Integration of External Design Criteria with MSC Integration of External Design Criteria with MSC.Nastran Structural Analysis and Optimization* D.K. Barker and J.C. Johnson Lockheed Martin Aeronautics Company, Fort Worth, Texas E.H. Johnson and D.P. Layfield MSC.Software Corporation, Santa Ana, California MSC 3rd Worldwide Aerospace Users Conference and Technology Showcase, April 8-10, 2002 Paper No. 2001-15 *Copyright ã 2001 Lockheed Martin Corporation. All rights reserved. Published by the MSC.Software Corporation with permission.

“Man-in-the-Loop” is Opportunity for Automation Motivation Airframe Structural Certification & Drawing Release Rigorous Application of Detail Strength Criteria FEA Internal Loads Feed “In-House” Methods Dependent on Engineering Data Exchange Internal Loads Database Detail Structural Analyses Structural Sizing Define motivation and place “Detail Stress Analysis” process in context: Occurs after conceptual/preliminary design, prior to feedback to CAD General structural characteristics have been established Local details must be assessed for structural certification Significant time spent: recovering freebody loads for analysis methods applying required structural increments “Man-in-the-Load” is opportunity for automation and improved performance Updated External Loads “Man-in-the-Loop” is Opportunity for Automation

MSC.Nastran Enhancements Enable Automation Laminate Modeling Enhancements Membrane Dominant Structure Stacking Sequence Negligible PCOMP Extensions Minimize Input LAM=MEM, SMEAR or SMCORE ½ SMEAR’d laminate Thickness Offset Improved Integration Methods Evaluated MSC.Nastran Toolkit Datablock Indexing Element Results in Material C.S. User Written Client Program MSC-Supplied Client Object Lib. API MSC.Nastran Executable DMAP Library DATABASE Enhancements Leveraged Through Partnership MSC Extends Core Nastran Product Lockheed Martin Improves Internal Integration MSC.Nastran API Server2 Server1 Server i External Criteria i = 1..10 External Responses for MSC.Nastran New DRESP3 Bulkdata Entry External Criteria Servers

Automation of Detailed Analysis & Sizing LM Aero Approach Emphasizes Rapid Structural Increment Fully Stressed Design (FSD) – No Sensitivities Structural Strength & Practicality Criteria Seamless Integration of Standalone External Criteria Input File Detail Analysis Tool Output File FE Result DB Template File Batch File Generator Elem. Set Ref. Variables Execute NASTRAN Solution Parse Input File Evaluate Element Criteria Enforce Practicality Criteria Update FE Bulkdata Generate VIEW Results Converged ? no yes Buckling Analysis Conceptual Input >>DBGET REFVAR… >>DBGET PROP… >>DBGET RESULT… … Title: Subtitle: Material: Panel Width: Panel Length: Panel Thick: Load Case 1: Load Case 2:

Practicality Criteria Edge View of 2-D Element Strip Plan View of 2-D Element Strip Element Centroid 1 2 3 Control of Property Drop-off Rate Strength Criteria Alone Not Sufficient Production Quality FEM Anticipate 50K Unique Properties Complex and Not Producible Practicalization Options Implemented Minimum Gage, Property Linking, Ply Percentage, Drop-off Rate, etc. Innovative Property Drop-off Approach Reduce Model Complexity Redistribute Load Concentrations Actual Drop- Off Rate Allowable Drop-Off Rate Intermediate Thickness Revised Thickness Initial Thickness

FSD Demonstration Problem Intermediate Complexity Wing (ICW) Composite Skins Metalic Understructure Membrane Dominant Skins 0, ±45, and 90-deg plies Uses PCOMP LAM=SMEAR Skins – 64 elements (4 layers/element) Caps – 110 elements Webs – 55 elements 357 Independent Design Variables Part Strength Criteria Practicality Criteria Skins fiber strain 2200me tension 2000me comp. panel stability min. layer = 0.025 in. min. ply % > 8% max. ply % < 60% drop-off rate < 0.02* Caps axial stress 27 ksi tension 28 ksi compression min. gage = 0.05 in. drop-off rate < 0.015* Webs max shear stress 24 ksi min. gage = 0.025 in. *Drop-off rate defined by equation 17 (see paper). Design Criteria FZ (103 lb) MX* (106 in-lb) MY*   Condition 43.316 2.231 -1.027 1 2 42.533 2.211 - .447 *Moments summed about wing root at mid-chord. Applied Static Load Conditions

FSD Convergence Characteristics Relaxation Factor Improves Distributed Convergence Tenforced = (Trequired / Tinit)a Tinit where “a” is user specified. Objective Converges Quickly FSD Enables Rapid Prediction of Target Weight Critical Criteria Converges More Slowly Negative Margins Present After Ten Iterations Objective Convergence 120 130 140 150 160 170 180 190 1 2 3 4 5 6 7 8 9 10 Iteration Number Total Weight (lb) a=0.50 a=0.75 a=1.00 Critical Criteria Convergence -0.45 -0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 1 2 3 4 5 6 7 8 9 10 Iteration Number Min Margin of Safety a=0.50 a=0.75 a=1.00

“Load Chasing” Effect Negative Margins Driven By Single Element Lower Aft-Spar Cap (Wing-Root Boundary) FSD Magnifies Inherent Stress Intensifiers Configuration: Aft Swept Wing Pushes Load Aft Modeling: Coarse Grid, Rigid Boundary Methodology: Increased Gage (i.e., Stiffness) Draws Load Sizing Increment Illustrates Gradual Stiffness Redistribution Critical Criteria Convergence (a=0.5) -0.5 -0.4 -0.3 -0.2 -0.1 1 2 3 4 5 6 7 8 9 10 Iteration Number Min Margin of Safety All Elements Lower Aft Spar Cap Excluded A B C D E F G H I J K L M N O P Q R -0.0055 -0.0050 -0.0045 -0.0040 -0.0035 -0.0030 -0.0025 -0.0020 -0.0015 -0.0010 -0.0005 -0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 Increment (in.) Upper Skin Design Increment at a=0.5, Iter=8

FSD Final Design Upper Skin Sized as Anticipated Thickness Decreases Radially From Aft Wing-Root Buckling Criteria Dominates Good Distributed Convergence Margins Range From 0.181 to -0.040 Manual Intervention Required to Restrict “Load Chasing” 1 - 2 - 3 - Min. Gage TM1 Buckling TM1 Strain Legend Critical Criteria & Margins A B C D E F G H I J K L M N O 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.275 0.300 0.325 0.350 0.375 0.400 0.425 0.450 Thickness (in.) Upper Skin for a=0.5, Iter=8

Integration with MSC.Nastran Optimization Synthetic Fiber Strain Constraints $ design constraints for fiber strain. DCONSTR, 3, 201, -2000., 2200. DCONSTR, 3, 202, -2000., 2200. DCONSTR, 3, 203, -2000., 2200. DCONSTR, 3, 204, -2000., 2200. $ synthetic fiber strain responses (Z2) $ (0, -45, +45, and 90 deg plies) DRESP2, 201, E1, 401 , DTABLE, A1 , DRESP1, 301, 302, 303 DRESP2, 202, E2, 401 , DTABLE, A2 DRESP2, 203, E3, 401 , DTABLE, A3 DRESP2, 204, E4, 401 , DTABLE, A4 $ intrinsic laminate strain $ (Ex, Ey, and Exy) for top surface (Z2) DRESP1, 301, EX, STRAIN, PCOMP, , 11, , 100 DRESP1, 302, EY, STRAIN, PCOMP, , 12, , 100 DRESP1, 303, EXY, STRAIN, PCOMP, , 13, , 100 $ strain transformation equation. DEQATN 401 thetar(theta,ex,ey,exy) = theta * PI(1) / 180. ; exfiber = 1.0e+6 * (ex*cos(thetar)**2 + ey*sin(thetar)**2 + exy*sin(thetar)*cos(thetar)) $ table of constant parameters (ply angles). DTABLE, a1, 0., a2, -45., a3, 45., a4, 90. Synthetic Ply Percentage Constraints $ design variable definition $ (0, -45, +45, 90 deg plies) DESVAR, 1, T1, 0.05, 0.025 DESVAR, 2, T2, 0.05, 0.025 DESVAR, 3, T3, 0.05, 0.025 DESVAR, 4, T4, 0.05, 0.025 DVPREL1, 1, PCOMP, 100, T1 , 1, 1. DVPREL1, 2, PCOMP, 100, T2 , 2, 1. DVPREL1, 3, PCOMP, 100, T3 , 3, 1. DVPREL1, 4, PCOMP, 100, T4 , 4, 1. $ design constraints for ply % boundaries DCONSTR, 2, 501, 8.0, 60.0 DCONSTR, 2, 502, 8.0, 60.0 DCONSTR, 2, 503, 8.0, 60.0 DCONSTR, 2, 504, 8.0, 60.0 $ synthetic ply percentage response DRESP2, 501, PRCNT1, 402 , DVPREL1, 1, 2, 3, 4, 1 DRESP2, 502, PRCNT2, 402 , DVPREL1, 1, 2, 3, 4, 2 DRESP2, 503, PRCNT3, 402 , DVPREL1, 1, 2, 3, 4, 3 DRESP2, 504, PRCNT4, 402 , DVPREL1, 1, 2, 3, 4, 4 $ ply percentage formulation. DEQATN 402 total(t1,t2,t3,t4,ti) = (t1 +t2 +t3 +t4); plyprcnt = 1.e2 * (ti / total) Smeared PCOMP Requires Synthetic Surface Strain Criteria DRESP2 Formulates Fiber Strain See Paper for Details External Response Server MSC.Nastran API Server2 Server1 Server i External Criteria i = 1..10 Integrated Detail Analysis Tools Production Integration Simplified Laminate Enables Ply Percentage Criteria Demonstrated With DRESP2 See Paper for Details External Response Server Implementation Underway Buckling Module Prototyped

MP Demonstration Problem FSD Demonstration Repeated Using MP Methodology Same Criteria Except Property Drop-off Not Applied Convergence Achieved After 5 Iterations Increase of 20 lbs Over FSD Solution All Criteria Are Satisfied Objective Convergence 100.00 110.00 120.00 130.00 140.00 150.00 160.00 1 2 3 4 5 6 Iteration Number Total Weight (lbs) Critical Criteria Convergence 0.00 1.00 2.00 3.00 4.00 5.00 6.00 1 2 3 4 5 6 Iteration Number Max Constraint Value

MP Final Design Upper Skin Contour Similar to FSD Slightly Thicker than FSD Thickness Added Forward of Center Spar Distributed Convergence Characteristics Minimum Margin is -0.005 Oversized Inboard Region Reduces Load In Lower Aft-Spar Cap Critical Criteria & Margins 1 - 2 - 3 - Min. Gage TM1 Buckling TM1 Strain Legend Upper Skin Final Iteration A B C D E F G H I J K L M 0.200 0.225 0.250 0.275 0.300 0.325 0.350 0.375 0.400 0.425 0.450 0.475 0.500 Thickness (in.)

Comparison of FSD and MP Designs Carry-Thru Bending Moment Distribution 100 200 300 400 500 600 700 800 18 30 42 54 66 Fuselage Station (in.) Bending Moment, MX (1000 in-lbs) FSD MP *Moments summed about wing root. MP A B C D E F G H I J K L 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 Ply Percentage 0-deg plies 90-deg 45-deg A B C D E F G H I J K L 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 50.0 55.0 60.0 Ply Percentage 0-deg plies 90-deg 45-deg MP Shifts Load Forward Reduces Load In Lower Aft-Spar Cap Transition From Compression-Buckling Design (Wing Root) to Shear-Buckling Design (Mid-Span) Minimal Transition Provides Evenly Balanced Wing-Bending and Wing-Torsion Efficiency

Summary and Conclusions LM Aero & MSC.Software Partnership New Functional Features for MSC.Nastran 2001 Improved Integration With “In-House” Tools Sample Problems Illustrate Strengths of FSD and MP MP FSD Criteria: Multi-Disciplinary Criteria (Sensitivities) Strength & Practicality Criteria Speed: Independent Local Analyses Size: Conceptual/Preliminary-Quality FEM Production-Quality FEM Intent: Define General Structural Characteristics Supports Structural Certification Effective Usage Scenario MP Addresses MDO Requirements at Concept/Prelim. Phase Establish Min. Structural Requirements (Gage, Ply %, etc.) FSD Provides Increment for Detail Strength Criteria

Acknowledgements Xiaoming Yu PCOMP Enhancements Shengua Zhang DRESP3 Development Vinh Lam and Steve Wilder MSC.Toolkit Enhancements