Lockheed Martin Aeronautics Company Integration of External Design Criteria with MSC.Nastran Structural Analysis and Optimization* D.K. Barker and J.C

Lockheed Martin Aeronautics Company

Integration of External Design Criteria with MSC.Nastran Structural Analysis and Optimization*

D.K. Barker and J.C. JohnsonLockheed Martin Aeronautics Company, Fort Worth, Texas

E.H. Johnson and D.P. LayfieldMSC.Software Corporation, Santa Ana, California

MSC 3rd Worldwide Aerospace Users Conference and Technology Showcase, April 8-10, 2002

Paper No. 2001-15

*Copyright 2001 Lockheed Martin Corporation. All rights reserved. Published by the MSC.Software Corporation with permission.

Lockheed Martin Aeronautics Company 2

Motivation

Airframe Structural Certification & Drawing Release Rigorous Application of Detail Strength Criteria FEA Internal Loads Feed “In-House” Methods Dependent on Engineering Data Exchange

InternalInternalLoadsLoads

DatabaseDatabase

InternalInternalLoadsLoads

DatabaseDatabase

DetailDetailStructuralStructuralAnalysesAnalyses

DetailDetailStructuralStructuralAnalysesAnalyses

UpdatedUpdatedExternalExternalLoadsLoads

UpdatedUpdatedExternalExternalLoadsLoads

StructuralStructuralSizingSizing

StructuralStructuralSizingSizing

““Man-in-the-Loop” is Opportunity for AutomationMan-in-the-Loop” is Opportunity for Automation““Man-in-the-Loop” is Opportunity for AutomationMan-in-the-Loop” is Opportunity for Automation


½ SMEAR’d laminate

Thickness Offset

½ SMEAR’d laminate

User WrittenClient Program

MSC-SuppliedClient Object Lib.

API

API

MSC.NastranExecutable

MSC.NastranDMAP Library D

AT

AB

ASE

MSC.Nastran API Server2

Server1

Server i

ExternalCriteria

i = 1..10

MSC.Nastran Enhancements Enable Automation

Laminate Modeling Enhancements Membrane Dominant Structure Stacking Sequence Negligible PCOMP Extensions Minimize Input LAM=MEM, SMEAR or SMCORE

Improved Integration Methods Evaluated MSC.Nastran Toolkit Datablock Indexing Element Results in Material C.S.

External Responses for MSC.Nastran New DRESP3 Bulkdata Entry External Criteria Servers

Enhancements Leveraged Through PartnershipEnhancements Leveraged Through Partnership• MSC Extends Core Nastran ProductMSC Extends Core Nastran Product• Lockheed Martin Improves Internal IntegrationLockheed Martin Improves Internal Integration

Enhancements Leveraged Through PartnershipEnhancements Leveraged Through Partnership• MSC Extends Core Nastran ProductMSC Extends Core Nastran Product• Lockheed Martin Improves Internal IntegrationLockheed Martin Improves Internal Integration


Execute NASTRAN SolutionExecute NASTRAN SolutionExecute NASTRAN SolutionExecute NASTRAN Solution

Parse Input FileParse Input FileParse Input FileParse Input File

Evaluate Element CriteriaEvaluate Element CriteriaEvaluate Element CriteriaEvaluate Element Criteria

Enforce Practicality CriteriaEnforce Practicality CriteriaEnforce Practicality CriteriaEnforce Practicality Criteria

Update FE BulkdataUpdate FE BulkdataUpdate FE BulkdataUpdate FE Bulkdata

Generate VIEW ResultsGenerate VIEW ResultsGenerate VIEW ResultsGenerate VIEW Results

Converged ?Converged ?Converged ?Converged ?nono

yesyes

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 FileInput FileInput FileInput File

Detail AnalysisDetail AnalysisToolTool

Detail AnalysisDetail AnalysisToolTool

Output FileOutput FileOutput FileOutput File

FEFEResultResult

DBDB

FEFEResultResult

DBDBTemplateTemplate FileFileTemplateTemplate FileFile

Batch FileBatch FileGeneratorGeneratorBatch FileBatch FileGeneratorGenerator

Elem. SetElem. SetRef. VariablesRef. Variables

Buckling AnalysisConceptual Input>>DBGET REFVAR… >>DBGET REFVAR… >>DBGET REFVAR… >>DBGET PROP… >>DBGET RESULT… >>DBGET RESULT… …

Title:Subtitle:Material:Panel Width:Panel Length:Panel Thick:Load Case 1:Load Case 2:…


Edge View of 2-D Element Strip

Plan View of 2-D Element Strip

Element CentroidElement Centroid

11 22 33

Control of Property Drop-off Rate

Initial ThicknessInitial Thickness

Practicality Criteria

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 Revised ThicknessRevised Thickness

Intermediate ThicknessIntermediate Thickness

Actual Drop-Actual Drop-Off RateOff Rate

AllowableAllowableDrop-OffDrop-Off

RateRate

AllowableAllowableDrop-OffDrop-Off

RateRate

Actual Drop-Actual Drop-Off RateOff Rate


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 elementsWebs – 55 elements

357 Independent Design Variables

FZFZ(10(1033 lb) lb)

MX*MX* (10(1066 in-lb) in-lb)

MY*MY* (10(1066 in-lb) in-lb)

ConditionCondition

43.31643.316 2.2312.231 -1.027-1.02711

22 42.53342.533 2.2112.211 - .447- .447

*Moments summed about wing root at mid-chord.*Moments summed about wing root at mid-chord.

Applied Static Load ConditionsApplied Static Load Conditions

PartPart Strength CriteriaStrength Criteria Practicality CriteriaPracticality Criteria

SkinsSkins fiber strainfiber strain 22002200 tension tension 20002000 comp. comp.panel stabilitypanel stability

min. layer = 0.025 in.min. layer = 0.025 in.min. ply % > 8%min. ply % > 8%max. ply % < 60%max. ply % < 60%drop-off rate < 0.02*drop-off rate < 0.02*

CapsCaps axial stressaxial stress 27 ksi tension27 ksi tension 28 ksi compression28 ksi compression

min. gage = 0.05 in.min. gage = 0.05 in.drop-off rate < 0.015*drop-off rate < 0.015*

WebsWebs max shear stressmax shear stress 24 ksi24 ksi

min. gage = 0.025 in.min. gage = 0.025 in.drop-off rate < 0.02*drop-off rate < 0.02*

*Drop-off rate defined by equation 17 (see paper).*Drop-off rate defined by equation 17 (see paper).

Design CriteriaDesign Criteria


FSD Convergence Characteristics

Relaxation Factor Improves Distributed Convergence

Tenforced = (Trequired / Tinit) Tinit where “” 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 10Iteration Number

To

tal W

eig

ht

(lb) =0.50

=0.75

=1.00

Critical Criteria Convergence

-0.45

-0.4

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

1 2 3 4 5 6 7 8 9 10

Iteration Number

Min

Ma

rgin

of

Sa

fety

=0.50

=0.75

=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 (=0.5)

-0.5

-0.4

-0.3

-0.2

-0.1

0

1 2 3 4 5 6 7 8 9 10

Iteration Number

Min

Ma

rgin

of

Sa

fety

All Elements

Lower Aft SparCap Excluded

ABCDEFGHIJKLMNOPQR

-0.0055-0.0050-0.0045-0.0040-0.0035-0.0030-0.0025-0.0020-0.0015-0.0010-0.0005-0.00000.00050.00100.00150.00200.00250.0030

Increment (in.)Upper Skin DesignIncrement at=0.5, Iter=8


FSD Final Design

Upper Skin Sized as Anticipated Thickness Decreases Radially From Aft Wing-Root Buckling Criteria Dominates

ABCDEFGHIJKLMNO

0.1000.1250.1500.1750.2000.2250.2500.2750.3000.3250.3500.3750.4000.4250.450

Thickness (in.)Upper Skin for=0.5, Iter=8

1 -2 -3 -

Min. GageTM1 BucklingTM1 Strain

Legend

Critical Criteria & Margins

Good Distributed Convergence Margins Range From 0.181 to -0.040 Manual Intervention Required to

Restrict “Load Chasing”


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, 303DRESP2, 202, E2, 401 , DTABLE, A2 , DRESP1, 301, 302, 303DRESP2, 203, E3, 401 , DTABLE, A3 , DRESP1, 301, 302, 303DRESP2, 204, E4, 401 , DTABLE, A4 , DRESP1, 301, 302, 303

$ intrinsic laminate strain$ (Ex, Ey, and Exy) for top surface (Z2)DRESP1, 301, EX, STRAIN, PCOMP, , 11, , 100DRESP1, 302, EY, STRAIN, PCOMP, , 12, , 100DRESP1, 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, 0.025DESVAR, 2, T2, 0.05, 0.025DESVAR, 3, T3, 0.05, 0.025DESVAR, 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 % boundariesDCONSTR, 2, 501, 8.0, 60.0DCONSTR, 2, 502, 8.0, 60.0DCONSTR, 2, 503, 8.0, 60.0DCONSTR, 2, 504, 8.0, 60.0

$ synthetic ply percentage response$ (0, -45, +45, 90 deg plies)DRESP2, 501, PRCNT1, 402 , DVPREL1, 1, 2, 3, 4, 1DRESP2, 502, PRCNT2, 402 , DVPREL1, 1, 2, 3, 4, 2DRESP2, 503, PRCNT3, 402 , DVPREL1, 1, 2, 3, 4, 3DRESP2, 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)

External Response Server Implementation Underway Buckling Module Prototyped

Integration with MSC.Nastran Optimization

Smeared PCOMP Requires Synthetic Surface Strain Criteria DRESP2 Formulates Fiber Strain See Paper for Details

External Response ServerExternal Response Server

MSC.NastranMSC.NastranMSC.NastranMSC.Nastran API Server2Server2Server2Server2

Server1Server1Server1Server1

Server iServer iServer iServer i

ExternalExternalCriteriaCriteria

i = 1..10

Integrated DetailIntegrated DetailAnalysis ToolsAnalysis Tools

ProductionIntegration

Simplified Laminate Enables Ply Percentage Criteria Demonstrated With DRESP2 See Paper for Details


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

To

tal W

eig

ht

(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

Ma

x C

on

stra

int

Va

lue


MP Final Design

Upper SkinFinal Iteration

ABCDEFGHIJKLM

0.2000.2250.2500.2750.3000.3250.3500.3750.4000.4250.4500.4750.500

Thickness (in.)

Critical Criteria & Margins

1 -2 -3 -

Min. GageTM1 BucklingTM1 Strain

Legend

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


Comparison of FSD and MP Designs

FSDFSD

ABCDEFGHIJKL

5.010.015.020.025.030.035.040.045.050.055.060.0

Ply Percentage

0-degplies

90-degplies

45-degplies

ABCDEFGHIJKL

5.010.015.020.025.030.035.040.045.050.055.060.0

Ply Percentage

0-degplies

90-degplies

45-degplies

Carry-Thru Bending Moment Distribution

0

100

200

300

400

500

600

700

800

18 30 42 54 66

Fuselage Station (in.)

Be

nd

ing

Mo

me

nt,

MX

(100

0 in

-lbs)

FSD

MP

*Moments summed about wing root.

Transition From Compression-Transition From Compression-Buckling Design (Wing Root) to Buckling Design (Wing Root) to

Shear-Buckling Design (Mid-Span)Shear-Buckling Design (Mid-Span)

MPMP

Minimal Transition Provides Minimal Transition Provides Evenly Balanced Wing-Bending Evenly Balanced Wing-Bending

and Wing-Torsion Efficiencyand Wing-Torsion Efficiency

MP Shifts Load MP Shifts Load ForwardForward

Reduces Load Reduces Load In Lower Aft-In Lower Aft-

Spar CapSpar Cap


Sample Problems Illustrate Strengths of FSD and MP

Summary and Conclusions

LM Aero & MSC.Software Partnership New Functional Features for MSC.Nastran 2001 Improved Integration With “In-House” Tools

MPMP FSDFSD

Criteria:Criteria: Multi-Disciplinary Criteria (Sensitivities)Multi-Disciplinary Criteria (Sensitivities) Strength & Practicality CriteriaStrength & Practicality Criteria

Speed:Speed: Independent Local AnalysesIndependent Local Analyses

Size:Size: Conceptual/Preliminary-Quality FEMConceptual/Preliminary-Quality FEM Production-Quality FEMProduction-Quality FEM

Intent:Intent: Define General Structural CharacteristicsDefine General Structural Characteristics Supports Structural CertificationSupports 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

Documents

Lockheed Martin Aeronautics Company Integration of External Design Criteria with MSC.Nastran Structural Analysis and Optimization* D.K. Barker and J.C