parametric studies were performed by perturbing
0.99995
one design variable at atime from its baseline value and
then running the complete HSCT 4.1 Analysis. In the 0.99990 J Design Variable 3
Z
parametric studies, design variables are perturbed by a (R°°tlCh°rd)_ I
maximum of 1% from their baseline values. 0.99985 _ _ .... _..
Structural responses (r, referred to as analytical 0.00000 >__, 1........... _- ........ *,
responses) are computed from Equation 12. Sensitivity 0.990 0.995 1.000 1.005 1.010
Design Variable 3(Normalized)
analyses are used to compute first order derivatives of
the response functions (dr/dv) at the baseline design Fig. 5. GTOW variation with design variable 3.
point (V_,seti,e).
dr 1.00002 [ c _ /
t ! -_-Parametric -- Analytic I //
r(v) = -_v(,,-','B,,5¢,,,¢) + rn,.,¢,,¢, (12) f L____ _/y
1.00001 ,_
Due to the large number of design variables
O
available for study, results for a small subset of the
design variables are presented in this paper; four of the
twenty-seven shape design variables (two chord
0.99999
lengths, one span length, and the wing planform area)
_.../j Design Variable 4
are selected for study. Further, only two of the 244 Z
0.99998y (Spa_
structural design variables (ply thicknesses in the
design variable zone at the wing break where the largest 0.00000 t...... _ _, ,,--'- .....
stresses occurred) are selected for study. 0.990 0.995 1.000 1.005 1.010
Design Variable 4(Normalized)
Weight Variations with Design Variables Fig. 6. GTOW variation with design variable 4.
Weight results are presented as the GTOW
normalized by the baseline GTOW. GTOW is plotted
1.0o0T002[ ÷Pa ame c--Anaiy],ic
as a function of the six selected design variables in
Figs. 5 to 10. The analytic GTOW curves are computed
using Equation 12 (linear approximations). Note that
the weight sensitivity calculations do not involve 1.000000 -
aeroelastic coupling. The analytic curves agreed with l 1.000001 i
the parametric curves. The GTOW axis is different in 0.999999
Figs. 5 to 8 (variations in shape variables) due to the Design Variable 5
_ ,_, /'/
large difference in the GTOW variations for each
variable. As described in the Weight Sensitivity section 0.999998 -> (Chord at__
and shown in Figs. 9 and 10 (variations in structural 0.000000 _ ._ .... _,,........ t ....
variables), weight is a linear function of the each of the '.990 0.995 1.000 1.005 l.OIO
structural design variables. Design Variable 5(Normalized)
Fig. 7. GTOW variation with design variable 5.
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1.0004 r Zone 40_//_
-*- Parametric _ Z A_
Upper Surface _ _"- 25035 _k_ -
Lower Surface 25082
_ 0.9998
Zone 41/ "xN...]
Z 0.9996 (Wing Planfo_ Fig. 11. Elements selected for stress responses.
> _ -_
0.0000 ...... + ........ _, -_-_-_-_ In Figs. 12 to 29, parametrically and analytically
0.990 0.995 1.000 1.005 1.010 computed SFI values are plotted as functions of the
Design Variable 7(Normalized)
design variables. All analytical SFI curves are
Fig. 8. GTOW variation with design variable 7. determined using Equation 12 where the uncoupled
stress sensitivity (obtained from GENESIS ® using
Equations 2 and 8) is used for the response sensitivity
1.00002 _ I -_- Parametric -- Analytic ]
term (dr(cid:0)dr). In the following plots this stress
sensitivity is represented as the slope of the analytic
stress curve.
1.00000 _ SFI responses for element 5140 (on the fuselage)
are plotted in Figs. 12 to 17. The ranges of the SFI axes
0.99999 _'-"_J
in Figs. 12 to 15 are identical for comparison purposes.
r Design Variable 184
The parametric SFI response curves in Figs. 12 to 15
0.99998 _ (0°Plies in_ are shallow curves (not quite linear). It is noted that the
slope of the parametric curves at the baseline design
0.00000 _ _,_, ...... t ..... _........ _
point (normalized design variable value of 1.0) are
0.990 0.995 1.000 1.005 1.010
different from the slope of the analytic (uncoupled)
Design Variable 184 (Normalized)
curve. The difference in the slopes varies from one
Fig. 9. GTOW variation with design variable 184. variable to another, but in general the difference is
significant. The ranges of the SFI axes in Figs. 16 and
17 are magnified from Figs. 12 to 15 because the
-o-Parametric -- Analytic
sensitivity of the SFI in the fuselage is much smaller
with respect to changes in the upper wing surface (zone
_ 1.00001
40) ply thicknesses. Because the sensitivity with
respect to variables 184 and 185 is very small, the SFI
00o00 response is more erratic. Some of this noise is the
result of round-off error due to passing results from one
0.99999 lJ Dei_ariable 185
analysis code to another using low-precision text
_ 0.99998 _" (+45° Plies in_ output. This noise could also be due to the nonlinearity
of the SFI response.
0._ _ ..... _ ...... t _ ' _ Note that the differences in the slopes of the
0.990 0.995 1.000 1.005 1.010
parametric and analytic (uncoupled) SFI response
Design Variable 185 (Normalized)
curves are larger in Figs. 12 to 15 than in Figs. 16 and
Fig. 10. GTOW variation with design variable 185. 17. Thus, the coupling effect (due to aeroelastic forces)
seems to be larger for the shape design variables than
Stress Variations with Design Variables for the structural design variables. The aeroelastic
Stress results are presented as stress failure index
forces are a function of the weight and the HSCT shape.
(SFI) values (Ref. 2). In the Analysis process, stresses
Shape variables affect both the shape and the weight,
are computed for eight plies of 2260 sized elements for while the structural design variables only affect the
six load conditions. Due to the large number of results
weight. Therefore, the shape variables have a larger
(108,480 responses), only subsets of these results are
coupling effect for the SFI responses than the structural
presented in this paper. Stress results are shown only variables; a conclusion, which is supported by Figs. 12
for one of the three +2.5g maneuver load conditions to 17.
and for three elements (see Fig. 11) with large stress
responses.
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1.01 i -_- Parametric -- Analytic_ I 1.01 [ ] -O-Parametric --Analytic ]
0l.OO!
0.99 ._ 0.99
1.00
"q._.0_.98 t--- n n ...... =--e----o__._.._.___________
o.97
0.97
,_ _ Design Variable 7
0 _"_ Design Variable 3 _ 0.96 _ (Wing Plan fo__
095_>
o.95____ _ ___2X_
0.00 r .......... _.... • _-_ ..... ,_-q 00011 ÷ _ +-......
0.990 0.995 1.000 1.005 1.010 0.990 0.995 1.000 1005 1.010
Design Variable 3(Normalized) Design Variable 7(Normalized)
Fig. 12. SFI variation with design variable 3for Fig. 15. SFI variation with design variable 7for
element 5140. element 5140.
0.9820
1.01 ! [ -B.Paramctric --Analytic_ [ -_ Parametric _ Analytic--]
1.00
0.99 i
IZ o ....._. _ 0.9816
0.9818 _.__@
0.98 _--_--'--------o---:'-_ .... m---aa_-a:t
_0.97 _" 0.9814 -
"_ I Design Variable 4 -- _ Design Variable 184
09812 (0° Plies in Z°ne 40)
_0.96 [ (Span_ (
0.95__,> _ _2_
0.00 [ ..... + ....... _..... _ ....... t 0 ,- _-'-_+- t ........... -_
0.990 0.995 1.000 1.005 1.010 0.990 0.995 1.000 1.005 1.010
Design Variable 4(Normalized) Design Variable 184(Normalized)
Fig. 13. SFI variation with design variable 4 for Fig. 16. SFI variation with design variable 184 for
element 5140. element 5140.
1.01
o9o ;
I-o-Parametric -- Analytic_.]. _
1.00
0.9818
0.99
_ 0.9816
0.98
j.-----
_0.97
_0.96 Design Variable 5 -- _ 0.9814
t (+45°Plies in Zone 40)./"]
r_
(Chord al_____
0.95
0.0000 .... . .-, ...... t ' '--_-t ..... _-_
0.990 0.995 !.000 1.005 1.010 0.990 0.995 1.000 1.005 1.010
Design Variable 5(Normalized) Design Variable 185 (Normalized)
Fig. 14. SFI variation with design variable 5 for Fig. 17. SFI variation with design variable 185 for
element 5140. element 5140.
SFI responses for element 25035 (on the upper
wing surface, see Fig. 11) are plotted in Figs. 18 to 23.
The ranges of the SFI axes in Figs. 18 to 21 are
identical for comparison purposes. The parametric SFI
responses in Figs. 18 to 21 are nearly linear functions
within the selected design variable range. Again, the
slopes of the parametric SFI curves are different from
the slopes of the analytic (uncoupled) SFI responses.
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TherangesoftheSFIaxesinFigs.22and23are 1.20 -
differentthanFigs.18to21becaustheesensitivitieasre -a-Parametric --Analytic ]
smallerU. nliketheSFIsensitivitieinsFigs.16and17, 1.15
thesensitivitieinsFigs.22and23arelargerthanthe
_ 1.I0
numericanloisein theSFIvariation.Thelarger
sensitivitieinsFigs.22and23arebecaustheethickness
ofelemen2t5035issizedbystructuradlesigvnariables 1.05
184and185.Asintheearliefrigurest,heeffecot fthe
1.00
couplingtermintheSFIsensitivitieisslargefrorthe
(Wing Planfo_
shapveariabletshanforthestructurvaal riables. 0.95_
0.00 t I ........ + , _ _-t
1.20 ! i -w Parametric --Analytic_ 0.990 0.995 1.000 1.005 1.010
Design Variable 7(Normalized)
1.15 _.j Fig. 21. SFI variation with design variable 7for
element 25035.
_ 1.05 1.072
o_100 t DesignVafiable 3 -"--,_--- i_ -_ Parametric --Analytic
1+068
o.95j._
1,064
0.990 0.995 1.000 1.005 1.010
Design Variable 3(Normalized) 1.060
Fig. 18. SFI variation with design variable 3 for
element 25035. 1.056
<
1.20 0.000 _ _I ..... _ ...... _ ......... t
I -o-Parametric --Analytic ]
0.990 0.995 1.000 1.005 1.010
Design Variable 184 (Normalized)
1.15 _
Fig. 22. SFI variation with design variable 184 for
1.10 element 25035.
1.072 { -_-Pammetric --Analylic ]
_ 1.00 _ Design Variable 4 /.-7
,_,_ i (Span_ /
_, 1.068
0.990 0.995 1,000 1.005 1.010
Design Variable 4(Normalized)
Fig. 19. SFI variation with design variable 4for 1.060 Design Varia
element 25035.
0.000 i _ ' _+ ....... _ ..... _
1.20 i I -O-Parametric --Analytic ]
1.15 0.990 0.995 1,000 1.005 1.010
Deign Variable 185 (Normalized)
_1.10 Fig. 23. SFI variation with design variable 185 for
1.05 element 25035.
1.00 i Design Variable 5 SFI responses for element 25082 (on the lower
_ (Chord atbre_ 2)_ wing surface, see Fig. 11) are plotted in Figs. 24 to 29.
f
The ranges of the SFI axes in Figs. 24 to 27 are
identical for comparison purposes. The parametric SFI
0.990 0.995 1.000 1.005 1.010 responses in Figs. 24 to 27 are nearly linear functions
Design Variable 5(Normalized) within the selected design variable range. Again, the
Fig. 20. SFI variation with design variable 5for slopes of the parametric SFI curves are slightly
element 25035. different from the slopes of the analytic (uncoupled)
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SFIresponseTsh. erangeosftheSFIaxesinFigs.28
0.82 -_
and29aremagnifiefdromFigs.24to27becausthee } L -z-Parametric -- Analytic ]
sensitivitoyftheSFIinthelowerwingsurfaciesmuch
smallerwithrespectto changeisn theupperwing
"_ 0.74
surface(zone40)plythicknesseAs.sbeforeb,ecause _, 0.78
thesensitivitwyithrespectotvariable1s84and185are
._ 0.70
verysmall,theeffectsofnoiseintheSFIresponsise
morepronouncedA.sintheearliefrigurest,heeffect 0.66 Design Variable 5
of the couplingterm
(Equation 7) in the SFI 0.62 (Chord at
sensitivities is larger for the shape variables than for the
structural variables. 0.00
_.990 0.995 1.000 1.005 1.010
Design Variable 5(Normalized)
Fig. 26. SFI variation with design variable 5for
element 25082.
0.82 [ [ -e-parametric -- Analytic !S
u°i _
0.74 1
070
Desigo ri le7
0.990 0.995 1.04)0 1.005 1.010 • _ ._ (WingPlanform Area).8
Design Variable 3(Normalized)
Fig. 24. SFI variation with design variable 3 for 0.62_ ''_ _..------- _
element 25082. 0.00 _...... I..... _ .... -t
0.990 0.995 1.000 1.005 1.010
Design Variable 7(Normalized)
0.82 ,
Fig. 27. SFI variation with design variable 7 for
0.78_....... -_-_ [ Parametric --Analytic I element 25082.
074f
0.7190
-o- Parametric -- Analytic ]
0.7185
_!"0t'66 f Design Variable 4 _"'-_
_0.7180
.'_ 0.7175
F t
0.990 0.995 1.Nit? 1.0t75 1.010 _ 0.7170 Design Variable 184
Design Variable 4(Normalized) (0°Plies in Zone 40)//7
0.7165
Fig. 25. SFI variation with design variable 4for
element 25082. 0.0000 ..... _ ....._. f ...........÷.... -1
0.990 0.995 1000 1.005 1.010
Design Variable 184 (Normalized)
Fig. 28. SFI variation with design variable 184 for
element 25082.
9
American Institute of Aeronautics and Astronautics
terms in the stress sensitivities and in parallel execution
0.7190
-a-Parametric -- Analytic ] of the HSCT4.1 system.
0.7185
References
_0.7180 _Walsh, J. L., Townsend, J. C., Salas, A. O., Samareh,
--_0.7175 J. A., Mukhopadhyay, V., and Barthelemy, J.-F.,
"Multidisciplinary High-Fidelity Analysis and
0.7170 Design Variable 185 Optimization of Aerospace Vehicles, Part 1:
(+45°Plies in Zone 40)//7 Formulation," AIAA Paper 2000-0418, January 2000.
0.7165
0.0000 ........ ÷ ...... +............ _ 2Walsh, J. L., Weston, R. P., Samareh, J. A., Mason, B.
0.990 0.995 1.000 1.005 1.010 H., Green, L. L., and Biedron, R. T., "Multidisciplinary
Design Variable 185 (Normalized) High-Fidelity Analysis and Optimization of Aerospace
Fig. 29. SFI variation with design variable 185 for Vehicles, Part 2: Preliminary Results," AIAA Paper
element 25082. 2000-0419, January 2000.
Performance of the analysis and sensitivity 3Barthelemy, J.-F.M., Wrenn, G. A., Dovi, A. R., Coen,
calculation methods is shown in Table 1. Computing P. G., and Hall, L.E., "Supersonic Transport Wing
the stress sensitivities with respect to all 271 design Minimum Weight Design Integrating Aerodynamics
variables by finite differences requires 272 executions and Structures," Journal of Aircraft, Vol. 31, No. 2,
of the entire Analysis process, about 1768 hours. In 1994, pp. 330--338.
comparison, the analytic (uncoupled) stress sensitivity
calculation requires only 7.0 hours. Thus while not as 4Giunta, A. A., and Sobieszczanski-Sobieski, J.,
accurate, the computational expense of the analytic "Progress Toward Using Sensitivity Derivatives in a
(uncoupled) sensitivity calculation is much lower than High-Fidelity Aeroelastic Analysis of a Supersonic
finite difference sensitivities. Transport," Proceedings of the 7th AIAA/USAF/NASA/
ISSMO Symposium on Multidisciplinary Analysis and
Table 1. CPU Time Required for Analyses Optimization, Part 1, St. Louis, MO, 1998, pp.441-
CPU Execution Time (hrs.) 453.
Process Analysis Finite Uncoupled
Difference Stress 5Giunta, A. A. "Sensitivity Analysis for Coupled Aero-
Structural Systems," NASA TM-1999-209367, August
Sensitivity, Sensitivity
1999.
Aero. 6.10 1659.20 6.10
Disp. 0.37 99.73 0.37
6Sobieszczanski-Sobieski, J., "Sensitivity of Complex,
Stress 0.03 9.07 0.03
Internally Coupled Systems," AIAA J., 28(1), 1990,
Stress/_v 0.00 0.00 0.50
pp.153-160.
Total 6.50 1768.00 7.00
7Sistla, R., Dovi, A. R., Su, P., and Shanmugasun-
Concluding Remarks daram, R., "Aircraft Design Problem Implementation
In this paper, a system for coupled aerodynamic Under the Common Object Request Broker Architec-
and structural analysis of a HSCT using the ture," 40th AIAA/ASME/ASCE/AHS/ASC Structures,
ModelCenter ® framework is presented. Formulations Structural Dynamics, and Materials Conference and
for weight and stress sensitivity derivatives are Exhibit, St. Louis, MO, 1999, pp. 1296-1305B.
presented. The stress sensitivities are shown to con-
stitute both uncoupled structural and coupled aero- 8"Process Integration Using ModelCenter®, '' Technical
structural derivative terms. Analytically computed White Paper, Phoenix Integration, Inc., Blacksburg,
GTOW sensitivities are shown to match slopes of VA, 2000.
parametric GTOW curves well. Parametric and
analytic (uncoupled) stress responses are compared and 9Woodward, F. A., "USSAERO Computer Program
demonstrate that the aero-structural coupling has a Development, Versions B and C," NASA CR-3228,
significant effect on the stress responses. The coupling April 1980.
effect is larger for the shape design variables than for
the structural design variables. Further research is l°Vanderplaats, G. N., GENESIS _ User's Manual,
recommended in analytic calculation of the coupled Version 5.0, Colorado Springs, CO, 1998.
10
American Institute of Aeronautics and Astronautics