MARC有限元收斂性問題及程序退出代碼說明

1、PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 1MAR101 Course Notes, Sec. 12, November 2005SECTION 12RESOLVING CONVERGENCE PROBLEMSPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 2MAR101 Course Notes, Sec. 12, November 2005PAT328, Section 3, March 2001MAR120, Lecture

2、 4, March 2001S12 - 3MAR101 Course Notes, Sec. 12, November 2005OverviewqNonlinear Analysis GuidelinesqInformation Available to HelpqAnalysis Troubleshooting: GeneralqAnalysis Troubleshooting: Criteria BehaviourqAnalysis Troubleshooting: EXIT NumbersPAT328, Section 3, March 2001MAR120, Lecture 4, Ma

3、rch 2001S12 - 4MAR101 Course Notes, Sec. 12, November 2005Nonlinear Analysis GuidelinesqConvergence of a nonlinear problem is mostly not simply to do with the convergence tolerance values or the criteria specified.it is an overall issue of model integrity and representation of realityqIt is strongly

4、 recommended that small tests be performed to gain experience of unknown (to you) element and solution types:1.To understand its limitations2.To ensure that it does provide the required behaviour for the actual simulation to be carried out3.To prevent expensive “surprises” at the end of a projectqSi

5、ngle element tests are preferable (where possible) since it is so much quicker and easier to verify the input and to evaluate the response with only a few degrees of freedomqThere are a number of sources of examples and benchmarks available that may help in this regard1.The MARC User Guide manual. T

6、his contains an increasing amount of worked examples written with the express intention of demonstrating the use of the facilities clearly2.The MARC Demonstration Problem manual (volume E). It is in Marc data file format only. The data files associated with this manual can be located in the Marc ins

7、tallation directory3.The NAFEMS suite of examples. Further information is available on their website ()PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 5MAR101 Course Notes, Sec. 12, November 2005Nonlinear Analysis GuidelinesqPerform and scrutinise the results from a sta

8、tic linear analysis to check the integrity and behaviour of the basic model. If the nonlinear model already exists1.For contact analyses, this would mean changing all contact conditions to GLUED2.For material nonlinearity simply increase the failure criteria so that it cannot be reached3.For geometr

9、ically nonlinear analyses turn off Large Displacement as well as any large strain material optionsqAdd each of the nonlinearities one by one to determine their effect on the solution and its convergence behaviour. For instance, start with contact, adding next any geometric nonlinearity and then fina

10、lly any material nonlinearity, etc.1.For contact analyses, contact conditions can be set to GLUED2.The next step would be TOUCHING, but with a separation force of 1e20qIf buckling is expected, a linear eigenvalue buckling analysis should be performed to obtain the linear buckling load. This will act

11、 as both a benchmark value to compare against as well as a useful aid in determining the load magnitude to be applied in the subsequent geometrically nonlinear analysisqAlways use engineering common sense and verify the plausibility of the results before making design decisions based upon themPAT328

12、, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 6MAR101 Course Notes, Sec. 12, November 2005Information Available to HelpPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 7MAR101 Course Notes, Sec. 12, November 2005qThe problem begins with error messages like:“Failure to conv

13、erge to tolerance” (EXIT 3002)“Error encountered in stress recovery” (EXIT 1009/1005)“The time step has become too small due to too many step cut-backs” (EXIT 3009)“Unable to reduce the time step below the minimum value allowed” (EXIT 3015)“Node on the boundary of a deformable body tried to slide ou

14、t of surface definition in a contact analysis” (EXIT 2400)qThe main place to look is the end of the OUTPUT file (.out)qA successful analysis looks like:*This is a successful completion to an MSC.Marcanalysis, indicating that no additional incremental data wasfound and that the analysis is complete*

15、MSC.Marc Exit number 3004qAn unsuccessful analysis looks like:*Analysis has failed to converge to required convergencetolerances. One of several error conditions has beendetected and the run aborted. The output will specifyadditional messages* MSC.Marc Exit number 3002Analysis MessagesEXIT NumberAss

16、ociated message for EXIT numberPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 8MAR101 Course Notes, Sec. 12, November 2005A typical nonlinear output file section:start of assembly cycle number is 0wall time = 12.00solver workspace needed for out-of-core matrix storage = 7612solver w

17、orkspace needed for in-core matrix storage = 10114matrix solution will be in-corestart of matrix solutionsingularity ratio 3.4185E-12end of matrix solutionmaximum residual force at node 7 degree of freedom 1 is equal to 1.156E-04maximum reaction force at node 35 degree of freedom 2 is equal to 2.809

18、E-01residual convergence ratio 4.117E-04maximum displacement change at node 3 degree of freedom 1 is equal to 1.013E-02maximum displacement increment at node 3 degree of freedom 1 is equal to 1.013E-02displacement convergence ratio 1.000E+00failure to converge to toleranceincrement will be recycledA

19、nalysis MessagesThe output file (.out) contains all messagesThe log file (.log) contains mainly the convergence informationThe status file (.sts) contains a summaryPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 9MAR101 Course Notes, Sec. 12, November 2005The Status FileqSummary of t

20、he convergence behaviour of the analysisqThings to look out for:Sudden jumps in the number of cycles (what happened?)Large number of separations throughout (a general contact issue)Large number of separations part way (contact lost? Contact causing local failure? Frictional forces overcome?)Large nu

21、mber of cut-backs throughout (load increment too large)Large number of cut-backs part-way (what happened?)PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 10MAR101 Course Notes, Sec. 12, November 2005Troubleshooting Analysis FailurePAT328, Section 3, March 2001MAR120, Lecture 4, March

22、 2001S12 - 11MAR101 Course Notes, Sec. 12, November 2005The figure shows contact occurring on only two nodes before non-convergencePerhaps the other part coming into contact slips away afterwards?Perhaps a more refined mesh on the contacted area is needed?Getting CluesqPost process what there isqThe

23、 deformed shape often gives obvious clues as to why the simulation is not convergingqExaggerating the deformation is a good way to pick up cracks in the model or localised effects from incorrect contact definitionqAnimating with a reasonable deformation exaggeration can also be of helpqIf convergenc

24、e is not achievable in the first increment it can be very helpful to specify that Marc continues “proceed when not converged” optionqThis means that a POST results file will be generatedqEven if an increment fails to converge it may provide a pointer to the problemContact.PAT328, Section 3, March 20

25、01MAR120, Lecture 4, March 2001S12 - 12MAR101 Course Notes, Sec. 12, November 2005qEnsure consistent units are used throughout model Note: N, MM, Kg are not consistentqReduce the time step. There may be significant nonlinearity occurring at the beginning Usual for contact May suggest an incorrect yi

26、eld value for material nonlinearity Buckling or significant rotation may have occurred Over-large element distortionqMake sure that the automatic cut-back capability is invokedqIf using the “fixed” load incrementation, change to the “adaptive” scheme and include the “automatic” criteriaqCheck that e

27、ach component of thestructure is restrained against rigid body motionBoundary conditions are the interface between the model and the rest of the worldGeneralUnstableStablePAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 13MAR101 Course Notes, Sec. 12, November 2005qSet “Contact Tolera

28、nce Bias” to 0.9 (particularly for shell contact) qSet “Contact Tolerance” to 0.0qThe rigid surface markers should always point towards the interior of the rigid body. If it does not, MSC.Marc may not detect the rigid surface and the deformable bodyqContact can be lost or not found because of too la

29、rge a load incrementqRefine the mesh in the area of slideline definitionsCoarse meshes can produce single point contact and promote instabilityNecessary to capture the contact interaction accurately if contact distribution is of importanceqAnalytical surface definition may be incorrect and causing “

30、bulbous” corner/edge contact surfacesqConsider smoothing the surfaces in contact if there are sharp features, e.g. insert a radius instead of a sharp corner for corner contactqInitial indeterminate contact state can lead to chatter model components in contact where possibleqRemove frictionContactRig

31、idRigidIncorrectCorrectDeformableDeformablePAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 14MAR101 Course Notes, Sec. 12, November 2005qReview and reconcile any initial contact over-closures and openingsqNodes initially penetrating significantly past the contact zone will be ignored

32、qIf this situation occurs at beginning of analysis, node will not be foundqIf it occurs later, the increment will be recycled with modified time stepContactPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 15MAR101 Course Notes, Sec. 12, November 2005qIf using the stress-free check to

33、make sure that the resulting elements will not be distorted too much when the slave nodes are moved by the program to lie on the master surface.ContactBeforeAfterPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 16MAR101 Course Notes, Sec. 12, November 2005Hyperelastic Material DataqCh

34、eck the material stability for elastomer materials (in “experimental data fitting”)qCheck that the material data covers the entire strain range:This can cause “elements inside out” errorsThe analysis may not converge if any part of the model experiences strains beyond the stability limits of the mat

35、erialqRevert to a lower order polynomial fit (e.g. Single-term Mooney) in the experimental data fittingqWhen fitting experimental data, engineering stress/strain data is expectedqAny material model in which the tangent stiffness is zero or negative will most often cause convergence problems(材料模型的接觸剛

36、度為零或負值導致收斂問題）PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 17MAR101 Course Notes, Sec. 12, November 2005qFor elasto-plastic materials, Cauchy stress and log plastic strain data is expectedAt large strains, there are significant differences in how the stresses and strains are define

37、dqBeware of data extrapolation: extend the work hardening data sufficiently to cover the entire strain rangeThe large stress value in the table is the one that is used if the specified range is exceededqIf a perfect plasticity model experiences convergence difficulties, use a more realistic plastici

38、ty model with non-zero work hardeningAny material model in which the tangent stiffness is zero or negative will often cause convergence problemsPlastic Material DataPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 18MAR101 Course Notes, Sec. 12, November 2005Include RealityqMake sure

39、all appropriate nonlinearities are includedqSome structures rely on “stress stiffening” effects for stability and would require a large displacement analysisqIs geometric nonlinearity required? Large deformations/rotations may be causing large non-physical strainsqIf large strains are present in the

40、 analysis, it is likely, for many materials, that failure is also present (e.g. plasticity)Without material failure included in a large strain analysis, an unrealistic problem is being solved for which there may not be a solutionqIt is unusual for a hyperelastic material to be in the small strain en

41、vironment make sure that a large strain option is requestedqIt is possible for many elasto-plastic analyses to be in the small strain environment but the addition of a robust large strain option is recommendedPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 19MAR101 Course Notes, Sec.

42、 12, November 2005“Breathing” or “Hourglass” ModeElementsqBe aware of the element mechanisms associated with reduced integration elementsqAlways specify assumed strain option for fully integrated 2D and 3D solid elements to eliminate over-stiff solutions in the presence of bendingqAlways specify the

43、 constant dilatation option for fully integrated 2D and 3D solid elements in large-strain plasticity to avoid volumetric lockingThis is due to over-constraints resulting from the incompressible nature of plastic deformationAlternatively, use reduced integration or Herrmann elementsqUse Hermann Eleme

44、nts with the hyperelastic materialsqMSC.Marc uses the global X-axis as the axis of symmetry for axisymmetric elementsPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 20MAR101 Course Notes, Sec. 12, November 2005The figure shows the mesh before (top) and after (bottom) deformation. Ele

45、ments on the left stretched more readily due to plastic necking. The analyst anticipated this and refined the mesh towards the left. A uniform mesh would have produced a poorer simulation.qSpecify a mesh so that the shape of the elements is reasonable throughout the entire analysisqAnticipate how th

46、e mesh will deform qFor example, make element sides shorter in the direction that will be elongated the mostElementsPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 21MAR101 Course Notes, Sec. 12, November 2005qIf the analysis is still recalcitrantremove nonlinearities to try and isol

47、ate the cause of the problem1.For contact analyses, this would mean changing all contact conditions to GLUED2.For material nonlinearity simply increase the failure criteria so that it cannot be reached3.For geometrically nonlinear analyses turn off large displacement as well as any large strain mate

48、rial optionsqAs a last resort, and with a good reasonTurn on non-positive definite (gives a slower equation solution) Turn on quasi-static inertial dampingqSome specific clues can be found by looking at the behaviour of the convergence ratios during the solutionGeneralPAT328, Section 3, March 2001MA

49、R120, Lecture 4, March 2001S12 - 22MAR101 Course Notes, Sec. 12, November 2005Convergence Criteria BehaviourMonotonic Divergence:qMaterial failure, e.g. point loads/supports causing massive localised failureqContact lost because of too large a load increment or wrong contact settingsqRefine the mesh

50、 in the area of slideline definitions. Coarse meshes can produce single point contact and promote instabilityqAnalytical surface definition may be incorrect and causing “bulbous” corner/edge contact surfacesqBuckling has occurred without arc-length methods requestedqReduce load step to reduce the am

51、ount of nonlinearity occurring in an incrementqConvergence criteria too slack? Tighten the convergence criteria, particularly for geometric nonlinearity the solution may be drifting too far from the true equilibrium positionqWere the rigid contact bodies extended sufficiently far?Convergence Toleran

52、ceConvergenceCriteriaNumber of iterationsActual variation ofconvergence criteriaIdeal variation ofconvergence criteriaPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 23MAR101 Course Notes, Sec. 12, November 2005Convergence Criteria BehaviourSlow Convergence:qNot uncommon in contact a

53、nalyses whilst contact is being establishedqConvergence tolerance too tight?qUse full Newton-Raphson to obtain full quadratic convergence characteristicsqFriction issues Check the relative sliding velocity is an appropriate value (1-10%)Use “stick-slip” modelUnfeasibly large friction coefficients (t

54、angential “chatter”)qElements (bars, beams, springs) that are simulating “stiff” members can cause round-off issues if their stiffnesses are arbitrarily large. Evaluate stiffnesses from “real” geometry and materialsqFollower force with the stiffness contribution gives a better convergence rate and m

55、ay help in the presence of large rotationsConvergence ToleranceConvergenceCriteriaNumber of iterationsActual variation ofconvergence criteriaIdeal variation ofconvergence criteriaPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 24MAR101 Course Notes, Sec. 12, November 2005Convergence

56、Criteria BehaviourSlow Convergence (cont.):qGap elements can produce slow displacement norm convergence behaviourBoth the iterative and incremental displacements associated with a high stiffness spring are tinyThis causes the displacement norm calculation of: to produce extremely small numbersThe ch

57、anges occurring in the displacement values are lost because of machine precisionqAnalytical contact surface definitions give a continuous normal and better convergence and would be better than a discrete surface definition for a coarse meshqA poorly conditioned system leads to consistently slow conv

58、ergenceLarge:Small element sizesStiff:Soft materialsPoor quality element shapesConvergence ToleranceConvergenceCriteriaNumber of iterationsActual variation ofconvergence criteriaIdeal variation ofconvergence criteriaPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 25MAR101 Course Note

59、s, Sec. 12, November 2005Convergence Criteria BehaviourOscillating Convergence:qA typical responseqSettling of contact use “iterative penetration detection” a recommended distance tolerance and bias valuesqThreshold material failureConvergence ToleranceConvergenceCriteriaNumber of iterationsActual v

60、ariation ofconvergence criteriaIdeal variation ofconvergence criteriaPAT328, Section 3, March 2001MAR120, Lecture 4, March 2001S12 - 26MAR101 Course Notes, Sec. 12, November 2005Convergence Criteria BehaviourOscillating Divergence:qBuckling is occurring; either real or numericalqCatastrophic materia