November 2019 Stabilization Damping For Nonlinear Convergence

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Twin CitiesANSYS User MeetingNovember 2019Stabilization Damping forNonlinear Convergence

Agenda1.2.3.4.5.Epsilon FEA IntroductionStabilization OverviewStabilization ProcedureStabilization Case StudiesQ&AANSYS User Meeting2

Intro to Epsilon Epsilon FEA provides engineering analysis (10 yrs!) Making Simulation Accurate– In-depth knowledge of the tools ANSYS Suite of Multi-Physics software– Experience with industry successes/failures Aerospace, Rotating Machinery, Electronics, Manufacturing, Packaging, etc.– We validate with calibration runs and hand-calcs Experienced Assessing Discretization Error Making Simulation Affordable––––Low hourly rates and/or fixed-price estimatesWe use specialized experienced engineersDetailed statements of work, scope and budget trackingAutomation (APDL, ACT, Journaling)ANSYS User Meeting3

Epsilon’s Customers Our customers need load-leveling with:– Analyst is a team-member, not a black-box Interface with same Epsilon analyst to leverage past experiences– Open and frequent communication– Any new FEA methods/lessons learned are well communicated– Schedule/budget fidelity with frequent status updates Achieved by using the right person, tools, and technical approach Our customers benefit from external expertise– We infuse up-to-date FEA methods/tools Leverage other industries’ FEA innovations– We share our knowledge, files, and lessons learned!– We help with tool selection, infrastructure adviceANSYS User Meeting4

Stabilization Damping Aids solver in converging rigid body motions– Force imbalance occurs resulting in high/infinite deflection– Still in static domain (time integration is off!)– Caused by pivoting, buckling, contact changes, etc. Stabilization is useful for analyses with stable beginning andend states but periods of instability STABILIZE command in APDL– Exposed in WorkbenchANSYS User Meeting5

Stabilization Vs.Arc Length Method Stabilization is an alternative to Arc Length Method, allowsfor simulating instability with Newton-Raphson Method– See previous user meeting documentation “Nonlinear Convergence”from November 2010 on our website– See PADT’s The Focus issue 14 from 2002– See Unstable Structures ANSYS documentation pageANSYS User Meeting6

Stabilization Damping Features1.Adds numerical viscous damping to affected nodes– Internal to the solver2.3.4.Damps “pseudo-velocity” of motion without requiring time stepreduction to characterize highly nonlinear activityAllows force-based loads to be used in analyses that would requiredisplacement-basedCan be applied globally (all nodes) or to individual contact regions– Aids in detecting abrupt changes in contact– Can also be applied locally by reverting non-stabilized regions to legacyelements5.6.7.Can be turned on/off between load steps or with restartsReduces number of iterations by allowing larger time stepsDoes not preclude the use of any other solver controls/contacts– Arc Length Method does not support nonlinear contactANSYS User Meeting7

Stabilization DampingLimitations1. Cannot simulate negative slope region ofload-displacement response curve– Snap-through regions, etc.– Requires global stability in end-state for results tobe viable2. Possible to overdamp analyses with overlylarge time stepping or damping ratios– Can force convergence to a wildly inaccurate result3. Damping dissipates energy from the model– Reduces accuracy, especially for nonlinearmaterials4. Helps with high-strain element distortionerrors, but not ones caused by other (linear)contacts in the modelANSYS User Meeting8

Global Stabilization DampingProcedure Enable global stabilization in the AnalysisSettings Reduce or Constant application– Reduce will start at prescribed stabilizationvalue and reduce linearly to zero by the end ofsolution– Constant applies stabilization through entiresolutionANSYS User Meeting9

Global Stabilization DampingProcedure Choose Energy or Damping Method– Energy method sets amount of energy allowedto be dissipated by damping– Ratio must be tuned based on load magnitudeand time step duration– Damping factor is calculated from energydissipation ratio and average element size– Alternatively, manually set damping factorANSYS User MeetingWe will vary these inputsin the case studies10

Global Stabilization DampingProcedure Set Damping Factor/Dissipation Ratio– Default energy dissipation ratio of 1E-4generally useful– Damping factor has no default value dueto being model-specific, caution whenusing First substep activation– Only required for models beginning in anunstable state, avoid if possible Can cause severe overdamping if not properlytuned Set Force Limit– Checks ratio of stabilization forces tointernal forces– Does not have any affect onconvergence/bisecting or solving, simplygives warnings when exceededANSYS User Meeting11

Contact Stabilization DampingProcedure Stabilization can beapplied at nonlinearcontacts only Useful for analyses withabrupt contact changesbut general global stability Set damping factor withinindividual contacts No energy option, mustcalculate your owndamping factorANSYS User MeetingWe will compare contactdamping to globaldamping in the casestudies12

Stabilization Damping Results Stabilization Energy Resultcan plot Energy dissipationper element Allows checking for excessivedamped energy as well asidentifying damped areas Not compatible with contactonly dampingANSYS User Meeting13

Case Study 1: Snap-ThroughSkipping Analysis Analysis begins in stable state, then as forceovercomes frictional contact at latch,experiences a short period of instabilitybefore coming to a new stable state restingon fixed blockNo actual buckling “snap through” isoccurring, but similar style forcedisplacement curveRepresentative of most model instabilities,such as due to buckling, material failure,abrupt contact changes, etc.Stabilization can be turned off for firstsubstepStabilization will help skip over the regionwhere the main member becomes unloadedand pseudo-velocity becomes very high, as aresult of a very high force controlled loadingANSYS User Meeting14

Case Study 1: Snap-ThroughSkipping Analysis For baseline comparison, re-solved– Since the end-state is known, we cansolve for this directly by skipping thefirst phase This will allow us to determine theeffect of damping energy loss onresults to a known control result Instabilities are localized to contactareas, so contact-only damping canalso be usedANSYS User Meeting15

Case Study 1: Damping Effectson Accuracy Example of a“missed” secondcontact detectionANSYS User Meeting16

Case Study 1: Damping Effectson Accuracy Example of a“missed” initialcontact detectionANSYS User Meeting17

Case Study 1: Damping Effectson Accuracy10 ampingDampingDampingStabilizationDeformation Energy# ofValueStress (psi) (in)(BTU)iterations0.052.49E 0610.44.23E-030.12.46E 0610.2338.27E-030.22.45E 0610.0691.72E-020.254.21E 051.00243.15E-040.54.21E nergyEnergy1.00E-045.00E-041.00E-031.00E-022.45E 064.21E 054.22E 052.42E 0610.0681.00241.002410.225% difference% differencein stressStabilizationin stressfromDeformation Energy# offromnominalStress (psi) (in)(BTU)iterations nominal84496.652.46E 255FAILED87484.864.21E 051.00245.64E-04680.69640.69 4.21E 051.00247.05E-04720.69680.69 4.22E 051.00241.84E-031060.8196FAILED 2.42E 0610.213 1.85E 00241479.865.42E-034.14E-046.18E-042.11E 0074484.96 2.51E 06640.69FAILED1480.91 4.22E 05281479.964.21E 05Nominal ValuesStress (psi) Deformation (in) # of iterations4.18E 8E-031.54E-02871869593499.43FAILED0.820.78 Solving with 10 initial substeps Damping that is either too low or too high results inunconverged solves or missed contact detection Damping values do not correlate with number of iterationsANSYS User Meeting18

Case Study 1: Damping Effectson Accuracy4 ampingDampingDamping% difference% differenceStabilizationin stressStabilizationin stressDeformation Energy# offromDeformation Energy# offromValueStress (psi) (in)(BTU)iterations nominalStress (psi) (in)(BTU)iterations ED 4.21E ED170FAILEDFAILEDFAILEDFAILED159FAILED0.84.22E 051.00241.48E-031140.82 2.45E 00E-045.00E-041.00E-031.00E-02FAILED2.45E 064.22E 054.21E 67E-02218FAILEDFAILED198486.874.22E 051710.91 2.42E 06390.72 2.38E 06Nominal ValuesStress (psi) Deformation (in) # of iterations4.18E 15E 001.904619578255124 Solve with 4 initial substeps rather than 10 Damping that is either too low or too high results inunconverged solves or missed contact detection Very few damping values lead to convergenceANSYS User MeetingFAILED0.83478.98468.5519

Case Study 1: Damping Effectson Accuracy% difference inDeformation # ofstress fromValue Stress (psi) (in)iterations nominalMethodContact Damping, 10 substeps0.054.21E 051.0023470.78Contact Damping, 10 substeps0.14.20E 051.00231780.42Contact Damping, 10 substepsContact Damping, 10 substeps0.24.21E 142.33Contact Damping, 1 substepContact Damping, 1 substepContact Damping, 1 substepContact Damping, 1 substep0.054.28E 051.00230.1FAILEDFAILED0.24.31E 051.00230.54.25E 051.0023Nominal ValuesStress (psi) Deformation (in) # of iterations4.18E 051.0024633.001.73 Contact damping of 0.1 provides most accurate stress value at expense ofnumber of iterations Single Substep has low iterations, but higher error Using program controlled time stepping, initial contact is ignored butsecondary contact detectedANSYS User Meeting20

Case Study 2: No Initial Contact Analysis of a tubular frame, held witha simple pin support at bottomcorner to allow rotations (as well asplanar symmetry)Vertical force at upper rear corner topush frame into nearby wall withfrictional contactFrame is not in initial contact withwall, and force magnitude issignificant enough to raise thepseudo-velocity beyond manageablesubstep sizesSince frame begins from an unstableposition, stabilization must be turnedon for first substep–Alternatively, contact stabilization can beused to slow the initial contactANSYS User Meeting21

Case Study 2: No Initial Contact For baselinecomparison, solvedwithout stabilization byrotating frame intoinitial contact Check for effects of timestep length as well asplasticityANSYS User Meeting22

Case Study 2: Time SteppingEffects on AccuracyLinear MaterialsReduceMethodGlobal Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1TimeStepping1s, 10 step1s, 4 step1s, 1 step4s, 10 step4s, 1 stepGlobal Energy Ratio 1E-4 1s, 10 stepGlobal Energy Ratio 1E-4 1s, 4 stepGlobal Energy Ratio 1E-4 1s, 1 stepGlobal Energy Ratio 1E-4 4s, 10 stepGlobal Energy Ratio 1E-4 4s, 1 stepContact Damping 0.1Contact Damping 0.1 1s, 10 step1s, 4 stepConstant%%differencedifferenceStabilizationin stressStabilizationin stressDeformation Energy# offromDeformation Energy# offromStress (psi) (in)(BTU)iterations nominalStress (psi) (in)(BTU)iterations nominal1.09E 063.41171.09E-031456.05 1.09E 063.41521.87E-031305.981.09E 063.41211.01E-031616.05 1.09E 063.41461.78E-031575.999.33E 05131.19E-0165-8.90 9.35E 0513.0610.11664-8.761.09E 063.41553.12E-041826.04 1.09E AILEDFAILEDFAILED30FAILED1.09E 061.09E 061.09E 061.09E 061.09E .046.046.036.046.031.09E 061.09E 066.48E 051.09E 066.48E 6.75N/AN/AN/A 1.03E 06N/AN/AN/A 1.03E 06Nominal ValuesStress (psi) Deformation (in) # of iterations1.02E 063.4139591123.4423.4328N/AN/A102800.910.87With program controlled time stepping (one substep), contact is often missed, or damped too highlyNote that Energy Dissipation Ratio method is unaffected by time step lengths, but Damping Factor isSignificantly less accurate than previous case study, likely due to extended sliding contactContact Damping significantly more accurate stresses than global damping, but less accurate deformation–Due to maximum stress being far from contact areaANSYS User Meeting23

Case Study 2: Time SteppingEffects on Accuracy Example of anoverdampedanalysis Highstabilizationenergy and lowaccuracyANSYS User Meeting24

Case Study 2: Time SteppingEffects on AccuracyLinear MaterialsMethodGlobal Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1ReduceTimeStepping1s, 10 step1s, 4 step1s, 1 step4s, 10 step4s, 1 stepGlobal Energy Ratio 1E-4 1s, 10 stepGlobal Energy Ratio 1E-4 1s, 4 stepGlobal Energy Ratio 1E-4 1s, 1 stepGlobal Energy Ratio 1E-4 4s, 10 stepGlobal Energy Ratio 1E-4 4s, 1 stepContact Damping 0.1Contact Damping 0.11s, 10 step1s, 4 stepConstant%%differencedifferenceStabilizationin stressStabilizationin stressDeformation Energy# offromDeformation Energy# offromStress (psi) (in)(BTU)iterations nominalStress (psi) (in)(BTU)iterations nominal1.51E 0517.6949.14E-026406.34 1.51E 0517.6941.13E-016686.361.51E 0517.6929.15E-027406.29 1.51E 0517.6921.13E-017576.351.51E 0517.6929.18E-027566.28 1.51E 0517.6930.113546986.331.51E 0517.6922.37E-026746.26 1.51E 0517.6922.93E-026956.271.51E 0517.6922.37E-026996.26 1.51E 0517.6922.93E-027136.251.51E 05FAILEDFAILED1.51E 8.51E-02FAILEDFAILED8.51E-02FAILED6845360684606.31 1.51E 05FAILEDFAILEDFAILEDFAILED6.31 1.51E FAILED6.29FAILEDN/AN/AN/A 1.47E 05N/AN/AN/A 1.47E 05Nominal ValuesStress (psi) Deformation (in) # of iterations1.42E 0517.6923658517.68617.686N/AN/A6935563.793.79 Bilinear material properties required a higher Energy Dissipation Ratio (1E3) for convergence Similar accuracy to linear case, contact damping less effective at increasingaccuracy25ANSYS User Meeting

Case Study 2: Time SteppingEffects on Accuracy BilinearDeformationANSYS User Meeting26

Case Study 3: InherentlyUnstable Models Same tubular frame asCase Study 2, with wallremoved Model has a largepivot/rigid bodyresponse to applied load– no nonlinear contacts Unstable equilibriumpoint does existANSYS User Meeting27

Case Study 3: InherentlyUnstable Models Can be solvedwithout stabilizationby applying load inequivalent vector todeformed shape Still requires use ofweak springs forinherent instability(very low reactionforce)ANSYS User Meeting28

Case Study 3: Time SteppingEffects on AccuracyLinear MaterialsMethodGlobal Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1ReduceTimeStepping1s, 10 step1s, 4 step1s, 1 step4s, 10 step4s, 1 stepGlobal Energy Ratio 1E-4 1s, 10 stepGlobal Energy Ratio 1E-4 1s, 4 stepGlobal Energy Ratio 1E-4 1s, 1 stepGlobal Energy Ratio 1E-4 4s, 10 stepGlobal Energy Ratio 1E-4 4s, 1 stepConstant%%differencedifferenceStabilizationin stressStabilizationin stressDeformation Energy# offromDeformation Energy# offromStress (psi) (in)(BTU)iterations nominalStress (psi) (in)(BTU)iterations nominal9.31E 0513.0532.05E-011000.01 9.31E 0513.0532.09E-0191-0.069.31E 0513.0371.95E-0178-0.02 9.29E ILEDFAILEDFAILED10FAILED9.30E 0513.0491.04E-0195-0.13 9.30E AILEDFAILEDFAILED11FAILED9.32E 059.31E 05FAILED9.32E 1FAILEDNominal ValuesStress (psi) Deformation (in) # of iterations9.31E 0513.051927759.29E 059.30E 055.04E 059.29E 055.04E 1-45.8250 Significant variations in accuracy depending on time stepping with littlecorrelation Reduce method significantly more accurate than Constant in all cases Overdamped case exists using program controlled time steppingANSYS User Meeting29

Case Study 3: Time SteppingEffects on Accuracy Example of anoverdampedanalysis Highstabilizationenergy and lowaccuracyANSYS User Meeting30

Case Study 3: Time SteppingEffects on AccuracyLinear MaterialsMethodGlobal Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1Global Damping 0.1ReduceTimeStepping1s, 10 step1s, 4 step1s, 1 step4s, 10 step4s, 1 stepGlobal Energy Ratio 1E-4 1s, 10 stepGlobal Energy Ratio 1E-4 1s, 4 stepGlobal Energy Ratio 1E-4 1s, 1 stepGlobal Energy Ratio 1E-4 4s, 10 stepGlobal Energy Ratio 1E-4 4s, 1 stepConstant%%differencedifferenceStabilizationin stressStabilizationin stressDeformation Energy# offromDeformation Energy# offromStress (psi) (in)(BTU)iterations nominalStress (psi) (in)(BTU)iterations nominal1.45E 0521.6882.76E-013980.08 1.45E 0521.693.00E-013970.101.45E 0521.6882.77E-013990.08 1.45E 0521.693.01E-013990.121.45E 0521.6892.73E-013930.11 1.45E 0521.690.29673840.111.45E 0521.6871.22E-013750.01 1.45E 0521.6871.29E-013870.041.45E 0521.6871.23E-013870.01 1.45E 0521.6871.30E-013850.031.45E 05FAILEDFAILED1.45E .04 1.45E 4170.04 1.45E 05FAILED25FAILEDFAILEDNominal ValuesStress (psi) Deformation (in) # of iterations1.45E EDFAILED0.03FAILED Bilinear materials converged more often due to necessary bisectingANSYS User Meeting31

Case Study 2: Time SteppingEffects on Accuracy BilinearDeformationANSYS User Meeting32

Conclusions1. Viable solution to momentarily unstable models2. Ideal to use local contact damping when possibleas opposed to global damping3. Stabilization Energy dissipated does notnecessarily correlate to lost accuracy4. Reduce method generally more accurate thanConstant and less likely to produceoverdamped/unconverged analyses5. Energy dissipation can result in either over orunder conservative stress predictions6. As with all analyses, sanity checks very importantANSYS User Meeting33

Input / QuestionsANSYS User Meeting34

within Epsilon

ANSYS User Meeting Stabilization Vs. Arc Length Method Stabilization is an alternative to Arc Length Method, allows for simulating instability with Newton-Raphson Method –See previous user meeting documentation “Nonlinear Convergence” from November 2010 on our website –See PADT’s The Focus issue 14 from 2002

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