FULLY STRESSED DESIGN in MSC.Nastran Presented by Erwin H. Johnson Project Manager MSC.Software 3rd MSC.Software Worldwide Aerospace Users Conference Toulouse, FRANCE April 8-10, 2002

AGENDA Introduction Theory Requirements Implementation Examples Concluding Remarks

ACKNOWLEDGMENTS The EA-3B Preliminary Design Model was provided by Mr. Kris Wadolkowski, Vice President, Aerostructures, Inc., San Diego, CA. Mr. Dan Barker and Mr. Michael Love of Lockheed- Martin Aeronautics provided important guidance during the development of the design requirements.

DESIGN SENSITIVITY & OPTIMIZATION ENHANCEMENTS IN THE 2001 RELEASE Discrete Variables Fully Stressed Design Enhanced text interface Support of FREQ3/4/5 Random Analysis Support Complex Eigenvalue Support External Response - DRESP3

DS&O RELATED ACTIVITES FOR THE MSC.Nastran 2002 RELEASE Performance Enhancements Eigenvector Sensitivity/Optimization Dynamic Response Enhancements Miscellaneous Enhancements Updated User’s Guide

INTRODUCTION Fully Stressed Design (FSD) has been implemented in the 2001 Release of MSC.Nastran Produces a design where each design variable is at its limit under at least one load case Provides a rapid means of performing initial sizing of aerospace vehicles Allows for the design of a virtually unlimited number of element sizes FSD is a well known design technique that has long been implemented in codes such as FASTOP, LAGRANGE and ASTROS

BACKGROUND for FSD in MSC.Nastran MSC.Software has been aware of FSD but has not previously implemented the technique because: –MSC.Software has concentrated on more general Mathematical Programming (MP) methods –FSD lacks a theoretical underpinning There are several motivations for implementing the technique –FSD is fast –FSD can handle many thousands of design variables, something our MP methods cannot do –Numerous client requests

FSD THEORY

FSD REQUIREMENTS Applicable for Static and Static Aeroelastic Analyses Supports multiple load cases and multiple boundary conditions Supports composite materials Allowable limits on Stress and/or Strain Limits can be imposed on design variables and property values Design Properties - Areas of rods - Thicknesses of plates (PSHELL and PSHEAR) - Thicknesses of composite layers

FSD LIMITATIONS Bar and Beam Cross Sections cannot be designed Ply Orientation is not an available design variable If an element is constrained, but there are no design properties associated with the element, the constraint is ignored. If a property is designed, but there are no constraints associated with the associated elements, the property is held invariant. Shape design variables are not supported. Material and Connectivity Properties are not supported. None of these limitations apply for Math Programming design tasks.

FSD INPUT The text interface developed for Math Programming is used for FSD –The DESSUB case control command identifies the constraints that are to be applied in each subcase –DESVAR and DVPREL1 entries define the designed properties –DRESP1 entries define the responses –DCONSTR entries define the constraints Other Case Control Commands and Bulk Data entries are ignored Two new parameters control the FSD algorithm: –FSDALP - The  relaxation parameter of the resizing algorithm (default = 0.9) –FSDMAX - Maximum number of FSD design cycles (default = 0)

FSD RELATIONSHIP to MATH PROGRAMMING FSD and Math Programming (MP) Design Cycles can be run sequentially –There are up to FSDMAX FSD design cycles followed by up to DESMAX MP design cycles –MP cycles can be skipped with DESMAX=0 The FSD result is often an excellent starting point for an MP design task All design model user inputs are honored in trailing MP design cycles –Additional ANALYSIS types (e.g. FLUTTER) can be included –DVGRID, DVPREL2, DVMRELi, DVCRELi, DRESP2 and DRESP3 entries are honored

FSD OUTPUT Output is very similar to that from standard MP jobs Since there is no approximate model, there is no output from the approximate model. Only results from exact analyses are printed The SUMMARY OF THE DESIGN CYCLE HISTORY looks a little different: NUMBER OF FINITE ELEMENT ANALYSES COMPLETED 10 NUMBER OF FULLY STRESSED DESIGN CYCLES COMPLETED 5 NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS 4 OBJECTIVE AND MAXIMUM CONSTRAINT HISTORY OBJECTIVE FROM OBJECTIVE FROM FRACTIONAL ERROR MAXIMUM VALUE CYCLE APPROXIMATE EXACT OF OF NUMBER OPTIMIZATION ANALYSIS APPROXIMATION CONSTRAINT INITIAL E E-01 1 FSD E+00 N/A E FSD E+00 N/A E E E E E-04

ALGORITHM FLOW CHART MP Initial Analysis MP Print Initial Design Y Y Preprocessing DESCYCLE = 0 Analysis Y Y Print Input/Output of Design REDESIGN DESCYCLE = DESCYCLE +1 Soft Convergence DESCYCLE >FSDMAX Hard Convergence

PRELIMINARY DESIGN MODEL EXAMPLE General loads model of a US Navy EA-3B aircraft Results shown here have no bearing on the actual structure Model was supplied by

DESIGN TASK FOR PRELIMINARY MODEL Problem Statistics GRIDs219 CBARs295 CQUAD4s CRODs69 CSHEARs77 PBARs - 43 PRODs3 PSHEARs25 PSHELLS -23 Static Load Cases responses Two Design Strategies - 1st Strategy - Existing PSHEARs, PSHELLs and PRODs were designed - 71 Design Variables -2nd Strategy - Each CROD,CQUAD4 and CSHEAR Element was independently designed Design Variables

RESULTS FOR PRELIMINARY MODEL

MAXIMUM CONSTRAINT AS A FUNCTION OF DESIGN CYCLE 1st Design Strategy2nd Design Strategy

DESIGN VARIABLES AS A FUNCTION OF DESIGN CYCLE 1st Design Strategy ( Design Appears Converged ) 2nd Design Strategy ( Not Yet Converged )

CANTILEVERED PLATE EXAMPLE Academic Problem to: – Test FSD with many design variables – Compare with Topology Optimization Results

DESIGN TASK FOR CANTILEVERED MODEL Symmetry has been used analyze half of the actual structure which has the load applied at the center of the tip face 8000 PSHELL properties in the half-model Each property is a design variable Variables have an upper limit of 1.0 and a small lower limit Limit applied on the von Mises stress in each element Final design is a function of the allowable stress –Smaller allowables require more structure –Looking for a design concept, not a viable design

CANTILEVERED PLATE RESULTS Answers depend on stress limit - 10 KSI is shown Result is a wishbone like structure FSD is not a strong topology optimization option

CONCLUDING REMARKS Fully Stressed Design is available in the 2001 Release of MSC.Nastran Enables rapid structural design of aerospace structures User Interface borrows from SOL 200 interface with two additional user parameters Possible future developments (with no current plans): –A specialized user interface to create the design –model –Extension to PBEAM, PBAR and/or PWELD properties User feedback is solicited