1. MODEL REDUCTION USING GUYAN, IRS, AND DYNAMIC METHODS
Christopher C. Flanigan
Quartus Engineering Incorporated
San Diego, California

2. Model Reduction Using Guyan, IRS, and Dynamic Methods AGENDA
Background and introduction
Guyan reduction
IRS reduction
Dynamic reduction
Comparison of reduction methods
Mode shape expansion
Conclusions

3. Must be confident that structure will survive operating environment
Background and Introduction MODAL SURVEY OFTEN PERFORMED TO VERIFY FINITE ELEMENT MODEL
Must be confident that structure will survive operating environment
Unrealistic to test flight structure to flight loads
Alternate procedure
Test structure under controlled conditions
Correlate model to match test results
Use test-correlated model to predict operating responses
Modal survey performed to verify analysis model
“Reality check”

4. Finite element model (FEM) Test
Background and Introduction TEST AND ANALYSIS DATA HAVE DIFFERENT NUMBER OF DOF
Finite element model (FEM)
10,000-1,000,000 DOF
Test
accelerometers
Compare test results to analysis predictions
Many other comparison techniques
Cross-ortho, MAC, COMAC, CORTHOG, etc.
Need a common basis for comparison

5. Test-analysis model (TAM)
Background and Introduction TEST-ANALYSIS MODEL (TAM) PROVIDES BASIS FOR COMPARISON
Test-analysis model (TAM)
Mathematical reduction of finite element model
Master DOF in TAM corresponds to accelerometer
Transformation (condensation)
Many methods to select optimum accelerometer locations
Many methods to perform reduction transformation
Sensor locations and transformation method critical for accurate TAM and test-analysis comparisons

6. Transformation Methods GUYAN REDUCTION IS THE INDUSTRY STANDARD METHOD
Robert Guyan, Rockwell, 1965
Pronounced “Goo-yawn”, not “Gie-yan”
Implemented in many commercial software codes
NASTRAN, I-DEAS, ANSYS, etc.
Start with static equations of motion
Assume forces at omitted DOF are negligible

7. Transformation Methods GUYAN REDUCTION IS A SIMPLE METHOD TO IMPLEMENT
Solve for motion at omitted DOF
Rewrite static equations of motion
Transformation matrix for Guyan reduction

8. Transformation Methods IRS REDUCTION ADDS FIRST ORDER MASS CORRECTION
Guyan neglects mass effects at omitted DOF
IRS adds first order approximation of mass effects

9. Transformation Methods DYNAMIC REDUCTION ALSO ADDS MASS CORRECTION
Start with eigenvalue equation
Replace eigenvalue with constant value L
Equivalent to Guyan reduction if L = 0

10. Guyan reduction Strengths Easy to implement Computationally efficient
Comparison of Reduction Methods EACH REDUCTION METHOD HAS STRENGTHS AND WEAKNESSES
Guyan reduction
Strengths
Easy to implement
Computationally efficient
Widely available in commercial software (NASTRAN, etc.)
Extensive use in pretest analysis and correlation
Works well for many structures when good A-set selection
Weaknesses
Poor treatment of mass at omitted DOF
Unacceptable accuracy for structures with high M/K
Errors if poorly selected A-set

11. IRS reduction Strengths Relatively easy to implement
Comparison of Reduction Methods EACH REDUCTION METHOD HAS STRENGTHS AND WEAKNESSES
IRS reduction
Strengths
Relatively easy to implement
NASTRAN rigid format alter
Computationally efficient
Generally more accurate than Guyan reduction
Weaknesses
Not COTS available
Inaccurate if poor A-set (Gordis, 1992)
Limited industry experience

12. Dynamic reduction Strengths Relatively easy to implement
Comparison of Reduction Methods EACH REDUCTION METHOD HAS STRENGTHS AND WEAKNESSES
Dynamic reduction
Strengths
Relatively easy to implement
NASTRAN rigid format alter
Computationally efficient
Generally more accurate than Guyan reduction
Weaknesses
Not COTS available
What is good choice for L?
Limited industry experience

13. Expand test mode shapes to FEM DOF
Comparison of Reduction Methods SHAPE EXPANSION IS AN ALTERNATIVE TO MATRIX REDUCTION
Expand test mode shapes to FEM DOF
Expansion and reduction give same results if same matrices used
Dynamic expansion based on eigenvalue equation
Computationally intensive, but computers are getting faster all the time!

14. TAM provides basis for test-analysis comparisons
Conclusions GUYAN, IRS, AND DYNAMIC REDUCTION ASSIST TEST-ANALYSIS CORRELATION
TAM provides basis for test-analysis comparisons
Many transformation methods
Guyan (static) reduction
IRS reduction
Dynamic reduction
Each method has strengths and weaknesses
Applicability to structures and models
Availability and experience
Robustness
Expansion methods should also be considered