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N87-1 1721
FLUTTER OPTIMIZATION IN FIGHTER AIRCRAFT DESIGN William E. Triplett McDonnell Aircraft Company St. Louis, MO OPTIMIZATION APPLICATIONS The efficient design of aircraft structure involves a series of compromises among various engineering disciplines. These compromises are necessary to ensure the best overall design. To effectively reconcile the various technical con- straints requires a number of design iteratlons, with the accompanying long elapsed time. Automated procedures can reduce the elapsed time, improve productivity and hold the promise of optimum designs which may be missed by batch processing.
This presentation includes several examples of optimization applications including aeroelastic constraints. Particular attention is given to the success or failure of each example and the lessons learned. The specific applications are shown in Figure I. The final two applications were made recently.
Design Program Configuration Phase COPS F-15 Stabilator 12 Conceptual TSO Preliminary Various Configurations 345 FASTOP Preliminary NASTRAN Beam-Rod Wing 67 NASTRAN Detail NASTRAN Beam-Rod Stabilator "Sensitivity" Figure 1 COPS ANALYTICAL MODEL Figure 2 illustrates the modeling of the stabilator in the Computerized Optimization Procedure for Stabilators (COPS); Reference l describes the procedure.
The analytical model is a single-cell torque box idealized by eight discrete rigid chord streamwise sections with three mass points per section. Quasi-steady aero- dynamic forces act at user specified locations in each section. Nondimensional geometrical design parameters may be specified for taper ratio, thickness ratios at root and tip chords, aspect ratio, leading edge sweep angle, tip cut-off angle, pitch axis hinge line angle, pitch axis intersection with the mean aerodynamic chord (MAC), and spar locations.
Y (Left) Z(+ Down) Figure 2 COPS CONCEPTUAL FLOW DIAGRAM A greatly simplified flow diagram is shown in Figure 3. The procedure synthe- sizes, from the input data, a stabilator which satisfies all system constraints except those for flutter and divergence. A systematic perturbation of design vari- ables for I) torsional stiffness, 2) balance weight, 3) pitch restraint and 4) roll restraint follows until the aeroelastic constraint is satisfied for minimum addi- tional weight. The procedure may be used in its basic sequential optimization scheme, where a new dynamic system is established after each iteration step. It may alternately be used in its simultaneous optimization mode, where each design variable is individually and exclusively evaluated from the same initial design point. The basic COPS program contains a realistic representation for every signi- ficant aspect of a believable stabilator flutter analysis and is fast enough, on the computer, to be used as an integral part of more encompassing aircraft systems optimization programs, as shown in the figure.
System Module ance Requirements and Sizes Surface Calculates Ld_ and Drag Coefhcqents i Satisfies Stablhty Margm and Perform- Calculates Load Distribution Aerodynamic I Sizes Hydraulic Aclualor /% • Synthesizes Strength Design StaDilator b • Calculates Shffness Distrlbuhons
ts--K 1
III _3 I Design Re-Evaluation Scheme to Determine | Weight Medule Scheme to Sahsly Flutter Assesses Effect of Current Stabulator Overall Ophmum • Calculates Weight Olstrnbuhon
X
Stabilator Constraint on Overall System • Updates Dnstrlbutions for Flutter • For Minimum Re-Evaluates Stabilator Status and • Variation of S{abll_tor Conhgurahon Moddicahons 'Z
i: o...,.s_ I Parameters
I Weight S(abilator Re-Sizes Stabilator and Aircratl for
]
Specified Aircraft Performance | DyMmkcs M oduie
:i
Calculates Aerodynamic Matrix Structural I Calcukates Stiffness and Inerha Matrix Assess Dynamic Status ot Stab_lator the O -- -- ator _Yes N° PayoRy_ s [_Ye Payoff II • Minimum Stabilator m • Optimized Overal_System Parameter Optimized Overall System Parameter Weight 1or Specified Nondimensionaf Geometry for Variable Geometry Stabllator ,.u,.
Fi gure 3 5O COPS EXAMPLE - EARLY CONCEPTUAL DESIGN FOR F-15 STABILATOR Using the semi-automatic "simultaneous" procedure, the COPS program was used to calculate the ratios of the change of flutter dynamic pressure to weight change (AQ/AW) for separate perturbations of stiffness at each of the elastic axis sta- tions, as shown in Figure 4a. Flutter was calculated for specified levels of AQ/AW and compared, in Figure 4b, with optimization runs based on a torsional stiffness distribution proportional to the fourth power of the local chord and separately by balance weights at the tip leading edge. The balance Weight of approximately 15 Ib is the minimum weight solution. Figure 4c shows the stiffness distributions for both the C4 and sensitivity approaches.
Sensitivities for Separate Comparison of Stiffness Perturbations of Stiffness Distributions tor Flutter 10 100 _32.6 Ib C 4 Distribulion Iteratio 5 Comparison of Weight for Flutter
\ /
10 I I I /i E.A, Station
8 oo,ioo, Icuto,to _-- 20.7 Ib
AQ/AW = 0,03cutoff AQ/AW Q 6 --_--_ ....
"_1 0"I/.I Jstrength ]6_ /--_Q/AW=0 0.1 Distribution 1 1/in, 2 \8 Ib/in.2 4 )' I I I I 0 C4 stiffness distribution 2 I _ AQ/Aw sensitivity distribution 10 8 Ib-in. 2 '__ [3 Balanceweight LE 8th section
0.01 -'E 0.1
420 430 440 450 460 470 480
L_2
Weight -Ib (b) 0 0.01 0 1 2 3 6 1 3 5 7 9 AW -Ib E.A. Station (a) (c) Figure 4 DETAIL DESIGN OF OPTIMUM F-15 STABILATOR Two separate configurations were considered for the final F-15 detail design, as shown in Figure 5a and discussed in Reference 2. The flutter model test results are summarized in Figure 5b. The 15-1b balance weight produces an overall increase in flutter speed with Mach number. The snag leading edge produces an overall increase in flutter speed, similar to that for the balance weight, at low speeds.
However, the speed variation with Mach number is quite different, with the snag showing an initial sharper drop with increasing Mach number followed by a subse- quent sharper rise with further Mach number increase. Analyses indicated the favorable sharper rise to be associated primarily with the aft shift in stabilator aerodynamic center attributable to the area removed by the snag. The snag offered a significant weight savings over the balance weight with no effect on subsonic drag, aircraft stability or flying qualities. A small supersonic drag penalty was offset by the attendant weight reduction.
Alternate Configurations Flutter Velocity vs Mach Number 1.6 BalanceWei'ght Snags[ 1.2 Unstable .. L'_,_-_ _...._ Snag /"_-_-_ _ \ \ Leading / _ _ \ \ Normalized Stable ..,.-_.q-_ Velocity 0.8 J__ "-Aircraft Envelope 0.4 f '_ laar°/g i_lutter
/ i l
SquaredTip for 15 Ib .4 0.2 0.4 0.6 0.8 1.0 1.2 OutboardLeading /4" " Edge Balance Weight--/ NormalizedMach Number (b) (a) Figure 5
AEROELASTIC TAILORING STUDY CONFIGURATIONS
Studies have been conducted on the use of the directional properties of compos-
ite material to provide design improvements for fighter aircraft as discussed in
Reference 3. The TSO (Aeroelastic Tailoring and Structural Optimization) computer
program, Reference 4, which was developed by the Air Force Flight Dynamics Labora-
tory (AFFDL), was used in these investigations. The configurations evaluated,
shown in Figure 6, covered a wide spectrum of fighter aircraft aerodynamic
surfaces, including I) the F-15 composite wing, 2) a preliminary design horizontal
tail, 3) a prototype aircraft movable outer panel, and 4) a conceptual wing for a
future aircraft. The TSO program was validated with the F-15 composite wing which
was designed to have the same distributed stiffness characteristics as the produc-
tion metal wing. In spite of the structural approximations required by the TSO
program, the predicted aeroelastic properties were surprisingly close to measured
val ues.
Aeroelastic Tailoring Studies J • Flutter, Strength and Loads J odynamic Drag _ Figure 6 AEROELASTIC TAILORING RESULTS Aeroelastic tailoring can play a significant role in the design of aircraft in various ways, as indicated in Figure 7. Specific detail is given for each configura- tion in References 3 and 5.
As currently configured, the TSO computer program is appropriate for use pri- marily in preliminary design. The restrictive structural modeling requirements of TSO lead to converged results which are generally qualitative and which must be liberally interpreted when converting to a design that can be built. The experi- ence gained in the validation studies of the F-15 composite wing design, however, indicates that skillful use of the procedure can also yield good results in final detail design.
F-15 Composite Wing • Drag Reduction and Increased Roll Effectiveness With No Weight Cost Preliminary Design Horizontal Tail • Composite Material Performs Dual Function of Strength and Flutter Balance Weight Prototype Aircraft Movable Outer Panel • Optimum Solution Based on Wing Root Pitch Restraint Increases Conceptual Design Wing • Significant Wing Twist Offering Potential Aerodynamic Benefits Forward Swept Wing • Zero Weight Cost for Divergence Figure 7 EQUIVALENT AFT SWEPT WING MODELS The optimized forward swept wing (FSW) was compared with three equivalent aft swept wings (ASW),shown in Figure 8,and evaluated for the same design constraints, as discussed in Reference 5. They are I) an Equivalent Leading Edge sweep, where the ASW leading edge sweep angle is the negative of the FSW leading edge sweep angle, 2) an Equivalent Elastic Axis sweep, and 3) a Flipped Wing. The wing geometry applies to all four wings. The wings were shifted longitudinally to give the same locations for the mean aerodynamic chords (MAC). The same aerodynamic and struc- tural models were used for all four wings. One of the apparent effects of the equivalent leading edge design is a structural bending axis that is about 20% shorter than the axis of the FSW. The bending axis for the flipped wing design, on the other hand, is about 12% longer.
ALE = _ 30.30 ° ATE --53.72 ° LEA= 221 in.
Wing Geometry NACA 64AOXX Theo Area 382.92 ft 2 Equivalent Aspect Ratio 3.80 Leading Edge 0.15 Taper Ratio ALE=30.30 ° MAC 228.9 in.
Span/2 ATE = -- 10.98 ° 209.5 in.
CR (Theo) LEA= 176 in.
31.4 in.
CT Mean Aero Chord 142.5 in.
Equivalent 86.3 in.
YMAC Elastic Axis t/c (Root) 0.052 ALE=48.45 ° t/c (Tip) 0.050 ATE= 19.31 ° LEA= 221 in.
Flipped Wing ALE = 53.72 ° ATE = 30.30 ° LEA = 248 in.
Figure 8
COMPARISON OF FORWARD SWEPT WING WITH
THREE EQUIVALENT AFT SWEPT WINGS
Each of the ASWswas optimized by TSOand the results are shown in Figure 9.
The FSWhas the highest torque box skin weight and the Equivalent LE ASW,which is
essentially a straight wing such as on the F-18, has the lowest weight. This
weight advantage of the nearly straight wing is a direct result of the reduced
structural axis length, which can be seen by comparing the bending momentnormal to
the elastic axis at the fuselage moldline. The air loading is also most favorable
for the design of the fuselage carry-through structure on the FSW and the straight
wing, as shown by considering both pitch and roll moments at the wing root. The
ASWsare divergence free but have an active flutter constraint. The FSW has favor-
able flutter properties, primarily because the frequency of the wing bending mode
changes very little with increasing airspeed. Coupling with the torsion modestill
occurs, but at a higher velocity than for the ASWs.
ASW ASW ASW FSW Equivalent Equivalent Flipped Elastic Optimum Leading Wing Axis Edge Composite Layer Orientation -80.9, -45, -45, -45, +11.1, O, O, O,
- deg(81, 82, (93 With
+45 Respect to Bending Axis) +14.5 +45 +45 227.5 118.9 Torque Box Skin Weight - Ib 162.1 158.9 Wash-in Angle at Tip - deg 5.1 -0.2 -5.1 (Elastic) Total Panel ]I Load 59,159 64,973 62,240 Roll Moment at Panel 11 Root About BL 60.8 - in.-IbxlO 6 4.03 4.51 4.10 3.78 Pitch Moment at Panel ]I 3.56 -1.65 5.63 6.08 Root About Xo - in.-Ibx106 Bending Moment Normal to Elastic Axis at Moldline - in.-IbxlO 6 6.32 4.27 4.47 454 Divergence Velocity - kt 936 NA NA NA (Required Velocity = 912) Flutter Velocity - kt 82O 76O 1,050 810 Aileron Roll Effectiveness= 0.29 Total RM/Rigid RM 1.13 0.43 0.35 Flexible/Rigid Panel ]1 Lift Ratio 0.80 1.19 1.01 0.85 Mach 0.9, Sea Level, 7.33 g Figure 9 FASTOP APPLICATION TO NASTRAN BEAM-ROD DYNAMIC MODEL The FASTOP (Flutter and Strength Optimization Program) computer program (Refer- ence 6) which was developed by the AFFDL, has been applied to a beam-rod vibration and flutter idealization of a wing/store flutter model. The chosen configuration for this detail design application was a wind tunnel model with two stores on an outboard pylon and wing tip missile on,as described in Reference 7. The NASTRAN model is shown in Figure lO. The NASTRAN beam elements are based on GJ and El stiffness distributions, referred to an elastic axis, with similar distributions for the lead- ing and trailing edge control surfaces and the missile. There are rigid bars to connect the various components with the proper boundary conditions. Concentrated- elasticity members are used to represent integral springs, e.g. actuators, wing fold, missile/launcher/wing interfaces and wing/fuselage attachment. Structural optimization is not feasible because FASTOP does not calculate stresses in the beam elements. Steady air loads are not required because the starting point is an existing strength design. It was felt that the chances for success would be excel- lent for this simple straightforward model which has only 147 structural members.
Figure 10 FASTOP ANALYTICAL CONSIDERATIONS and computational difficulties were encountered in convert- Many approximations ing the NASTRAN model to FASTOP, as indicated in Figure II.
Strength Analysis • Concentrated Elasticity Converted to Pseudo Rigid Beams • Rigid Bars Converted to Pseudo Rigid Beams • Grid Points Renumbered to Satisfy Bandwidth Requirement • Trailing Edge Control Surface Actuator Beams Placed in Plane of the Wing • Pylon and Stores Eliminated From Analysis Vibration Analysis • Diagonal Inertia Matrix to Satisfy Positive Definite Check • Vibration Calculated for Only 20 Normal Modes • Frequency Comparison Better Than Expected Considering Structural Compromises Unsteady Aerodynamics • Three-Dimensional Missile Model Converted to Flat Plate to Satisfy Interpolation Procedure Flutter Analysis • Non-Optimum Weight Factors Defined for Each Beam Element • Resizing Permitted Only for Main Torque Box and Control Surfaces Figure 11
FASTOP FLUTTER OPTIMIZATION RESULTS
The results shown in Figure 12 look promising until one examines the redesign
changes in the individual elements. The first 3 design cycles add increments of
weight to the structural elements in proportion to their flutter velocity deriva-
tives, _Vf/_W i, provided the derivatives are larger than an arbitrary minimum.
This arbitrary minimum, which is not specified by the user, leads to an uneven span-
wise distribution with peaks and valleys. It suffers from the lack of a built-in
French Curve, which would smooth out the peaks and valleys to create a near-optimum
design that could be built. The design cycles 4-10 continue the optimization by
adjusting the weight distribution, while maintaining the desired flutter velocity.
This weight adjustment reduces the increments along the wing torque box and builds
up a large mass at the leading edge of the wing. The final design has only a large
mass at the leading edge, near mid span, much like a forward mounted engine on a
transport aircraft wing.
1.0
10 _,_ _ _,_ 9876 5 4
0.9
Normalized
Flutter
Velocity
0.8
150 2OO 250 Weight Change - Ib Figure 12 SENSITIVITY ANALYSIS DATA PREPARATION This approach to flutter optimization is based on a "sensitivity" technique similar to that first explored in conjunction with the development of the COPS program, which is described in Figure 4. The study was done in an extremely short elapsed time using existing flutter data sets for a beam-rod stabilator idealization based on NASTRAN and Doublet lattice. The only new data required are the GJ versus number of 45 ° plies per skin for several elastic axis (EA) stations, as shown in Figure 13a. With these data the change in GJ versus elastic axis station can be calculated for various weight increments, as shown in Figure 13bo StrengthData Weight Data 300 280 AW=41b _13 12 111101 9181716 5 4 I _ NASTRAN Stations
',.. IIIll
I 250 B A E.A. Siations 3 Ib i I 200 / 20o \ C 160 \ _ 5_.._lb GJ i AGJ 2 Ib I 106 Ib-in. 2 120 " " "_ _-_ 106 ib-in. 2 _ _ _ '_
•
,_,_ ,,X_ rE"
,o
• ..._.,,. -,_'-_ _.t_ 0 0 8 20 32 44 A B C D E Number of 45 ° Plies Per Skin Elastic Axis (a) (b) Figure 13 6O SENSITIVITY OPTIMIZATION RESULTS The steps in the sensitivity optimization study are given in Figure 14. Each step of the redesign is based on batch submittals of the NASTRAN flutter routines, followed by a conscious choice for the elements to be used in the subsequent step.
After step 4 it is possible, by the use of engineering judgment, to specify a redesign distribution which satisfies the flutter requirement and is practical to build. These studies are state of the art in all respects and are quicker, cheaper and more accurate than possible with any currently available automatic optimization procedure.
Step1 Step2 Step3 InitialDesign Redesign 1 (8 Ib) Redesign 2 (12 Ib) AW= 2 Ib Increments AW= 2 Ib Increments _,W= 2 Ib Increments Station VF* Redesign Station V F Redesign Station VF Redesign W W W 13 0.864 13 0.936 13 0.961 12 0.865 12 0.937 12 0.963 11 0868 11 0.940 11 0.965 10 0.868 !0 0.940 10 0.965 9 0.873 9 0.961 2
j-9 0.945 2
8 0.872 8 0.961 2 18 0.943 2 7 0939 2 7 0.964 2 7 0.879 2 6 0.877 2 6 0.939 2 6 0.964 2 _" 5 0.881 2 5 0.943 2 ,_ f5 0.968 4 _4 0.878 2 4 0.944 2 14 0.969 4 Redesign 1 8 Ib Redesign 2 12 Ib Redesign 3 16 Ib Step6 Verification Step4 Step5 Redesign 3 (16 Ib) Engineering Judgment Redesign 5 (20 Ib) _I,W= 1 Ib Increments TestCase AW = 1 Ib Increments Station VF Redesign Station VF Redesign Station V F Redesign W W W 13 0.983 13 1 003 12 0.984 12 12 1.004 11 1.003 _Fll 0.986 I 11 1 10 1 10 1.003 t,10 0.985 1 9 1.003 Step 5 9 0.982 2 9 2 8 1.002 is 8 0.982 2 8 2 OK 7 1.002 7 0.983 2 7 3 6 0.983 2 6 3 6 1.002 5 4 5 1.0O3 5 0.984 4 4 0.984 4 4 4 4 1.004 Redesign 4 18 Ib Redesign 5 20 Ib *v F is normalized to Vrequlred MF=I.0 Figure 14 CONCLUSIONS AND RECOMMENDATIONS The following conclusions are appropriate in the area of flutter optimization.
I) COPS, or a similar routine, is suitable for use in conceptual design for individual lifting surfaces when the geometry is undefined.
TSO is suitable for use in preliminary design for individual lifting
2)
surfaces when the geometry is defined but there is still no well-defined structural model. Limitations in the structural model allow only limited use in detail design.
3) FASTOP is based on a sound concept but is not general enough for use in detail design and is too difficult to use in preliminary design.
4) NASTRAN based semi-automatic sensitivity techniques are the preferred
approach for detail designs when the structural model is well defined but the flutter speed is deficient.
Since NASTRAN is the accepted industry standard for structural analyses it seems appropriate to either I) incorporate flutter optimization routines in NASTRAN or 2) ensure that any alternate program developments have a complete one.to-one rela- tionship to NASTRAN in all respects, and are designed to include generation of input data by graphics procedures.
Conclusions
• COPS Is Suitable for Conceptual Design • TSO Is Suitable for Preliminary Design • NASTRAN Sensitivity Technique Is Suitable for Detail Design
Becommendations
• Incorporate Flutter Optimization in NASTRAN • If Alternate Procedurej Ensure Complete One-to-One Relationship to NASTRAN Including Graphics Generation of Bulk Data Figure 15 REFERENCES l • Triplett, W. E., and Ising, K. D., "Computer Aided Stabilator Design Including Aeroelastic Constraints," Journal of Aircraft, July 1971.
o Shelton, J. D., and Tucker, P. B., "Minimum Weight Design of the F-15 Empen- nage for Fl utter," AIAA/ASME/SAE 16th Structures, Structural Dynamics and Materials Conference (SSDM), Denver, Colorado, 27-29 May 1975.
• Triplett, W. E., "Aeroelastic Tailoring Studies in Fighter Aircraft Design," Journal of Aircraft, July 1980.
o Lynch, R. W., Rogers, W. A., and Braymen, W. W., "Aeroelastic Tailoring of Advanced Composite Structures for Mil itary Aircraft ," AFFDL-TR-76-100, Vol. III, February 1978.
o Triplett, W. E., "Aeroelastic Tailoring of a Forward Swept Wing and Compari- sons with Three Equivalent Aft Swept Wings ,, AIAA/ASME/ASCE/AHS 21st Struc- tures, Structural Dynamics and Materials Conference (SSDM), Seattle, Wash., 12- 14 May, 1980.
• Markowitz, J., and Isakson, G., "FASTOP-3: A Strength, Deflection, and Flutter Optimization Program for Metallic and composite Structures," AFFDL-TR- 78-50, Ma X 1978.
o Triplett, W. E., "Wind Tunnel Correlation Study of Aerodynamic Modeling for F/A-18 Wing-Store Tip-Missile Flutter," AIAA/ASME/ASCE/AHS 24th Structures, Structural Dynamics and Materials Conference (SSDM), Lake Tahoe, Nev., 2-4 May 1983. (Journal of Aircraft, Spring 1984)