MSC.Nastran Structural Optimization

Applications for Aerospace Structures

MSC.Nastran Structural Optimization

Applications for Aerospace Structures

Jack Castro – Sr. Technical Representative/Boeing Technical managerJack Castro – Sr. Technical Representative/Boeing Technical manager

Agenda

MSC.Nastran optimization overviewAirframe Sizing ApplicationModel tuning and test / analysis correlationDetailed panel design

What is “Design Optimization”

Automated modifications of the analysis model parameters to achieve a desired objective while satisfying specified design requirements.

As an analyst or designer, we have all performed some sort of “optimization”

Brute-force optimizationTrial and Error

Optimization Problem Statement

Design Variables:

Find {X} = { X1, X2, …, XN } e.g., thickness of a panel, area of a stiffener

Objective Function:

Minimize F(X)e.g., weight

Optimization Problem Statement (cont.)

Subject to:

Inequality constraints:Gj (X) < 0 j = 1,2,….,LDesign Criteria and margins

Side constraints:Xi

L < Xi < XiU i = 1,2,….,N

Gage allowables

What are the Possible Applications?

Structural design improvements and sizingGeneration of feasible designs from infeasible designsModel matching to produce similar structural responsesSystem parameter identificationConfiguration evaluationsSensitivity analysisOthers - (depends on designer’s creativity)

Basic Features Implemented in MSC.Nastran

Easy access to design synthesis capabilities

Concept of design modelFlexible for design model representation

User-supplied equation interpretation capability

MSC.Nastran Implementation of Structural Optimization

ConstraintScreeningConstraintScreening

InitialDesign

InitialDesign

StructuralResponseAnalysis

StructuralResponseAnalysis

SensitivityAnalysisSensitivityAnalysis

Finite ElementAnalysis

ImprovedDesignImprovedDesign

ApproximateModel

ApproximateModel

The required number ofIterations of the external loop

must be small.

OptimizerOptimizer

Many Times

One time around the loop is referred to as a design cycle or design iteration.

MSC.Nastran Implementation of Structural Optimization

Implemented in SOL 200Provides sensitivity informationMultidisciplinaryVariety of Design Variables

Element and material propertiesOffsets, orientation vectors

Variety of Responses for objective or constraintsDisplacement, stress, force, stability derivatives, flutter damping values and most other output quantitiesEquation derived responsesExternal subroutine derived responses

Strengths of MSC.Nastran Structural Optimization

Efficient performance for small- to large-scale problemsReliable convergence characteristicsFlexible user interface and user-defined equations and subroutinesFull implementation of approximation conceptsContinuous enhancements

General FunctionsSolution Sequence

SOL 200Analysis Types supported

Statics Normal ModesBucklingDirect Frequency ResponseModal Frequency ResponseModal Transient ResponseStatic AeroelasticAeroelastic flutterDirect and Modal Complex Eigenvalue

Multi-disciplinary Example Setup

SOL 200CENDSPC = 100DESOBJ(MIN) = 15ANALYSIS = STATICSSUBCASE 1

SUBTITLE = STATIC LOAD 1DESSUB = 10DISP = ALLLOAD = 1

SUBCASE 2SUBTITLE = STATIC LOAD 2DESSUB = 20STRESS = ALLLOAD = 2

SUBCASE 3SUBTITLE = Flutter ANALYSIS = FLUTTERDESSUB = 30METHOD = 3FLUTTER=10

SUBCASE 4SUBTITLE = Static AeroANALYSIS = SAERODESSUB = 40TRIM=4

BEGIN BULK..

ENDDATA

Types of Optimization

MSC.Nastran supports the following two classes of optimization:

Sizing optimization (e.g., thickness of plate, cross sectional areas of stiffeners, etc.)Shape optimization (e.g., optimizing the largest allowable size of a hole in a plate.)Shape and sizing optimization can be performed simultaneously

Specific Applications

Airframe Sizing ProcessTest / Analysis CorrelationDetailed Panel Design

Airframe Sizing

SOL 200 used extensively for airframe sizing at Boeing, Lockheed, Fairchild-Dornier and othersRecent Examples

Boeing Sonic CruiserBoeing 7E7 (ongoing)Lockheed F-35FD 728/928 series regional aircraft

Airframe Sizing

Typically Multi-disciplinaryStaticsFlutterPerformance/Control Effectiveness (static aeroelasticity)

Airframe SizingObjective

Weight MinimizationDesign Variables

Thicknesses, areas, offsetsCross-section properties and dimensions

MSC.Nastran supports defining beam cross-sections by defining dimensions of standard section types (ROD, RECT,TUBE,CHAN,etc.)User can define additional section types that are not provided by MSC

Airframe Sizing

Typical ConstraintsStress and force (DRESP1)Panel Buckling (DRESP3)Design criteria calculations (DRESP2 or DRESP3)Manufacturability criteria (DRESP2 or DRESP3)Flutter damping values (DRESP1)Performance rates and effectiveness (e.g. roll rate and roll effectiveness) (DRESP1 or DRESP2)

Airframe Sizing – Key Ingredients

DRESP3 - User definable and programmable response equationsNew Composite Options

Membrane or bending onlySmeared

Discrete Optimization – Best design variable value selected from user supplied set of allowed values

Airframe Sizing – DRESP3

DRESP3 – External Response Calculator

Funded by Lockheed MartinExclusive use until mid-2001

Available, but undocumented in MSC.Nastran V2001Formally introduced and documented in MSC.Nastran V2004

Airframe Sizing – DRESP3

DRESP3 ApplicationsDesign criteria that are calculated by in-house programs

Strength criteriaBuckling criteriaPracticality criteria

Cost analysisAny user function that has some dependence on the design variables and responses available in SOL 200

Airframe Sizing – DRESP3

DRESP3 FeaturesFortran or C external subroutine using inputs from NastranCommon Inputs

Design variable valuesMost any Nastran computed response (for example, displacements, forces, stresses and many othersNode, Element and Material dataExternal data

Airframe Sizing – Composites

New PCOMP Laminate OptionsFunded by Lockheed Martin

Exclusive use until mid-2001Available, but undocumented in MSC.Nastran V2001Formally introduced and documented in MSC.Nastran V2004

Airframe Sizing – Composites

New PCOMP laminate options MEM – Membrane OnlyBEND – Bending onlySMEAR – Smeared or averaged stiffness for preliminary sizing applications

User specifies thickness of plies for each ply angle, and ignores stacking order Bending stiffness [B] computed by factoring membrane stiffness [A] by T3/12

SMCORE – Similar to SMEAR but for facesheet/core laminates

Airframe Sizing – Discrete Optimization

Discrete SizingOptimization first performed using continuous design variablesContinuous design variables then re-sized to discrete values based upon user supplied listsDiscrete step can be done after each design cycle or only once at end of the runEnsures final property values consistent with available manufacturing gages

Airframe Sizing – Discrete Optimization

Four Discrete re-sizing optionsRound up to nearest design variableRound off to the nearest design variableConservative Discrete Design

Rounds up or down depending on which most satisfies constraints

Design of Experiment

Airframe Sizing – Additional Options

Fully Stressed DesignMSC.Nastran Toolkit

Integration of in-house codes to Nastran using client-server methodsDirect access of MSC.Nastran databaseExecution of MSC.Nastran modules instead of entire solution sequencesUser customized applications

Airframe Sizing - ExampleFairchild Dornier FD 728 regional aircraft wing box (reference 2)

Airframe Sizing - ExampleDesign Variable Summary

Airframe Sizing - ExampleDesign Criteria Summary

Airframe Sizing - Conclusion“The achieved sizing results of the wing box proved that is is very efficient to apply MDO in a real life aircraft design cycle. Once all the tools for pre- and post-processing were in place, it became clear that the sizing process could be completed in a much shorter time than that of a traditional means” (reference 2)“Furthermore, the MDO sizing process produced the much desired minimum weight design with its economic and performance benefits” (reference 2)

Airframe Sizing - ReferencesReference 1: Lockheed-Martin

Integration of External Design Criteria with MSC.Nastran Structural Analysis and Optimization. Paper No. 2001-15, MSC.Software 2002 Worldwide Aerospace and Technology Showcase,D.K. Barker, J.C. Johnson, E.H. Johnson, D.P. Layfield

Reference 2: Fairchild-DornierMultidisciplinary Design Optimization Of A Regional Aircraft Wing Box. G. Schuhmacher, I. Murra, L. Wang, A. Laxander, O.J. O’Leary. 9th AIAA Symposium on Multidisciplinary Analysis and Optimization, September, 2002. Paper: AIAA 2002 5406

Test – Analysis Correlation

SOL 200 is useful tool to aid in model updating to match testCorrelation to Ground Vibration Test (GVT)Model Tuning

EigenvaluesEigenvectors (V2004)Frequency Response Function (FRF)

Test – Analysis Correlation

ProcessDefine Error Function as objectiveApply design variables that influence desired outputsConstrain desired quantities to near test values

Test – Analysis Error Functions

Typical Error function:Minimizeωai = ith analysis responseωti = ith test responseWti = ith weighting factor

Responses can be displacements, accelerations, frequencies or any computed response (DRESP1, DRESP2 or DRESP3)Error Function input on DEQATN entry referenced by DRESP2 and selected by DESOBJ as objective function.

2

i ai

tiaii ) - (wt∑ ω

ωω

Test – Analysis Error Functions

More complex error functionsBayesian parameter EstimationIncorporates uncertainties in both test and model data

Test – Analysis Design Variables

Which model parameters are uncertain that influence desired response?

Typical design variablesStructural and viscous damping properties

Useful for matching FRF peak amplitudesMaterial properties and densitiesMass distributions and offsetsSpring stiffness for fasteners, bolts, welds and other general connectionsGages

Thicknesses, section dimensions, etc.

Test - Analysis ConstraintsPlace bounds on desired responses

Example: Analysis response = test response +-3%

Place constraint on desired mass and center of gravity location if mass is being changed or redistributed

See section 3.3 V70.7 MSC.Nastran Release Notes

Place upper and lower bound gage constraints based upon model uncertainties

Test – Analysis Guidelines

Matching important mode frequencies is easiest to set up

Caution: No guarantee that resulting mode shapes agree with test

Instead of frequency only matching, consider also…

Matching frequency response function at key nodes, orMatching eigenvector response at key nodes (V2004)

Test – Analysis Guidelines

Recommend pre-test planningMSC.Procor

Determine good drive point(s)Determine good accelerometer locations

Recommend running a modal assurance criteria (MAC) check after optimization to compare analysis modes to test modes

MSC.ProcorMSC.Nastran POSTMACA.V200x

Model Updating Reference

Updating MSC/NASTRAN Models to Match Test Data, Ken Blakely, The MacNeal-Schwendler Corporation. Presented at the 1991 MSC World Users’ Conferencehttp://www.mscsoftware.com/support/library/conf/wuc91/p05091.pdf

Detailed Panel Design

Detailed Panel Design

Objective: Minimize WeightConstraints

Buckling critical load factor >= 1.0Maximum Von Mises Stress < 30000 psi

Design VariablesPlate ThicknessFrame HeightStringer Height

Detailed Panel DesignPanel does not initially meet buckling criteria. Critical Load Factor = .91

Detailed Panel DesignAfter Optimization, buckling criteria satisfied, weight minimized. Critical Load Factor=1.0

Detailed Panel Design

Objective Function History

Detailed Panel Design

Design Variable History

Detailed Panel Design

Maximum Design Constraint History

Comparison of Objective function to Constraint History

Detailed Panel Design

Detailed Panel Design Setup

Case Control

Detailed Panel Design Setup

Design Model

Detailed Panel Design Guidelines

Define reasonable design variablesDefine appropriate design constraints

StressDisplacementLaminate or ply failure criteria

Use DRESP1, DRESP2 or DRESP3 as requiredBuckling

Shape design variables can be incorporated to size cutouts