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 Comparison of reduction methods Mode shape expansion Conclusions

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”

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 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

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

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

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

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

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

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

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

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

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!

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