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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