MODEL REDUCTION USING GUYAN, IRS, AND DYNAMIC METHODS

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MODEL REDUCTION USINGGUYAN, IRS, AND DYNAMIC
METHODS

• Christopher C. Flanigan
• Quartus Engineering Incorporated
• San Diego, California

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Model Reduction Using Guyan, IRS, and Dynamic
MethodsAGENDA

• Background and introduction
• Guyan reduction
• IRS reduction
• Dynamic reduction
• Comparison of reduction methods
• Mode shape expansion
• Conclusions

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Background and IntroductionMODAL SURVEY OFTEN
PERFORMEDTO 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

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Background and IntroductionTEST AND ANALYSIS
DATA HAVEDIFFERENT NUMBER OF DOF

• Finite element model (FEM)
• 10,000-1,000,000 DOF
• Test
• 50-500 accelerometers
• Compare test results to analysis predictions
• Many other comparison techniques
• Cross-ortho, MAC, COMAC, CORTHOG, etc.
• Need a common basis for comparison

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Background and IntroductionTEST-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

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Transformation MethodsGUYAN REDUCTION IS
THEINDUSTRY 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

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Transformation MethodsGUYAN REDUCTION IS
ASIMPLE METHOD TO IMPLEMENT

• Solve for motion at omitted DOF
• Rewrite static equations of motion
• Transformation matrix for Guyan reduction

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Transformation MethodsIRS REDUCTION ADDSFIRST
ORDER MASS CORRECTION

• Guyan neglects mass effects at omitted DOF
• IRS adds first order approximation of mass effects

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Transformation MethodsDYNAMIC REDUCTION
ALSOADDS MASS CORRECTION

• Start with eigenvalue equation
• Replace eigenvalue with constant value L
• Equivalent to Guyan reduction if L 0

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Comparison of Reduction MethodsEACH REDUCTION
METHOD HASSTRENGTHS 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

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Comparison of Reduction MethodsEACH REDUCTION
METHOD HASSTRENGTHS 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

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Comparison of Reduction MethodsEACH REDUCTION
METHOD HASSTRENGTHS 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

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Comparison of Reduction MethodsSHAPE EXPANSION
IS ANALTERNATIVE 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!

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ConclusionsGUYAN, IRS, AND DYNAMIC
REDUCTIONASSIST 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