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 LockheedMartin 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
The resizing algorithm for FSD can be summarized as :
t inew   i /  all   t i
old
where :
t  designed property
i  index to indicate which property contains the design parameter
and the design response
σ  response quantity, such as stress
  a real number (0.0    1.0)
And the old and new superscrip ts refer to before and after the resizing.
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
•NUMBER OF FULLY STRESSED DESIGN CYCLES COMPLETED
•NUMBER OF OPTIMIZATIONS W.R.T. APPROXIMATE MODELS
10
5
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
4.828427E+00
-3.234952E-01
• 1
FSD
2.668171E+00
N/A
4.203515E-02
•. . . . .
• 3
FSD
2.541077E+00
N/A
6.268603E-02
• 6
2.709053E+00
2.709045E+00
2.640250E-06
3.502930E-04
Preprocessing
DESCYCLE = 0
ALGORITHM
FLOW CHART
Analysis
Initial
Analysis
Print Initial
Design
Y
MP
Y
DESCYCLE
>FSDMAX
DESCYCLE =
DESCYCLE +1
Print
Input/Output of
Design
Hard
Convergence
Y
MP
REDESIGN
Soft
Convergence
Y
MP
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
- 339 GRIDs
- 235 CRODs
- 43 PRODs
219 CBARs
69 CSHEARs
3 PSHEARs
295 CQUAD4s
77 PBARs
25 PSHELLS
- 23 Static Load Cases - 23093 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 - 654 Design Variables
RESULTS FOR PRELIMINARY MODEL
Attribute
1st Design Strategy
2nd Design Strategy
# of Design Variables
71
654
# of Constraints
46194
46194
Final Weight
13.196
8.477
# of FSD Cycles
44
50 (FSDMAX)
# of MP Cycles
1
3
CPU Time per FSD Cycle
6.1
10.9
CPU Time per MP Cycle
16.3
464.1
Largest Design Variable
17.01
61.2
MAXIMUM CONSTRAINT AS A
FUNCTION OF DESIGN CYCLE
1st Design Strategy
2nd 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