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FEM FOR THE TEST ENGINEER

FEM FOR THE TEST ENGINEER. Christopher C. Flanigan Quartus Engineering Incorporated San Diego, California USA 18th International Modal Analysis Conference (IMAC-XVIII) San Antonio, Texas February 7-10, 2000. DOWNLOAD FROM THE QUARTUS ENGINEERING WEB SITE. http://www.quartus.com.

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FEM FOR THE TEST ENGINEER

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  1. FEMFOR THE TEST ENGINEER Christopher C. Flanigan Quartus Engineering Incorporated San Diego, California USA 18th International Modal Analysis Conference (IMAC-XVIII) San Antonio, Texas February 7-10, 2000

  2. DOWNLOAD FROM THEQUARTUS ENGINEERING WEB SITE http://www.quartus.com

  3. FEM PEOPLE ARE REALLY SMART • Or so they would have you believe!

  4. FEM for the Test EngineerTOPICS • There’s reality, and then there’s FEM • FEM in a nutshell • FEM strengths and challenges • Pretest analysis • Model reduction • Sensor placement • Posttest analysis • Correlation • Model updating

  5. There's reality and then there's FEM

  6. There’s Reality, and Then There’s FEMREALITY IS VERY COMPLICATED! • Many complex subsystems • Unique connections • Advanced materials • Broadband excitation • Nonlinearities • Flight-to-flight variability • Chaos • Extremely high order behavior

  7. There’s Reality, and Then There’s FEMFEM ATTEMPTS TOSIMULATE REALITY • Fortunately, reality is surprisingly linear • Material properties ( vs. ) • Tension vs. compression • Small deflections (sin  = ) • Load versus deflection • Allows reasonable opportunity simulate reality using FEM

  8. There’s Reality, and Then There’s FEMREMEMBER THAT FEMONLY APPROXIMATES REALITY • Reality has lots of hard challenges • Nonlinearity, chaos, etc. • FEM limited by many factors • Engineering knowledge and capabilities • Basic understanding of mechanics • Computer and software power • But it’s the best approach we have • Experience shows that FEM works well when used properly FEM Ahead!

  9. FEM Strengths and ChallengesTEST IS NOT REALITY EITHER! • Test article instead of flight article • Mass simulators, missing items, boundary conditions • Excitation limitations • Load level, spectrum (don’t break it!) • Nonlinearities • Testing limitations • Sensor accuracy and calibration • Data processing • But it’s the best “reality check” available

  10. FEMin a Nutshell

  11. FEM for the Test EngineerFEM IN A NUTSHELL • Divide and conquer! • Shape functions • Elemental stiffness and mass matrices • Assembly of system matrices • Solving • Related topics • Element library • Superelements

  12. FEM in a NutshellCLOSED FORM SOLUTIONS, ANYONE? • Consider a building • Steel girders • Concrete foundation • Can you write an equation to fully describe the building? • I can’t! • Even if possible, probably not the best approach • Very time consuming • One-time solution

  13. FEM in a NutshellDIVIDE AND CONQUER! • Behavior of complete structure is complex • Example: membrane • Divide the membraneinto small pieces • Buzzword: “element” • Feasible to calculate properties of each piece • Collection of pieces represents structure

  14. FEM in a NutshellSHAPE FUNCTIONS ARE THE FOUNDATION OF FINTE ELEMENTS • Shape function • Assumed shape of element when deflected • Some element types are simple • Springs, rods, bar • Other elements are more difficult • Plates, solids • But that’s what Ph.D.’s are for! • Extensive research • Still evolving (MSC.NASTRAN V70.7) Spring K X F F = K X

  15. FEM in a NutshellELEMENT STIFFNESS MATRIXFORMED USING SHAPE FUNCTIONS • Element stiffness matrix • Relates deflections of elemental DOF to applied loads • Forces at element DOF when unit deflection imposed at DOFi and other DOFj are fixed • Example: linear spring (2 DOF) Spring K X F F = K X

  16. FEM in a NutshellELEMENT MASS MATRIXHAS TWO OPTIONS • Lumped mass • Apply 1/N of the element mass to each node • Consistent mass • Called “coupled mass” in NASTRAN • Use shape functions to generate mass matrix • In practice, usually little difference between the two methods • Consistent mass more accurate • Lumped mass faster 1/4 1/4 1/4 1/4

  17. M = 1 K = 2 M = 2 K = 5 M = 3 K = 1 FEM in a NutshellSYSTEM MATRICES FORMEDFROM ELEMENT MATRICES

  18. FEM in a NutshellCALCULATE SYSTEM STATICAND DYNAMIC RESPONSES • Static analysis • Normal modes analysis • Transient analysis

  19. FEM in a NutshellCOMMERCIAL FEM ISSUES • Element libraries • Springs, rods, beams, shells, solids, rigids, special • Linear and parabolic (shape functions, vertex nodes) • Commercial codes • NASTRAN popular for linear dynamics (aero, auto) • ABAQUS and ANSYS popular for nonlinear • Superelements (substructures) • Simply a collection of finite elements • Special capabilities to reduce to boundary nodes • Assemble system by addition I/F nodes

  20. FEM in a NutshellHONORARY DEGREE IN FEM-OLOGY!

  21. FEM for the Test EngineerFEM STRENGTHS AND CHALLENGES

  22. FEM Strengths and ChallengesFEM IS VERY POWERFUL FORWIDE ARRAY OF STRUCTURES • Regular structures • Fine mesh • Sturdy connections • Seam welds • Well-defined mass • Smooth distributed • Small lumped masses • Linear response • Small displacements General Dynamics Control-Structure Interaction Testbed

  23. FEM Strengths and ChallengesFEM HAS MANY CHALLENGES • Mesh refinement • How many elements required? • Stress/strain gradients, mode shapes • Material properties • A-basis, B-basis, etc. • Composites • Dimensions • Tolerances, as-manufactured • Joints • Fasteners, bonds, spot welds continued...

  24. FEM Strengths and ChallengesFEM HAS MANY CHALLENGES • Mass modeling • Accuracy of mass prop DB • Difficulty in test/weighing • Secondary structures • Avionics boxes, batteries • Wiring harnesses • Shock mounts • Nonlinearities • (large deformation, slop, yield, etc.) • Pilot error!

  25. Moravec, H., “When Will Computer Hardware Match the Human Brain?”Robotics Institute Carnegie Mellon University http://www.transhumanist.com/volume1/moravec.htm FEM Strengths and ChallengesFEM ASSISTED BY ADVANCESIN H/W AND S/W POWER • Computers • Moore’s law for CPU • Disk space, memory • Software • Sparse, iterative • Lanczos eigensolver • Domain decomposition • Pre- and post-processing • Increasing resolution • Closer to reality

  26. FEM Strengths and ChallengesFEM CONTINUES TO IMPROVEABILITY TO SIMULATE REALITY • Model resolution • Local details • Some things stillvery difficult • Joints • Expertise • Mesh size, etc. • FEM is not exact • Big models do not guarantee accurate models • That’s why testing is still required!

  27. Develop FEM Pretest Analysis Test Posttest Correlation FEM for the Test EngineerPRETEST ANALYSIS

  28. Pretest AnalysisMODAL 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”

  29. Pretest Analysis - TAMTEST AND ANALYSIS DATA HAVEDIFFERENT NUMBER OF DOF • Model sizes • FEM = 10,000-1,000,000 DOF • Test = 50-500 accelerometers • Compare test results to analysis predictions • Need a common basis for comparison

  30. Pretest Analysis - TAMTEST-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 perform reduction transformation • Transformation method and sensor selection critical for accurate TAM and test-analysis comparisons

  31. Pretest Analysis - TAM 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

  32. Pretest Analysis - TAM Transformation MethodsGUYAN REDUCTION IS ASIMPLE METHOD TO IMPLEMENT • Solve for motion at omitted DOF • Rewrite static equations of motion • Transformation matrix for Guyan reduction

  33. Pretest Analysis - TAM Transformation MethodsTRANSFORMATION VECTORSESTIMATE MOTION AT “OTHER” DOF

  34. Pretest Analysis - TAM Transformation MethodsTRANSFORMATION VECTORS CANREDUCE OR EXPAND DATA TAM Display

  35. Pretest Analysis - TAM Transformation MethodsDISPLAY MODEL RECOVERED USING TRANSFORMATION VECTORS

  36. Pretest Analysis - TAM Transformation MethodsIRS REDUCTION ADDSFIRST ORDER MASS CORRECTION • Guyan neglects mass effects at omitted DOF • IRS adds first order approximation of mass effects

  37. Pretest Analysis - TAM Transformation MethodsDYNAMIC REDUCTION ALSOADDS MASS CORRECTION • Start with eigenvalue equationReplace eigenvalue with constant value L • Equivalent to Guyan reduction if L = 0

  38. Pretest Analysis - TAM Transformation MethodsMODAL TAM BASED ONFEM MODE SHAPES • Partition FEM mode shapes • Pseudo-inverse to form transformation matrix

  39. Pretest Analysis - TAM Transformation MethodsEACH REDUCTION METHOD HASSTRENGTHS AND WEAKNESSES

  40. Pretest Analysis - TAM Transformation MethodsSTANDARD PRACTICE FAVORSGUYAN REDUCTION • Guyan reduction used most often • Easy to use and commercially available • Computationally efficient • Widely used and accepted • Good accuracy for many/most structures • Use other methods when Guyan is inadequate • Modal TAM very accurate but sensitive to FEM error • IRS has 1st order mass correction but can be unstable • Dynamic reduction seldom used (how to choose L)

  41. Pretest Analysis - Sensor PlacementSENSOR PLACEMENT IMPORTANTFOR GOOD TAM AND TEST • Optimize TAM • Minimize reduction error • Optimize test • Get as much independent data as possible • Focus on uncertainties • High confidence areas need only modest instrumentation • More instrumentation near critical uncertain areas (joints) • Common sense and engineering judgement • General visualization of mode shapes

  42. Pretest Analysis - Sensor PlacementMANY ALGORITHMS FORSENSOR PLACEMENT • Kinetic energy • Retain DOF with large kinetic energy • Mass/stiffness ratio • Retain DOF with high mass/stiffness ratio • Iterated K.E. and M/K • Remove one DOF per iteration • Effective independence • Retain DOF that maximize observability of mode shapes • Genetic algorithm • Survival of the fittest!

  43. Pretest Analysis - Sensor PlacementSENSOR PLACEMENT ALGORITHMCLOSELY LINKED TO TAM METHOD • Guyan or IRS reduction • Must retain DOF with large mass • Iterated K.E. or M/K • Mass-weighted effective independence • Modal or Hybrid reduction • Effective independence • Genetic algorithm offers best of all worlds • Examine tons of TAMs! • Seed generation from other methods • Cost function based on TAM method

  44. Pretest Analysis - Sensor PlacementPRETEST ANALYSIS ASSISTSPLANNING AND TEST • Best estimate of modes • Frequencies, shapes • Accelerometer locations • Optimized by sensor placementstudies • TAM mass and stiffness • Real-time ortho and x-ortho • Frequency response functions • Dry runs/shakedown prior to test

  45. FEM for the Test EngineerTEST CONSIDERATIONS Develop FEM Pretest Analysis Test Posttest Correlation

  46. Test ConsiderationsPRETEST DATA ALLOWSREAL-TIME CHECKS OF RESULTS • Traditional comparisons • What if test accuracy goals aren’t met? • Keep testing (different excitement levels, locations, types) • Stop testing (FEM may be incorrect!) • Decide based on test quality checks • Experienced test engineer extremely valuable!

  47. FEM for the Test EngineerPOSTTEST CORRELATION Develop FEM Pretest Analysis Test Posttest Correlation

  48. Posttest CorrelationCORRELATION MUST BE FAST! • FEM almost always has some differences vs. test • Very limited opportunity to do correlation • After structural testing and data processing complete • Before operational use of model • First flight of airplane • Verification load cycle of spacecraft • Need methods that are fast! • Maximum insight • Accurate

  49. Posttest CorrelationNO UNIQUE SOLUTION FOR POSTTEST CORRELATION • More “unknowns” than “knowns” • Knowns • Test data (FRF, frequencies, shapes at test DOF, damping) • Measured global/subsystem weights • Unknowns • FEM stiffness and mass (FEM DOF) • No unique solution • Seek “best” reasonable solution “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”

  50. FEM Updates Test OK? Done Posttest CorrelationMANY CORRELATION METHODS • Trial-and-error • Stop doing this! It's (almost)the new millenium! • Too slow for fast-paced projects • Not sufficiently insightful for complex systems • FEM matrix updating • FEM property updating • Error localization

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