Abaqus收敛培训教材教案Obtaining a Converged Solution with Abaqus

Abaqus收敛培训教材教案Obtaining a Converged Solution with Abaqus Obtaining a Converged Solution with AbaqusObtaining a Converged Solution with AbaqusDay1?Lecture1Introduction toNonlinear FEA?Workshop1Nonlinear Spring?Lecture2Nonlinear FEAwith Abaqus/Standard?Lecture3Solution ofUnstable Problems?Workshop2Reinforced PlateUnder CompressiveLoads?Lecture4Why AbaqusFails toFind aConverged Solution?Workshop3Crimp FormingAnalysis?Lecture5Convergence Problems:Contact Simulations?Workshop4Contact:Beam Lift-Off?Workshop5Contact:Stabilization1Obtaining aConverged Solutionwith AbaqusDay2?Lecture6Convergence Problems:Element Behavior?Workshop6Element Selection?Lecture7Convergence Problems:Constraints andLoading?Lecture8Convergence Problems:Materials?Workshop7Limit LoadAnalysis?Workshop8Ball ImpactObtaining aConverged Solutionwith AbaqusLegal NoticesTheAbaqus Softwaredescribed in this documentation is availableonly underlicense fromDassault Systmes andits subsidiaryand may be usedor reproducedonly in aordance withthe termsof suchlicense.This documentationand thesoftware described in this documentation aresubject tochange withoutprior notice.Dassault Systmes andits subsidiariesshall notbe responsiblefor theconsequences of any errorsor omissionsthat mayappear inthisdocumentation.No partof thisdocumentation may be reproducedor distributedin anyform withoutprior writtenpermission of Dassault Systmes orits subsidiary.?Dassault Systmes,xx.Printed in the UnitedStates ofAmericaAbaqus,the3DS logo,SIMULIA andCATIA aretrademarks orregistered trademarks ofDassaultSystmes orits subsidiariesin theUS and/or othercountries.Other pany,product,and servicenames may be trademarksor servicemarksof their respectiveowners.For additionalinformation concerningtrademarks,copyrights,and licenses,see theLegal Noticesin theAbaqus6.10Release Notesand thenotices at:.simulia./products/products_legal.html.2Obtaining aConverged Solutionwith AbaqusRevisionStatusLecture15/10Updated for6.10Lecture25/10Updated for6.10Lecture35/10Updated for6.10Lecture45/10Updated for6.10Lecture55/10Updated for6.10Lecture65/10Updated for6.10Lecture75/10Updated for6.10Lecture85/10Updated for6.10Workshop15/10Updated for6.10Workshop25/10Updated for6.10Workshop35/10Updated for6.10Workshop45/10Updated for6.10Workshop55/10New for6.10Workshop65/10Updated for6.10Workshop75/10Updated for6.10Workshop85/10Updated for6.10Workshop Answers15/10Updated for6.10Workshop Answers45/10Updated for6.10Workshop Answers55/10New for6.10Workshop Answers65/10Updated for6.10Workshop Answers75/10Updated for6.10Workshop Answers85/10Updated for6.1034Notes5Notes6Introduction toNonlinear FEALecture1L1.2Obtaining aConverged Solutionwith AbaqusOverview?Why Use FEA to Solve Mechanics Problems?What is Convergence?When is a Problem Nonlinear?Properties of Linear Problems in Mechanics?Properties of Nonlinear Problems in Mechanics?Numerical Techniques for Solving Nonlinear Problems7Why Use FEA to Solve Mechanics Problems?L1.4Obtaining aConverged Solutionwith AbaqusWhyUse FEAto SolveMechanics Problems?Understand the behavior of a design?Finite element analysis(FEA)is auseful toolfor studyingthebehaviorof variousmechanical designs.Example:Burst loadanalysis of a micro-channel tube.Tube mustwithstand threetimes themaximum workingpressure.8L1.5Obtaining aConverged Solutionwith AbaqusWhyUse FEAto SolveMechanics Problems?AB2.01.51.00.50.00.5.10.15.x10-3XMIN1.463E-05XMAX1.354E-02YMIN1.562E+02YMAX1.725E+03x103Bulge Displacement(in)Internal Pressure(psi)A)Comparison ofMises stressin tubeB)Predicted burstpressure intubeOperating PressureOverload PressureL1.6Obtaining aConverged Solutionwith AbaqusWhyUse FEAto SolveMechanics Problems?Reduce productcosts anddevelopment time?FEA canreduce productcosts anddevelopment timeby:?Identifying formingproblems priorto toolingfabrication.?Minimizing toolingrework(see the following figure).?Reducing overallprototyping effortwhile identifyingshortings in the design.?Minimizing theamount ofmaterial usedduring fabrication.9L1.7Obtaining aConverged Solutionwith AbaqusWhyUse FEAto SolveMechanics Problems?Incorporating FEAin developmentcyclestamp pre-prototype partsinitialdesignfabricate“soft”toolingnumerical simulationdesign modificationsrework softtoolingstamp productionpartsrework hardtoolingstamp prototypepartsfabricate“hard”toolingnumerical simulationL1.8Obtaining aConverged Solutionwith AbaqusWhyUseFEAtoSolveMechanicsProblems?Only wayto getan answer?FEA can be usedto predictthe abilityof adesign to withstand extreme loading conditionsthat cannotbe duplicatedin anexperiment.?Hopefully theseextreme loadingconditions will be consideredearly in the design process.?An exampleof such a finiteelementanalysis is the simulation of the abilityof anoffshore platformtowithstand the forcesproduced bya hundred-year storm.10L1.9Obtaining aConverged Solutionwith AbaqusWhyUseFEAtoSolveMechanicsProblems?Unfortunately someextremeloadingconditions arenever imaginedduring thedesignprocess.?Consider thecase of the bucklingof asolar panelunder asevere thermaltransient.?The panelnever returnedto itsoriginal configurationwhen thenormal operatingtemperature wasrestored,rendering ituseless.?It wouldhave beenextremely difficultto simulatethis loadingon the structure,which isover120-inches long,in alaboratory;FEA was the onlytool availableto investigatethe proposeddesignmodificationsfor subsequentpanels thatwere produced.What is Convergence?11L1.11Obtaining aConverged Solutionwith AbaqusWhat is Convergence?In FEA“convergence”can implymultiple meanings?Mesh convergence?Time integrationauracy?Convergence ofnonlinear solution procedure?Solution auracyL1.12Obtaining aConverged Solutionwith AbaqusWhat is Convergence?Mesh convergence?Increasing the number ofelements in the modelwill causethe solution to approachthe analyticalsolution of the equationsthat governthe response.?Applies bothto linearand nonlinear analysis.?Applies forh-based elementtechnology used in Abaqus.?At somepoint furthermesh refinementyields littleor nochange insolution,and the mesh is assumed tohave“converged.”12L1.13Obtaining aConverged Solutionwith AbaqusWhatis Convergence?A fewexceptions to themeshconvergence rule:?Singular solutions(e.g.,fracture mechanics).?Localization problemswhere materialdamage canaumulate inparticular regionsof the model.?Abaqus providesspecial techniquesto reducemesh dependenceof localizationeffects forsoftening materials,such asconcrete.Lodygowski,T.,“Shear Bandsand Failurein Adiabaticand FractureTests,”ABAQUS UsersConference,1996,pp.523-536.L1.14Obtaining aConverged Solutionwith AbaqusWhatis Convergence?Abaqus providestools toevaluate meshconvergence?Strain jumpsat nodes(SJP)written toprinted output(.dat)and results(.fil)files?Contouring optionsin Abaqus/Viewer:?Quilt plots?Discontinuity plots?Error estimatesand adaptiveremeshing?Not discussedhere;see AdaptiveRemeshing with Abaqus/Standard lecturenotes.13L1.15Obtaining aConverged Solutionwith AbaqusWhatis Convergence?Mesh convergenceexample:load bearingbracket213fixedTwisted about the1-directionpulledL1.16Obtaining aConverged Solutionwith AbaqusWhatis Convergence?Discontinuity parisonbetween coarseand refinedmeshesDiscontinuities inmaximum principalstressDiscontinuity85%of averagedstressDiscontinuity0vRealNonlinearEquilibrium PDEsFvNumericalTechniques forSolving NonlinearProblems24L1.37Obtaining aConverged Solutionwith AbaqusNumericalTechniques forSolving NonlinearProblems?For nonlinear,static,structural mechanicsproblems,the system of equationsis thestatement ofstatic equilibrium:P I=0,where?Many differenttechniques havebeen proposedfor solvingsuch nonlinearsystems of equations.?In allcases thetotal appliedload is broken downinto smallincrements.?An approximate solution isobtained foreachload increment.?It islikely thatseveral iterations will beneeded toobtain an approximate solutionthat is sufficiently aurate.TVdV I.L1.38Obtaining aConverged Solutionwith AbaqusNumericalTechniques forSolving NonlinearProblems?Two ofthe morerobust iterative methods are the?Newton-Raphson techniqueand the?quasi-Newton technique.?Both areincremental/iterativemethods.?Both areavailable in Abaqus/Standard.25L1.39Obtaining aConverged Solutionwith AbaqusNumericalTechniques forSolving NonlinearProblems?Newton-Raphson technique?With thistechnique,which isdescribedindetail inLecture2,each iterationinvolves theformulation andsolution oflinearized equilibrium equations.?Each iterationconsists ofdefining theterms in the equilibrium equations(forming the stiffness matrix)and solvingthe resultingsystem.?The solutionfrom an iteration isdeemed sufficientlyaurate ifthe errorin theequilibriumequationis smallerthan certaintolerances:tolerances P I R.L1.40Obtaining aConverged Solutionwith AbaqusNumericalTechniques forSolving NonlinearProblems?Quasi-Newton method?The quasi-Newton methoddiffers fromthe full Newton-Raphson methodin howfrequently thestiffness matrix is recalculated.?In thefullNewton-Raphson methodthestiffnessis recalculatedin everyiteration.?In the quasi-Newton methodit is not recalculatedin everyiteration.?Thus,the quasi-Newton methodcan providesubstantial savingsof putationaleffort ifthe numberof iterationsdoes notincrease.?In Abaqusthequasi-Newton methodreforms thestiffness matrixevery eightiterations.?This defaultvalue canbe modifiedbythe user.26L1.41Obtaining aConverged Solutionwith AbaqusNumericalTechniques forSolving NonlinearProblems?The quasi-Newton methodis mostsuessful whenthe systemofequationsis largeandthestiffness matrixis notchanging muchfrom iterationto iteration.?This canbe thecase in a dynamic analysis usingimplicit timeintegration orinasmall-displacement analysiswith localplasticity.?The quasi-Newton methodin Abaqus/Standard hasthefollowinglimitations:?It cannotbe usedwith unsymmetricproblems,which includesfully coupledtemperature-displacement analysesand problemswith highfriction coefficients.L1.42Obtaining aConverged Solutionwith AbaqusNumericalTechniquesforSolvingNonlinearProblems?Usage:*SOLUTION TECHNIQUE,TYPE=QUASI-NEWTON2728Notes29Notes30Nonlinear FEAwith Abaqus/StandardLecture2L2.2Obtaining aConverged Solutionwith AbaqusOverview?Equilibrium Revisited?Nonlinear Solution Methods?Abaqus/Standard ConvergenceCriteria:An Overview?Automatic TimeIncrementation?Contact Convergence31Equilibrium RevisitedL2.4Obtaining aConverged Solutionwith AbaqusEquilibriumRevisited?The basicstatement ofstatic equilibriumis that the internal(I)and external(P)forces shouldbalance:P I0.32L2.5Obtaining aConverged Solutionwith AbaqusEquilibriumRevisited?In a nonlinear problemtheinternal forces inthe model,I(u,t,f i,),maybea nonlinear function of:u(displacement)(strain)t(time)(temperature)fi(user-defined fieldvariables)Other variablesThehistoryofany oftheabovevariables?In anonlinear problemtheexternal forces inthe model,P,may alsobeanonlinearfunction of suchindependent variablesas uandt.Nonlinear Solution Methods33L2.7Obtaining aConverged Solutionwith AbaqusNonlinear Solution Methods?Consider ananalysis inwhich youknow thetotal loadapplied andthe(initial)stiffness ofthestructure.?The goalis to find the final displacement.?In alinearanalysis thefinaldisplacement couldbe foundwith onecalculation.?In anonlinear problemthis isnot possiblebecause thestructures stiffnesschanges asit deforms.LoadPu?DisplacementNonlinear forcevs.displacement curveP0u0L2.8Obtaining aConverged Solutionwith AbaqusNonlinear Solution Methods?The solution of suchanonlinear problem requiresan incremental/iterative technique.?The solutionprovided withsuchatechnique is an approximationoftheactual solution to thenonlinearproblem:?There isgenerally noexact solutionto theseequations so?Abaqus solvesthe equationiteratively?by usingthe Newton-Raphson method?to find anapproximatesolution?that minimizesthe residuals!0.P I34L2.9Obtaining aConverged Solutionwith AbaqusNonlinear Solution Methods?Using Abaqus?The loadhistory versustime isdefined as a sequenceof steps.?Each step is brokenup intoa sequenceof time increments.?You specifya guessfor the initial timeincrement*statict-initial,t-step?Abaqus determines all othertimeincrement sizes usingits automatictime incrementationalgorithm.?At the endof each incrementthe currentload magnitudeis calculatedby Abaqusasafunctionoftime usingthe conceptof loada