MSC.Nastran Structural Optimization Applications for Aerospace Structures

Transcription

1 MSC.Nastran Structural Optimization Applications for Aerospace Structures Jack Castro Sr. Technical Representative/Boeing Technical manager Jack Castro Sr. Technical Representative/Boeing Technical manager

2 Agenda MSC.Nastran optimization overview Airframe Sizing Application Model tuning and test / analysis correlation Detailed panel design

3 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 optimization Trial and Error

4 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

5 Optimization Problem Statement Subject to: (cont.) Inequality constraints: G j (X) < 0 j = 1,2,.,L Design Criteria and margins Side constraints: X il < X i < X U i i = 1,2,.,N Gage allowables

6 What are the Possible Applications? Structural design improvements and sizing Generation of feasible designs from infeasible designs Model matching to produce similar structural responses System parameter identification Configuration evaluations Sensitivity analysis Others - (depends on designer s creativity)

7 Basic Features Implemented in MSC.Nastran Easy access to design synthesis capabilities Concept of design model Flexible for design model representation User-supplied equation interpretation capability

8 MSC.Nastran Implementation of Structural Optimization Constraint Constraint Screening Screening Initial Initial Design Design Structural Structural Response Response Analysis Analysis Sensitivity Sensitivity Analysis Analysis Finite Element Analysis Improved Improved Design Design The required number of Iterations of the external loop must be small. Approximate Approximate Model Model Many Times Optimizer Optimizer One time around the loop is referred to as a design cycle or design iteration.

9 MSC.Nastran Implementation of Structural Optimization Implemented in SOL 200 Provides sensitivity information Multidisciplinary Variety of Design Variables Element and material properties Offsets, orientation vectors Variety of Responses for objective or constraints Displacement, stress, force, stability derivatives, flutter damping values and most other output quantities Equation derived responses External subroutine derived responses

10 Strengths of MSC.Nastran Structural Optimization Efficient performance for small- to largescale problems Reliable convergence characteristics Flexible user interface and user-defined equations and subroutines Full implementation of approximation concepts Continuous enhancements

11 General Functions Solution Sequence SOL 200 Analysis Types supported Statics Normal Modes Buckling Direct Frequency Response Modal Frequency Response Modal Transient Response Static Aeroelastic Aeroelastic flutter Direct and Modal Complex Eigenvalue

12 Multi-disciplinary Example Setup SOL 200 CEND SPC = 100 DESOBJ(MIN) = 15 ANALYSIS = STATICS SUBCASE 1 SUBTITLE = STATIC LOAD 1 DESSUB = 10 DISP = ALL LOAD = 1 SUBCASE 2 SUBTITLE = STATIC LOAD 2 DESSUB = 20 STRESS = ALL LOAD = 2 SUBCASE 3 SUBTITLE = Flutter ANALYSIS = FLUTTER DESSUB = 30 METHOD = 3 FLUTTER=10 SUBCASE 4 SUBTITLE = Static Aero ANALYSIS = SAERO DESSUB = 40 TRIM=4 BEGIN BULK.. ENDDATA

13 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

14 Specific Applications Airframe Sizing Process Test / Analysis Correlation Detailed Panel Design

15 Airframe Sizing SOL 200 used extensively for airframe sizing at Boeing, Lockheed, Fairchild-Dornier and others Recent Examples Boeing Sonic Cruiser Boeing 7E7 (ongoing) Lockheed F-35 FD 728/928 series regional aircraft

16 Airframe Sizing Typically Multi-disciplinary Statics Flutter Performance/Control Effectiveness (static aeroelasticity)

17 Airframe Sizing Objective Weight Minimization Design Variables Thicknesses, areas, offsets Cross-section properties and dimensions MSC.Nastran supports defining beam crosssections by defining dimensions of standard section types (ROD, RECT,TUBE,CHAN,etc.) User can define additional section types that are not provided by MSC

18 Airframe Sizing Typical Constraints Stress 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)

19 Airframe Sizing Key Ingredients DRESP3 - User definable and programmable response equations New Composite Options Membrane or bending only Smeared Discrete Optimization Best design variable value selected from user supplied set of allowed values

20 Airframe Sizing DRESP3 DRESP3 External Response Calculator Funded by Lockheed Martin Exclusive use until mid-2001 Available, but undocumented in MSC.Nastran V2001 Formally introduced and documented in MSC.Nastran V2004

21 Airframe Sizing DRESP3 DRESP3 Applications Design criteria that are calculated by inhouse programs Strength criteria Buckling criteria Practicality criteria Cost analysis Any user function that has some dependence on the design variables and responses available in SOL 200

22 Airframe Sizing DRESP3 DRESP3 Features Fortran or C external subroutine using inputs from Nastran Common Inputs Design variable values Most any Nastran computed response (for example, displacements, forces, stresses and many others Node, Element and Material data External data

23 Airframe Sizing Composites New PCOMP Laminate Options Funded by Lockheed Martin Exclusive use until mid-2001 Available, but undocumented in MSC.Nastran V2001 Formally introduced and documented in MSC.Nastran V2004

24 Airframe Sizing Composites New PCOMP laminate options MEM Membrane Only BEND Bending only SMEAR 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 T 3 /12 SMCORE Similar to SMEAR but for facesheet/core laminates

25 Airframe Sizing Discrete Optimization Discrete Sizing Optimization first performed using continuous design variables Continuous design variables then re-sized to discrete values based upon user supplied lists Discrete step can be done after each design cycle or only once at end of the run Ensures final property values consistent with available manufacturing gages

26 Airframe Sizing Discrete Optimization Four Discrete re-sizing options Round up to nearest design variable Round off to the nearest design variable Conservative Discrete Design Rounds up or down depending on which most satisfies constraints Design of Experiment

27 irframe Sizing Additional Options Fully Stressed Design MSC.Nastran Toolkit Integration of in-house codes to Nastran using client-server methods Direct access of MSC.Nastran database Execution of MSC.Nastran modules instead of entire solution sequences User customized applications

28 Airframe Sizing - Example Fairchild Dornier FD 728 regional aircraft wing box (reference 2)

29 Airframe Sizing - Example Design Variable Summary

30 Airframe Sizing - Example Design Criteria Summary

31 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)

32 Airframe Sizing - References Reference 1: Lockheed-Martin Integration of External Design Criteria with MSC.Nastran Structural Analysis and Optimization. Paper No , MSC.Software 2002 Worldwide Aerospace and Technology Showcase,D.K. Barker, J.C. Johnson, E.H. Johnson, D.P. Layfield Reference 2: Fairchild-Dornier Multidisciplinary Design Optimization Of A Regional Aircraft Wing Box. G. Schuhmacher, I. Murra, L. Wang, A. Laxander, O.J. O Leary. 9 th AIAA Symposium on Multidisciplinary Analysis and Optimization, September, Paper: AIAA

33 Test Analysis Correlation SOL 200 is useful tool to aid in model updating to match test Correlation to Ground Vibration Test (GVT) Model Tuning Eigenvalues Eigenvectors (V2004) Frequency Response Function (FRF)

34 Test Analysis Correlation Process Define Error Function as objective Apply design variables that influence desired outputs Constrain desired quantities to near test values

35 Test Analysis Error Functions Typical Error function: Minimize ai = i th analysis response ai ti 2 i ( ) ti = i th test response Wt i = i th 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. i wt ω - ω ω ai

36 Test Analysis Error Functions More complex error functions Bayesian parameter Estimation Incorporates uncertainties in both test and model data

37 Test Analysis Design Variables Which model parameters are uncertain that influence desired response? Typical design variables Structural and viscous damping properties Useful for matching FRF peak amplitudes Material properties and densities Mass distributions and offsets Spring stiffness for fasteners, bolts, welds and other general connections Gages Thicknesses, section dimensions, etc.

38 Test - Analysis Constraints Place 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

39 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, or Matching eigenvector response at key nodes (V2004)

40 Test Analysis Guidelines Recommend pre-test planning MSC.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.Procor MSC.Nastran POSTMACA.V200x

41 Model Updating Reference Updating MSC/NASTRAN Models to Match Test Data, Ken Blakely, The MacNeal- Schwendler Corporation. Presented at the 1991 MSC World Users Conference ry/conf/wuc91/p05091.pdf

42 Detailed Panel Design

43 Detailed Panel Design Objective: Minimize Weight Constraints Buckling critical load factor >= 1.0 Maximum Von Mises Stress < psi Design Variables Plate Thickness Frame Height Stringer Height

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

45 Detailed Panel Design After Optimization, buckling criteria satisfied, weight minimized. Critical Load Factor=1.0

46 Detailed Panel Design Objective Function History

47 Detailed Panel Design Design Variable History

48 Detailed Panel Design Maximum Design Constraint History

49 Detailed Panel Design Comparison of Objective function to Constraint History

50 Detailed Panel Design Setup Case Control

51 Detailed Panel Design Setup Design Model

52 Detailed Panel Design Guidelines Define reasonable design variables Define appropriate design constraints Stress Displacement Laminate or ply failure criteria Use DRESP1, DRESP2 or DRESP3 as required Buckling Shape design variables can be incorporated to size cutouts