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MODEL REDUCTION USING GUYAN, IRS, AND DYNAMIC METHODS

MODEL REDUCTION USING GUYAN, IRS, AND DYNAMIC METHODS. Christopher C. Flanigan Quartus Engineering Incorporated San Diego, California. Model Reduction Using Guyan, IRS, and Dynamic Methods AGENDA. Background and introduction Guyan reduction IRS reduction Dynamic reduction

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MODEL REDUCTION USING GUYAN, IRS, AND DYNAMIC METHODS

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

  2. 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

  3. 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”

  4. 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

  5. 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

  6. 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

  7. Transformation MethodsGUYAN REDUCTION IS ASIMPLE METHOD TO IMPLEMENT • Solve for motion at omitted DOF • Rewrite static equations of motion • Transformation matrix for Guyan reduction

  8. Transformation MethodsIRS REDUCTION ADDSFIRST ORDER MASS CORRECTION • Guyan neglects mass effects at omitted DOF • IRS adds first order approximation of mass effects

  9. Transformation MethodsDYNAMIC REDUCTION ALSOADDS MASS CORRECTION • Start with eigenvalue equation • Replace eigenvalue with constant value L • Equivalent to Guyan reduction if L = 0

  10. 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

  11. 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

  12. 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

  13. 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!

  14. 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

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