Aeroelastic Tailoring Study of N+2 Low-Boom Supersonic Commercial Transport Aircraft

Aeroelastic Tailoring Study of an N+2 Low - boom

Supersonic Commercial Transport Aircraft

Prepared For:

AIAA Aviation 2015

AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference

June 22 - 26, Dallas, Texas

Prepared By: Chan - gi Pak, Ph.D.

Structural Dynamics Group, Aerostructures Branch (Code RS)

NASA Armstrong Flight Research Center

Overview

 Supersonic Commercial Transport Aircraft Design

 Game Change Approach in Aircraft Design

 Multidisciplinary Design Optimization tool

 Multidisciplinary Analysis of the Baseline Configuration

 Structural and Aerodynamic Models

 Modal Analyses

 Flutter Analyses

 Trim Analyses

 Landing and Ground Control Loads

 Buckling and Strength Analyses

 First Optimization Run

 Second Optimization Run

 Third Optimization Run

 Conclusions

 Future Studies

Chan - gi Pak - 2 Structural Dynamics Group

Supersonic Commercial Transport Aircraft Design

 Major Issues  Safety  Light weight airframe can cause strength, buckling, aeroelastic , and aeroservoelastic problems.

 Sonic boom  Supersonic flight of “commercial transport” aircraft allowed only over the ocean.

HSCT  Perceived Loudness in decibels  NASA’s N+2 goal: 85 PLdB  Concorde: 104 PLdB  High Speed Civil Transport (HSCT ): 99 PLdB  Fuel efficiency  Light weight airframe  Reduced drag  Developing N+2 Low - boom Supersonic Commercial Transport (LSCT) aircraft  Boeing Lockheed Martin  Lockheed Martin: 79 PLdB  Gulf Stream  Aerion with “Airbus” Concorde Aerion Chan - gi Pak - 3 Structural Dynamics Group Boeing Gulf Stream

Game Change Approach in Aircraft Design

Problem Statement  Design innovations are needed to further down the weight of an aircraft which current design technologies can take care of .

Long Term Objective  Use aeroelastic tailoring theory and active flexible motion control technique to satisfy the overall strain, aeroelastic , and aeroservoelastic instability requirements within given flight envelopes  Use curvilinear sparib concept as well as composite ply angles for aeroelastic tailoring Approach  Simultaneously update structural as well as control design variables during early design phase  Perform topology optimization with curvilinear sparibs e  Use aeroelastic tailoring up to V L V  Use aeroservoelastic tailoring between V and 1.15 V L L Current Study Flutter Boundary Use  Optimize baseline aircraft model Aeroservoelastic  U se Lockheed Martin’s configuration Tailoring  Use aeroelastic tailoring up to 1.15 V L Equivalent Speed Use Curvilinear sparibs Aeroelastic Tailoring 1.15 V V L L Mach Number 0.5 1.0 Chan - gi Pak - 4 Structural Dynamics Group

Multidisciplinary Design Optimization tool

 Based on Object - Oriented Optimization tool Update MSC/NASTRAN sol 103  Open MDAO, Model Center, Visual Doc, etc.

NASTRAN Total weight, CG location, input Curvilinear mass moment of inertia, Surrogate Sparib Frequencies, & mode shapes : Incorporated : Modules are being developed Gain/Phase Modal Optimizer : Not included yet Margins MSC/NASTRAN for small weight ADS; DOT; In - house code for large weight GA; & BBBC Update P I = 𝑊 W 𝑇 Weight ZAERO(ASE) Objective input MSC/NASTRAN sol 105 Design 3 Function J & O tool Object In - house code for computing MS Variables Constraints ZAERO code for flutter analyses Oriented Use safety factor of 1.5 G(x) I n - house code for flutter speed Strength Flutter Optimization tracking V F Failure Load Tool P I ≡ 1 − F M S ≡ − 1 1 . 15 V Design Load × Safety Factor L In - house P I ≡ − mi n ( MS Buckling s Script ASE tools Performance … Commands Indices In - house code for computing BLF Use safety factor of 1.5 Landing & CFD Based … Loads & Flutter Ground Control 2 2 Update P I ≡ 1 2 − positive min BLF − 1 2 B Processing ZAERO(Trim) Air Loads input Trim In - house code for massaging splined loads Chan - gi Pak - 5 Structural Dynamics Group

Multidisciplinary Analysis of the

Baseline Configuration

Structural and Aerodynamic Models

Top Down View Front View Front View Flow Through Top View Top View Bottom View Bottom View Side View Side View  MSC/NASTRAN structural model  ZAERO unsteady aerodynamic model  Total number of grids: 55,635  5,060 surface elements  Six Mach numbers: 0.66, 0.89, 1.41, 1.80, 2.00, and 2.30  Sixteen reduced frequencies: 0., 0.005, 0.01, 0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.35, 0.40, 0.45, 0.50, 0.65, 0.80, 1.0 Chan - gi Pak - 7 Structural Dynamics Group

Modal Analyses of the Baseline Configuration

 Based on six configurations  Gear up  DTOW(Design Take Off Weight), FFEP(Full Fuel Empty Payload), M2W(Mach 2 Weight), & ZFW(Zero Fuel Weight)  DTOW=FFFP (Full Fuel Full Payload)  ZFW=EFFP (Empty Fuel Full Payload)  Gear down  DTOW(or FFFP) and DLW(Design Landing Weight)

Natural Frequency (Hz)

Mode

Notes Gear - up Gear - down

Number

DTOW FFEP M2W ZFW DTOW DLW

7 2.049 2.055 2.071 2.266 2.048 2.158 Aft fuselage torsion

2.235 2.262 2.277 2.554 2.238 2.424 First symmetric fuselage bending

9 2.498 2.509 2.539 2.993 2.503 2.714 First symmetric wing bending

10 2.754 2.769 2.935 3.415 2.752 3.265 First anti - symmetric wing bending

3.060 3.069 3.115 3.731 3.057 3.403 Symmetric tail bending

3.562 3.608 3.689 4.044 3.574 3.945 Forward fuselage lateral bending

13 4.440 4.449 4.511 4.790 4.429 4.602 First anti - symmetric tail bending

4.456 4.537 4.555 5.532 4.437 5.142 Second symmetric wing bending

4.818 4.842 5.146 5.832 4.809 5.542 Second anti - symmetric wing bending

16 5.449 5.465 5.550 6.158 5.444 5.994 Symmetric aft inner wing bending

Chan - gi Pak - 8 Structural Dynamics Group

Flexible Mode Shapes (gear up: DTOW)

Aft fuselage torsion First symmetric fuselage bending First symmetric wing bending Z nodal line Z nodal line Z nodal line rd nd st 3 Mode: 2.498 Hz 2 Mode: 2.235 Hz 1 Mode: 2.049 Hz Forward fuselage lateral bending First anti - symmetric wing bending Symmetric tail bending Z nodal line Y nodal line Z nodal line th th th 4 Mode: 2.754 Hz 5 Mode: 3.060 Hz 6 Mode: 3.562 Hz Chan - gi Pak - 9 Structural Dynamics Group

Flutter Analyses of the Baseline Configuration

0.10  Based on four structural configurations at six Mach numbers Use damping definition in Fig.6  Gear up 0.05 1% damping  DTOW, FFEP, EFEP, & ZFW 0.00  Mach numbers of 0.66, 0.89, 1.41, 1.80, 2.00, & 2.30 -0.05 Damping -0.10 -0.15 : Empty Fuel Empty Payload (EFEP) : Full Fuel Empty Payload (FFEP) -0.20 : Zero Fuel Weight (ZLW) : Design Take-Off Weight (DTOW) 0 100 200 300 400 500 600 700 800 900 1000 20k 10k -10k S.L.

Speed (Keas) DTOW at M=0.66 (a) V-g Curves Payload Based on 1% 6.00 damping 30k 40k 5.00 50k Fuel 4.00 60k Speed (Keas) 70k Inside 15% margin line Frequency (Hz) 3.00 1.15V L V L 2.00 0 100 200 300 400 500 600 700 800 900 1000 0 0.5 1 1.5 2 2.5 Speed (Keas) Mach Number (b) V-f Curves Chan - gi Pak - 10 Structural Dynamics Group

Trim Analyses of the Baseline Configuration

 Trim flight conditions Load Load Mach Landing Case Maneuver Weight Altitude Trim Variables Factor Number Gear ID 100 Pull up 2.5g 0.66 DTOW Up SL BF( R=L ) 200 Push over - 1g 0.66 DTOW Up SL BF( R=L ) 300 Pull up 2.5g 0.48 DTOW Up SL BF( R=L ) 400 Pull up 2.5g 2.00 M2W Up 49 , 770ft BF=TEF( R=L ) 500 Push over - 1g 2.00 M2W Up 49 , 770ft BF( R=L ) 600 Pull up 2.5g 1.41 DTOW Up 49 , 770ft BF=TEF=AIL1=AIL2( R=L ) 700 Pull up 2.5g 0.66 ZFW Up SL BF( R=L ) 800 Push over - 1g 0.66 ZFW Up SL BF( R=L ) 900 Pull up 2.5g 2.00 ZFW Up 49 , 770ft BF=TEF( R=L ) 1000 Push over - 1g 2.00 ZFW Up 49 , 770ft BF( R=L ) 1100 Steady roll 0g 0.48 DTOW Up SL Load Case 2100+2300 1200 Abrupt roll 0g 0.48 DTOW Up SL Load Case 2200+2300 Trailing-Edge Flap 1300 Steady roll 1.67g 0.48 DTOW Up SL Load Case 2100+2400 1400 Abrupt roll 1.67g 0.48 DTOW Up SL Load Case 2200+2400 (R) (L) 1500 Landing 1g 0.3092 DTOW Down SL BF( R=L ) 1600 Cruise 1g 1.80 DTOW Up 55 , 000ft BF=TEF( R=L ) 1700 Gust Loads 2.7g 0.89 ZFW Up 20 , 000ft BF( R=L ) 1800 Landing 1g 0.3092 DLW Down SL BF( R=L ) Aileron #1 (R) Aileron #1 (L) 2100 Steady roll 0g 0.48 DTOW Up SL AIL1=AIL2( R= - L ) Aileron #2 (R) Aileron #2 (L) 2200 Abrupt roll 0g 0.48 DTOW Up SL AIL1=AIL2( R= - L ) 2300 Pull up 0 g 0.48 DTOW Up SL BF( R=L ) (R) (L) 2400 Pull up 1.67g 0.48 DTOW Up SL BF( R=L ) Body Flap Chan - gi Pak - 11 Structural Dynamics Group

Trim Analyses of the Baseline Configuration (continue)

Load Case 100 200 300 400 500 600 700 800 900  Trim results Trim Analysis Symmetric  In general trim angles are larger than NASTRAN Nx (G) - 0.007 - 0.003 - 0.005 0.001 0.002 - 0.004 - 0.016 - 0.006 0.003 Nz (G) 2.5 - 1.0 2.5 2.5 - 1.0 2.5 2.5 - 1.0 2.5 results.

Pdot (rad/s /g) None None None None None None None None None Qdot (rad/s /g) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 Pb/2V (rad) None None None None None None None None None Qc/2V (rad) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 7.75 - 2.50 14.37 8.32 - 2.81 16.90 4.10 - 1.04 5.07  °)  Body Flap  °) 2.01 - 6.07 6.12 - 5.25 5.42 - 25.68 - 8.01 - 1.59 - 12.92 - 5.25 - 25.68 - 12.92 Trailing - Edge Flap  °) - 25.68 Aileron #1  °) Aileron #2  °) - 25.68 Mach Number 0.66 0.66 0.48 2.00 2.00 1.41 0.66 0.66 2.00 Altitude (ft) SL SL SL 49770 49770 49770 SL SL 49770 Weight Configuration DTOW DTOW DTOW M2W M2W DTOW ZFW ZFW ZFW Gear Configuration Up Up Up Up Up Up Up Up Up Load Case 1000 1100 1200 1300 1400 1500 1600 1700 1800 Trim Analysis Sym. Asymmetric (sym. + Anti - sym.) Symmetric Nx (G) 0.004 - 0.002 - 0.002 - 0.004 - 0.004 - 0.002 0.002 - 0.022 - 0.001 Nz (G) - 1.0 0.0 0.0 1.67 1.67 1.0 1.0 2.7 1.0 Pdot (rad/s /g) None 0.0 0.0014 0.0 0.0014 None None None None Qdot (rad/s /g) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 NASTRAN Pb/2V (rad) None 0.0410 0.0 0.0410 0.0 None None None None aerodynamic Qc/2V (rad) 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 - 1.44 0.40 0.40 9.74 9.74 13.91 6.02 4.95 9.07 model  °)  11.89 - 2.86 - 2.86 3.14 3.14 8.00 - 9.87 - 13.20 22.52 Body Flap  °) Trailing - Edge Flap  °) - 9.87 19.07 48.63 19.07 48.63 Aileron #1  °) 19.07 48.63 19.07 48.63 Aileron #2  °) Mach Number 2.00 0.48 0.48 0.48 0.48 0.3092 1.80 0.89 0.3092 Altitude (ft) 49770 SL SL SL SL SL 55000 20000 SL Flat panels for Weight Configuration ZFW DTOW DTOW DTOW DTOW DTOW DTOW ZFW DLW fuselage and engine Gear Configuration Up Up Up Up Up Down Up Up Down Chan - gi Pak - 12 Structural Dynamics Group Load Case Number Load Right - MLG Left - MLG NLG

Landing and Ground Control Loads of the

Cases FX 0.0 0.0 0.0

Baseline Configuration

FY 0.0 0.0 0.0 Static FM 𝑆𝑡 d W Condition 𝐶𝐺 2 𝑀𝐺 𝑇  Landing loads 0 . 5d W Ground Control Loads FZ 𝐶𝐺 2 𝑁𝐺 𝑇 FM FN = 𝑆𝑡 𝑆𝑡 = d 𝑁𝐺 2 𝑀𝐺 d 𝑁𝐺 2 𝑀𝐺  Ground control loads FX 0 . 8FM 0 . 8FM 0.0 𝑆𝑡 𝑆𝑡 FY 0.0 0.0 0.0  Emergency landing loads (applied to three engine structures) 3 - point 3009 (DTOW) 2 d FM + 2 ( 𝑍 − 𝑍 0 . 8FM braked roll & 4009 (DLW) 𝐶𝐺 2 𝑀𝐺 𝑆𝑡 𝐶𝐺 𝑀𝐺𝐶𝑃 FZ FM FM  9G forward loading; 1.5G rearward loading; 3G sideway loading; & 𝑆𝑡 𝑆𝑡 d 𝐶𝐺 2 𝑁𝐺 6G downward loading Landing Loads FX 0 . 8FM 0 . 8FM 0.0 𝑆𝑡 𝑆𝑡 2 - point 3010 (DTOW) FY 0.0 0.0 0.0 braked roll & 4010 (DLW) Load Cases Case Number Load Right - MLG Left - MLG NLG FZ 0.0 FM FM 𝑆𝑡 𝑆𝑡 FX 0 . 25 FM 0 . 25 FM 0 . 25 FN FX 0 . 8FM 0 . 8FM 0.0 𝐿𝑣 𝐿𝑣 𝐿𝑣 𝑆𝑡 𝑆𝑡 Level + 300 1 (DTOW) FY 0.0 0.0 0.0 FY 0.0 0.0 0.0 & 4001 (DLW) Trim load W f d 𝜇𝐸 FZ 𝑇 𝐶𝐺 2 𝑁𝐺 FM = f W FM FN = f W 𝐿𝑣 𝐿𝑀𝐺 𝑇 𝐿𝑣 𝐿𝑣 𝐿𝑁𝐺 𝑇 Dynamic d + 𝐶𝐺 2 𝑀𝐺 3011 (DTOW) d d + 𝜇𝐸 FX ( 0 . 8 × 0 . 8 FM ( 0 . 8 × 0 . 8 FM ( 0 . 8 × 0 . 8 FN roll 𝑁𝐺 2 𝑀𝐺 𝑁𝐺 2 𝑀𝐺 𝐿𝑣 𝐿𝑣 𝐿𝑣 & 4011 (DLW) Spin up + 3002 (DTOW) where, 𝐸 = 𝑍 − 𝑍 − ( 𝑋 − braking 𝐶𝐺 𝑁𝐺𝐶𝑃 𝐶𝐺 FY 0.0 0.0 0.0 FZ FM FM 𝑆𝑡 𝑆𝑡 & 4002 (DLW) Trim load 𝑋 𝑆 𝑁𝐺𝐶𝑃 FZ 0 . 8FM 0 . 8FM 0 . 8FN 𝐿𝑣 𝐿𝑣 𝐿𝑣 𝑍 − 𝑍 𝑀𝐺𝐶𝑃 𝑁𝐺𝐶𝑃 ( and 𝑆 = 𝑋 − 𝑋 𝐶𝐺 𝑁𝐺𝐶𝑃 FX − ( 0 . 8 × 0 . 8 FM − ( 0 . 8 × 0 . 8 FM − ( 0 . 8 × 0 . 8 FN 𝐿𝑣 𝐿𝑣 𝐿𝑣 𝑋 − 𝑋 𝑀𝐺𝐶𝑃 𝑁𝐺𝐶𝑃 Spring back 3003 (DTOW) FY 0.0 0.0 0.0 FX 0.0 0.0 0 . 25FN 𝑆𝑡 + Trim load & 4003 (DLW) Turning 3012 (DTOW) FY 0 . 5FM 0 . 5FM 0 . 5FN FZ 0 . 8FM 0 . 8FM 0 . 8FN 𝑆𝑡 𝑆𝑡 𝑆𝑡 𝐿𝑣 𝐿𝑣 𝐿𝑣 Condition & 4012 (DLW) FZ FM FM FN FX ( 0 . 4 × 0 . 75 FM ( 0 . 4 × 0 . 75 FM 0 . 4 FN Lateral 𝑆𝑡 𝑆𝑡 𝑆𝑡 𝐿𝑣 𝐿𝑣 𝐿𝑣 3004 (DTOW) FX 0.0 0.0 0.0 Nose wheel drift + FY ( 0 . 25 × 0 . 75 FM ( 0 . 25 × 0 . 75 FM 0 . 25 FN 𝐿𝑣 𝐿𝑣 𝐿 𝑣 3013 (DTOW) & 4004 (DLW) yaw & FY 0.0 0.0 0 . 8FN 𝑆𝑡 Trim load FZ 0 . 75FM 0 . 75FM FN & 4013 (DLW) 𝐿𝑣 𝐿𝑣 𝐿𝑣 steering (1) FZ FM FM FN 𝑆𝑡 𝑆𝑡 𝑆𝑡 Right one FX 0 . 25 FM 0.0 0.0 𝐿𝑣 3005 (DTOW) FX 0 . 8FM 0.0 0.0 𝑆𝑡 gear + Trim FY 0.0 0.0 0.0 Nose wheel & 4005 (DLW) FY 0.0 0.0 0.0 30 14 (DTOW) load FZ FM 0.0 0.0 yaw & 𝐿𝑣 2 d FM + ( 𝑍 − 𝑍 0 . 8FM & 40 14 (DLW) 𝐶𝐺 2 𝑀𝐺 𝑆𝑡 𝐶𝐺 𝑀𝐺𝐶𝑃 𝑆𝑡 steering (2) FZ FM FM FX 0.0 0 . 25 FM 0.0 Left one 𝑆𝑡 𝑆𝑡 𝐿𝑣 d 3006 (DTOW) 𝐶𝐺 2 𝑁𝐺 gear + Trim FY 0.0 0 .0 0.0 FX 0.0 0.0 & 4006 (DLW) 0 . 8FM 𝑆𝑡 load FZ 0.0 0.0 Nose wheel FM 𝐿𝑣 FY 0.0 0.0 0.0 30 15 (DTOW) yaw & FX 0.0 0.0 0.0 Side load ( & 40 15 (DLW) 2 d FM + 𝑍 − 𝑍 0 . 8FM 𝐶𝐺 2 𝑀𝐺 𝑆𝑡 𝐶𝐺 𝑀𝐺𝐶𝑃 𝑆𝑡 3007 (DTOW) steering (3) FZ FM FM 𝑆𝑡 𝑆𝑡 FY ( 0 . 8 × 0 . 5 FM ( 0 . 6 × 0 . 5 FM 0.0 RtoL + 𝐿𝑣 𝐿𝑣 d & 4007 (DLW) 𝐶𝐺 2 𝑁𝐺 Trim load FZ 0.0 0 . 5 FM 0 . 5 FM 𝐿𝑣 𝐿𝑣 FX 0.0 − 0 . 55FM − 0 . 55FM 𝑆𝑡 𝑆𝑡 Reversed 30 16 (DTOW) FX 0.0 0.0 0.0 Side load FY 0.0 0.0 0.0 3008 (DTOW) braking & 40 16 (DLW) FY − ( 0 . 6 × 0 . 5 FM − ( 0 . 8 × 0 . 5 FM 0.0 LtoR + FZ FM FM 0.0 𝐿𝑣 𝐿𝑣 𝑆𝑡 𝑆𝑡 & 4008 (DLW) Trim load FX 0.0 0.0 0.0 FZ 0 . 5 FM 0 . 5 FM 0.0 𝐿𝑣 𝐿𝑣 30 17 (DTOW) 2G Taxi FY 0.0 0.0 0.0 DTOW f =0.36; f =0.0639; Trim load case ID = 1500 𝐿𝑀𝐺 𝐿𝑁𝐺 & 40 17 (DLW) FZ 2FM 2FM 2FN 𝑆𝑡 𝑆𝑡 𝑆𝑡 DLW f =1.20; f =0.1477; Trim load case ID = 1800 𝐿𝑀𝐺 𝐿𝑁𝐺 𝜇 = 0 . 80 ; f=2.00 Chan - gi Pak - 13 Structural Dynamics Group

Buckling and Strength Analyses

Wing  Based on five analysis sets Analysis Gear Weight Load Cases Set Configuration Condition 1 Up DTOW 100, 200, 300, 600, 1100, 1200, 1300, 1400, & 1600 2 Up ZFW 700, 800, 900, 1000, & 1700 Center Line 3 Up M2W 400 & 500 3001 ~ 30 17 + 3018 ~ 3021 (emergency) + 1500 (for Case 300; DTOW 4 Down DTOW landing) 4001 ~ 40 17 + 4018 ~ 4021 (emergency) + 1800 (for 5 Down DLW landing)  Minimum buckling load factors from each analysis set Passenger Floor Minimum Analysis Gear Weight Case Load Case Buckling Load Buckling Set Configuration Condition Number Factor 1 Up DTOW 300 2.5G pull up; M=0.48 0.152 yes Buckling Center Engine Main Landing Gear Bay 2 Up ZFW 1700 2.7G gust loads; M=0.89 0.195 yes Buckling Load Factor > 1 or 3 Up M2W 400 2.5G pull up; M=2.00 0.151 yes 4 Down DTOW 3006 Left one gear landing 1.71 no Buckling Load Factor < 0 : requirement 5 Down DLW 4006 Left one gear landing 1.52 no  Minimum margins of safety from each analysis set Minimum Analysis Gear Weight Case Load Case Margin of Failure Margin of safety > 0 : requirement Set Configuration Condition Number Safety Safety factor = 1.5 1 Up DTOW 1400 1.67G abrupt roll; M=0.48 - 0.999 yes 2 Up ZFW 1700 2.7G gust loads; M=0.89 - 0.998 yes Failure Load 3 Up M2W 400 2.5G pull up; M=2.00 - 0.997 yes MS ≡ − 1 Design Load × Safety Factor 4 Down DTOW 3013 Nose wheel yaw & steering (1) - 0.781 yes 5 Down DLW 4003 Spring back landing - 0.657 yes Chan - gi Pak - 14 Structural Dynamics Group

First Optimization Run

Design Variables for the First Optimization Run

 Baseline configuration is in infeasible domain.

Wing tip spars & ribs  Manually increase 111 ply thicknesses.

 Wing, tail, inner - wing, and fuselage skins  Three variables st rd nd th

• 1 , 3 , & 2 = 4

Upper skins  Wing, inner - wing, and tail spars & ribs and fuselage bulkheads and walls Lower skins  One variable st nd rd th

• 1 =2 =3 =4

 Inner - wing spars & ribs  One variable th

• 5

st 1 : 0 ° nd 2 : 45 ° Spars, ribs, rd 3 : 90 ° Fuselage skins bulkheads, & floors th 4 : - 45 ° th 5 : 0 ° th 6 : - 45 ° th 7 : 90 ° th 8 : 45 ° th Infeasible 9 : 0 ° Feasible Symmetric stacking of nine plies Structural components affected into a composite laminate by thickness design variables Chan - gi Pak - 16 Structural Dynamics Group

First Optimization Run

Functions Performance indices Note s 2 2 ( ( DTOW Objective 𝐹 𝐗 = P I = 𝑊 W 𝑇 V F Flutter 𝑔 ( 𝐗 = P I = 1 . − < 0 .

𝑗 F 15% margin 1 . 15 V L constraint j = 1 , 2 , … , 6 2 2 𝑔 ( 𝐗 = P I = ( 1 / 2 − positive min ( BLF − 1 / 2 < 0 .

Buckling 𝑗 B Safety factor = 1.5 constraint j = 7 , 8 , … , 11 𝑔 ( 𝐗 = P I = − min ( MS ) < 0 .

Strength 𝑗 s Safety factor = 1.5 constr aint j = 12 , 13 , … , 16 : Empty Fuel Empty Payload (EFEP) : Full Fuel Empty Payload (FFEP)  Objective: total weight of gear up DTOW case : Zero Fuel Weight (ZLW) : Design Take-Off Weight (DTOW)  Flutter constraints 20k 10k -10k S.L.

 Gear Up DTOW at M=0.66, 0.89, & 1.41 Payload Based on  Gear up FFEP at M=0.66, 0.89, & 1.41 1% damping 30k  Buckling & strength constraints  Minimum “buckling load factor” & minimum “margin of safety” from 40k five analysis sets Analysis Gear Weight 50k Fuel Load Cases Set Configuration Condition 60k 1 Up DTOW 100, 200, 300, 600, 1100, 1200, 1300, 1400, & 1600 Speed (Keas) 2 Up ZFW 700, 800, 900, 1000, & 1700 70k 3 Up M2W 400 & 500 3001 ~ 30 17 + 3018 ~ 3021 (emergency) + 1500 (for 1.15V 4 Down DTOW L landing) V L 4001 ~ 40 17 + 4018 ~ 4021 (emergency) + 1800 (for 100 5 Down DLW landing) 0 0.5 1 1.5 2 2.5 Mach Number Chan - gi Pak - 17 Structural Dynamics Group

First Optimization Run (continue)

Performance Index Design Configuration Before Optimization Iteration 1 Iteration 7 Objective Function Total Weight DTOW; GU 332738 425764 364105 𝑔 𝐗 DTOW; GU; M=0.66 0.067(V) - 0.362 - 0.342 𝑔 𝐗 DTOW; GU; M=0.89 0.048(V) - 0.543 - 0.096 𝑔 𝐗 DTOW; GU; M=1.41 - 0.079 - 1.34 - 0.297 𝑔 𝐗 FFEP; GU; M=0.66 0.066(V) - 0.365 - 0.337 Flutter 𝑔 𝐗 FFEP; GU; M=0.89 0.034(V) - 0.586 - 0.094 𝑔 𝐗 FFEP; GU; M=1.41 - 0.095 - 1.32 - 0.255 𝑔 𝐗 DTOW; GU 0.152(V) - 1.05 - 1.29 Constraint 𝑔 𝐗 ZFW; GU 0.186(V) - 2.36 - 3.09 Functions 𝑔 𝐗 M2W; GU 0.151(V) - 1.28 - 1.91 𝑔 𝐗 𝑗 𝑔 𝐗 DTOW; GD - 0.960 - 3.27 - 3.88 1 0 Buckling 𝑔 𝐗 DLW; GD - 0.561 - 0.308 - 1.07 1 1 𝑔 𝐗 DTOW; GU 0.999(V) - 0.267 - 0.161 1 2 𝑔 𝐗 ZFW; GU 0.998(V) - 0.780 - 0.061 1 3 𝑔 𝐗 M2W; GU 0.997(V) - 0.179 - 0.537 1 4 𝑔 𝐗 DTOW; GD 0.781(V) - 0.751 - 5.63e - 6 1 5 Strength 𝑔 𝐗 DLW; GD 0.657(V) - 0.210 - 0.320 1 6 Weight penalty (%) 0 28.0 9.43 Manual Optimization based on DOT.

update Design Design infeasible feasible Active and near active constraints from strength analyses.

Chan - gi Pak - 18 Structural Dynamics Group

First Optimization Run (continue)

 Total thickness changes Mass balancing 5.0 Wing tip 2.0 spars & ribs Upper skins Lower skins 1.0 1.0 16.0 Spars, ribs, Fuselage skins bulkheads, & floors 10.0 Aft 1.0 Color spectrums represent 1.0 Forward “thickness after”/“thickness before”.

Chan - gi Pak - 19 Structural Dynamics Group

First Optimization Run (continue)

 Strain distribution of the active and near active constraints Gear up Forward Gear down Aft Main landing gear bay Forward (b) Near active constraint (from strength 2; load case #1700) Active element Gear up Aft Main landing gear bay Main landing Forward Aft gear bay (a) Active constraint (from strength 4; load case #3013) (c) Near active constraint (from strength 1; load case #300) Chan - gi Pak - 20 Structural Dynamics Group

Second Optimization Run

Design Variables for the Second Optimization Run

Forward  Composite ply angles of the six zones Bottom up Top down Zone 1  Design variables are ply angles of the Zone 1 view view nd th 2 and 4 layers. Aft nd th  Design variable linking 2 = - 4 Aft  Use discrete design variables Zone 4 Discrete Value Ranges values 0° 0 . 0 ° ≤ P ly angle < 2 . 5° 5° 2 . 5 ° ≤ P ly angle < 7 . 5° Zone 2 7 . 5 ° ≤ P ly angle < 12 . 5 ° 10° Zone 3 12 . 5 ° ≤ P ly angle < 17 . 5° 15° st 17 . 5 ° ≤ P ly angle < 22 . 5° 20° 1 : 0° nd Zone 5 25° 22 . 5 ° ≤ P ly angle < 27 . 5° 2 : 45° rd 30° 3 : 90° 27 . 5 ° ≤ P ly angle < 32 . 5° th 4 : -45° 32 . 5 ° ≤ P ly angle < 37 . 5° 35° 37 . 5 ° ≤ P ly angle < 42 . 5° 40° th 5 : 0° 42 . 5 ° ≤ P ly angle < 4 7 . 5° 45° Zone 6 50° 47 . 5 ° ≤ P ly angle < 52 . 5° th 6 : -45° 55° 52 . 5 ° ≤ P ly angle < 57 . 5° th 7 : 90° 57 . 5 ° ≤ P ly angle < 62 . 5° 60° th 8 : 45° 62 . 5 ° ≤ P ly angle < 67 . 5° 65° th 9 : 0° 67 . 5 ° ≤ P ly angle < 72 . 5° 70° 75° Aft 72 . 5 ° ≤ P ly angle < 77 . 5° Forward 77 . 5 ° ≤ P ly angl e < 82 . 5° 80° 82 . 5 ° ≤ P ly angle < 87 . 5° 85° 87 . 5 ° ≤ P ly angle ≤ 90 . 0° 90° Chan - gi Pak - 22 Structural Dynamics Group

Second Optimization Run

Functions Performance indices Note s DV ( ( ( ( S afety factor = 1.5 Objective 𝐹 𝐗 = − { 0 . 5 𝑔 𝐗 + 0 . 5 𝑔 𝐗 + 𝑔 𝐗 } 12 13 15 V F Infeasible Flutter 𝑔 ( 𝐗 = P I = 1 . − < 0 .

𝑗 F 15% margin 1 . 15 V domain L constraint Active j = 1 , 2 , … , 6 constraint 2 2 𝑔 ( 𝐗 = P I = ( 1 / 2 − positive min ( BLF − 1 / 2 < 0 .

Buckling 𝑗 B Safety factor = 1.5 constraint j = 7 , 8 , … , 11 𝑔 ( 𝐗 = P I = − min ( MS ) < 0 .

Strength 𝑗 s Safety factor = 1.5 constraint Tolerance j = 12 , 13 , … , 16  Purpose: Create more offset for active constraints Constraint nd th  Objective: performance index from the 2 and 4 strength analysis sets Feasible boundary domain  Flutter constraints DV  Same as the first optimization run DV : Design Variable i i  Buckling & strength constraints  Same as the first optimization run except performance indices for the objective function Analysis Gear Weight Load Cases Set Configuration Condition 1 Up DTOW 100, 200, 300, 600, 1100, 1200, 1300, 1400, & 1600 2 Up ZFW 700, 800, 900, 1000, & 1700 3 Up M2W 400 & 500 3001 ~ 30 17 + 3018 ~ 3021 (emergency) + 1500 (for 4 Down DTOW landing) 4001 ~ 40 17 + 4018 ~ 4021 (emergency) + 1800 (for 5 Down DLW landing) Chan - gi Pak - 23 Structural Dynamics Group

Second Optimization Run (continue)

Performance Index Design Configuration Starting BBBC 1 BBBC 2 Objective Function − 0 . 5 𝑔 𝐗 + 0 . 5 𝑔 𝐗 + 𝑔 𝐗 } 0.111 0.337 0.348 12 13 15 𝑔 𝐗 DTOW; GU; M=0.66 - 0.342 - 0.341 - 0.342 𝑔 𝐗 DTOW; GU; M=0.89 - 0.096 - 0.096 - 0.096 𝑔 𝐗 DTOW; GU; M=1.41 - 0.297 - 0.299 - 0.297 𝑔 𝐗 FFEP; GU; M=0.66 - 0.337 - 0.336 - 0.337 Flutter 𝑔 𝐗 FFEP; GU; M=0.89 - 0.094 - 0.095 - 0.094 𝑔 𝐗 FFEP; GU; M=1.41 - 0.255 - 0.257 - 0.255 𝑔 𝐗 DTOW; GU - 1.29 - 1.50 - 1.38 Constraint 𝑔 𝐗 ZFW; GU - 3.09 - 3.63 - 3.09 Functions 𝑔 𝐗 M2W; GU - 1.91 - 2.00 - 2.23 𝑔 𝐗 𝑗 𝑔 𝐗 DTOW; GD - 3.88 - 4.22 - 4.19 1 0 Buckling 𝑔 𝐗 DLW; GD - 1.07 - 1.07 - 1.07 1 1 𝑔 𝐗 DTOW; GU - 0.161 - 0.214 - 0.232 1 2 𝑔 𝐗 ZFW; GU - 0.061 - 0.141 - 0.145 1 3 𝑔 𝐗 M2W; GU - 0.537 - 0.204 - 0.542 1 4 𝑔 𝐗 DTOW; GD - 5.63e - 6 - 0.159 - 0.159 Strength 1 5 𝑔 𝐗 DLW; GD - 0.320 - 0.435 - 0.419 1 6 Design Variables Starting BBBC 1 BBBC 2 nd 1 (2 rib at inner - wing) 45 ° 15 ° 15 ° 2 (floor at main landing gear bay) 45 ° 65 ° 65 ° 3 (center wall at main landing gear bay) 45 ° 65 ° 55 ° 4 (aft bulkhead at main landing gear bay) 45 ° 65 ° 55 ° 45 ° 5 (aft fuselage skin 1) 30 ° 40 ° 45 ° 6 (aft fuselage skin 2) 50 ° 55 ° Big - Bang Big - Crunch algorithm; number of population=60; number of Big - Bang Big - Crunch=2; discrete design variables Chan - gi Pak - 24 Structural Dynamics Group

Third Optimization Run

Third Optimization Run

Functions Performance indices Note s 2 2 ( ( DTOW Objective 𝐹 𝐗 = P I = 𝑊 W 𝑇 V F Flutter 𝑔 ( 𝐗 = P I = 1 . − < 0 .

𝑗 F 15% margin 1 . 15 V L constraint j = 1 , 2 , … , 6 2 2 𝑔 ( 𝐗 = P I = ( 1 / 2 − positive min ( BLF − 1 / 2 < 0 .

Buckling 𝑗 B Safety factor = 1.5 constraint j = 7 , 8 , … , 11 𝑔 ( 𝐗 = P I = − min ( MS ) < 0 .

Strength 𝑗 s Safety factor = 1.5 constr aint j = 12 , 13 , … , 16  Objective: total weight of gear up DTOW case  Flutter constraints  Gear Up DTOW at M=0.66, 0.89, & 1.41  Gear up FFEP at M=0.66, 0.89, & 1.41  Buckling & strength constraints  Minimum “buckling load factor” & minimum “margin of safety” from five analysis sets Analysis Gear Weight Load Cases Set Configuration Condition 1 Up DTOW 100, 200, 300, 600, 1100, 1200, 1300, 1400, & 1600 2 Up ZFW 700, 800, 900, 1000, & 1700 3 Up M2W 400 & 500 3001 ~ 30 17 + 3018 ~ 3021 (emergency) + 1500 (for 4 Down DTOW landing) 4001 ~ 40 17 + 4018 ~ 4021 (emergency) + 1800 (for 5 Down DLW landing) Chan - gi Pak - 26 Structural Dynamics Group

Third Optimization Run

Performance Design Starting Iteration 1 Iteration 2 Iteration 3 Iteration 4 Iteration 5 Iteration 6 Iteration 7 Index Configuration Objective Total Weight DTOW; GU 364105 363810 Function 𝑔 𝐗 DTOW; M=0.66 - 0.342 - 0.341 𝑔 𝐗 DTOW; M=0.89 - 0.096 - 0.096 𝑔 𝐗 DTOW; M=1.41 - 0.297 - 0.297 𝑔 𝐗 FFEP; M=0.66 - 0.337 - 0.336 Flutter 𝑔 𝐗 FFEP; M=0.89 - 0.094 - 0.094 𝑔 𝐗 FFEP; M=1.41 - 0.255 - 0.256 𝑔 𝐗 DTOW; GU - 1.38 - 1.38 Constraint 𝑔 𝐗 ZFW; GU - 3.09 - 3.44 Functions 𝑔 𝐗 M2W; GU - 2.23 - 2.04 𝑔 𝐗 𝑗 𝑔 𝐗 DTOW; GD - 4.19 - 3.95 1 0 Buckling 𝑔 𝐗 DLW; GD - 1.07 - 1.07 1 1 𝑔 𝐗 DTOW; GU - 0.232 - 0.227 1 2 𝑔 𝐗 ZFW; GU - 0.145 - 0.141 1 3 𝑔 𝐗 M2W; GU - 0.542 - 0.261 1 4 𝑔 𝐗 DTOW; GD - 0.159 - 6.16e - 5 1 5 Strength 𝑔 𝐗 DLW; GD - 0.419 - 0.359 1 6 Weight penalty (%) 9.43 9.34 Optimization based on DOT.

Chan - gi Pak - 27 Structural Dynamics Group

Conclusions

 The Lockheed Martin’s pre - matured N+2 LSCT aircraft is optimized in this study through the use of a multidisciplinary design optimization tool developed at the NASA AFRC .

 The baseline design of the pre - matured N+2 LSCT aircraft was infeasible when ZAERO based aeroelastic analyses were used .

 This probably means that the aerodynamic loads distribution computed using ZAERO trim analysis are different than the MSC Nas tra n generated aerodynamic loads.

 The starting configuration of the optimization run should be an achievable design and weight penalty for this was 93,026 lb.

 28.0 % increase from baseline  During the first optimization run, the weight reduction was 61,659 lb , and therefore weight penalty at the end of the first optimization run is 31,367 lb.

 Optimization was based on DOT optimizer  Active constraint: minimum margin of safety value is associated with the structural component located at the second rib of the inner wing near the main landing gear bay area.

 Nose wheel yaw and steering case number 1  First near active constraint: minimum margin of safety value at the floor of main landing gear bay  2.7g gust load case at Mach 0.89 and altitude of 20,000 ft  9.4% increase from baseline  Second near active constraints: flutter speeds with DTOW and FFEP at Mach 0.89  Mass balancing effect to increase the flutter speeds  The second optimization run was prepared to increase tolerance distance for the active and the first near active constraints.

 Create more room for reducing total weight of the aircraft  Use six ply angles as design variables  Optimization was based on Big - Bang Big - Crunch algorithm with discrete design variables.

 Can’t change weight property, but can change strength property. Therefore, can create tolerance for future weight optimization run Chan - gi Pak - 28 Structural Dynamics Group

Questions ?

Deflection, Weight D & DT Stress, & Strain Structural Model Buckling Tuning Aerodynamic Frequency & Acoustic Model Tuning Optimizer Mode Shape Load Objective Flutter & Sonic Boom ??

Function J & Design O tool Divergence Constraints Variables Central Executive G(x) Module Gain/Phase NPSS Margins Script Performance … Commands Curvilinear Indices Lift & Drag Sparibs … Adaptive Landing & Flexible Motion Taxiing Control CFD Based Trim Flutter

Future Studies

 Use lifting surface based aerodynamics

 Use curvilinear sparibs to further reduce the weight of N+2 LSCT

 Find % weight reduction through curvilinear sparibs technique

 Add active control design variables

 Use a eroelastic tailoring up to V

L

 Use active control between V and 1.15V

L L

 Find % weight reduction through game changing approach

 Use CFD based aerodynamics

 Use more accurate air loads for optimizations

Chan - gi Pak - 30 Structural Dynamics Group

Backup: Object - Oriented MDO Tool

Object - Oriented MDO tool

 Optimization is based on in - house Object - Oriented Optimization tool  Equivalent to the following codes  Open MDAO, Model Center, Visual Doc, etc.

Pre - Post - processor  Four optimizer codes are available.

processor # i Need to develop;  Gradient based algorithms (Local optimizers) # i Depends on Discipline Optimizer  DOT Analysis code # i  ADS Pre - Objective  Global optimizers (Gradient free algorithms) Design Function J & processor Post - Object  Genetic Algorithm Variables Constraints #j processor Oriented  Big - Bang Big - Crunch Algorithm G(x) #j Optimization Discipline  Update design p re - processor m odule Tool #j Analysis code;  Update MSC/NASTRAN input file Commercial and/or Pre - Script Performance  Modal analysis module in - house codes processor Commands Indices  Perform modal analysis using MSC/NASTRAN sol. 103 #k Post - …  Save following data processor Discipline  Total weight, CG location, mass moment of inertia #k #k  Frequencies & mode shapes and global mass matrix  Weight post - processor module  Use MSC/NASTRAN sol 103 results for small weight.

 MSC/NASTRAN results has number of digit issue.

 Use in - house weight computation code for large weight.

P I = 𝑊 W 𝑇 Chan - gi Pak - 32 Structural Dynamics Group

Object - Oriented MDO tool (continue)

 Flutter analysis and flutter post - processor modules  Use ZAERO code for flutter analyses  Use an in - house flutter speed tracking program V V F F V > 1 . 15 V 1 . − < 0 . P I ≡ 1 . − F L F 1 . 15 V 1 . 15 V L L  Update ZAERO pre - processor, trim analysis, trim loads pre - processor modules  Update ZAERO input data  Based on total weight, CG locations, moment of inertias, and global mass matrix  Use ZAERO code for trim analysis  Create design loads for various design configurations  Post - process the splined loads  Create symmetric and anti - symmetric loads  Landing and ground control loads pre - processor module  Compute corresponding design loads using in - house code  Landing loads  Ground control loads  Emergency landing loads Chan - gi Pak - 33 Structural Dynamics Group

Object - Oriented MDO tool (continue)

 Buckling and strength analyses and strength post - processor modules  Based on MSC/NASTRAN sol. 105  Use in - house strength post - processor code  Safety factor of 1.5 is used for all metal and composite materials in this study.

Failure Load Failure Load 1 − < 0 M S ≡ − 1 .

D esign Load × Safety Factor < Failure Load P I ≡ − mi n ( MS s Design Load × Safety Factor Design Load × Safety Factor  Buckling post - processor module  Use in - house code  Buckling Load Factor (BLF) 0 ≤BLF ≤1 : Buckling predicted BLF<0 or BLF>1: Buckling not predicted 2 2  Buckling predicted: 0 ≤ BLF ≤ 1 − 1 2 ≤ BLF − 1 2 ≤ 1 2 B LF − 1 2 ≤ 1 2 2 2  Buckling not predicted: B LF − 1 2 > 1 2 1 2 − BLF − < 0 .

2 2 P I ≡ 1 2 − positive min BLF − 1 2 B Chan - gi Pak - 34 Structural Dynamics Group