ABAQUS-Standard-ABAQUS-Standard-基基础教程础教程2003,ABAQUS软件公司北京代表处.A1.2内容提要内容提要ElementsinABAQUSStructuralElements(ShellsandBeams)vs.ContinuumElementsModelingBendingUsingContinuumElements用实体单元模拟弯曲StressConcentrations应力集中Contact接触IncompressibleMaterials不可压缩材料MeshGeneration网格生成SolidElementSelectionSummaryABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京办事处.Elements in ABAQUSABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.4Elements in ABAQUSABAQUS单元库中提供广泛的单元类型，适应不同的结构和几何特征单元库中提供广泛的单元类型，适应不同的结构和几何特征The wide range of elements in the ABAQUS element library provides flexibility in modeling different geometries and structures. Eachelementcanbecharacterizedbyconsideringthefollowing:单元特性：Family单元类型Numberofnodes节点数Degreesoffreedom自由度数Formulation公式Integration积分ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.5单元类型（单元类型（Family） Afamilyoffiniteelementsisthebroadestcategoryusedtoclassifyelements.同类型单元有很多相同的基本特。Elementsinthesamefamilysharemanybasicfeatures.同种类单元又有很多变化：Therearemanyvariationswithinafamily.Elements in ABAQUSspecial-purposeelementslikesprings,dashpots,andmassescontinuum(solidelements)shellelementsbeamelementsrigidelementsmembraneelementstrusselementsinfiniteelementsABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.6Elements in ABAQUSNumber of nodes节点数节点数(interpolation)Anelementsnumberofnodesdetermineshowthenodaldegreesoffreedomwillbeinterpolatedoverthedomainoftheelement.ABAQUSincludeselementswithbothfirst-andsecond-orderinterpolation.插值函数阶数可以为一次或者两次First-orderinterpolationSecond-orderinterpolationABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.7Elements in ABAQUS自由度数目自由度数目Degrees of freedomTheprimaryvariablesthatexistatthenodesofanelementarethedegrees of freedominthefiniteelementanalysis.Examplesofdegreesoffreedomare:Displacements位移Rotations转角Temperature温度Electricalpotential电势ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.8公式公式FormulationThemathematicalformulationusedtodescribethebehaviorofanelementisanotherbroadcategorythatisusedtoclassifyelements.Examplesofdifferentelementformulations:Planestrain平面应变Planestress平面应力Hybridelements杂交单元Incompatible-modeelements非协调元Small-strainshells小应变壳元Finite-strainshells有限应变壳元Thickshells后壳Thinshells薄壳Elements in ABAQUSABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.9积分积分Integration单元的刚度和质量在单元内的采样点进行数值计算，这些采样点叫做“积分点”Thestiffnessandmassofanelementarecalculatednumericallyatsamplingpointscalled“integrationpoints”withintheelement.数值积分的算法影响单元的行为Thenumericalalgorithmusedtointegratethesevariablesinfluenceshowanelementbehaves.ABAQUS包括完全积分和减缩积分。ABAQUSincludeselementswithboth“full”and“reduced”integration.Elements in ABAQUSABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.10Full integration:完全积分完全积分The minimum integration order required for exact integration of the strain energy for an undistorted element with linear material properties.Reduced integration:简缩积分简缩积分The integration rule that is one order less than the full integration rule.Elements in ABAQUSFirst-orderinterpolationFullintegrationSecond-orderinterpolationReducedintegrationABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.11Elements in ABAQUSElement naming conventions: examples 单元命名约定B21:Beam,2-D,1st-orderinterpolationCAX8R:Continuum,AXisymmetric,8-node,ReducedintegrationDC3D4:Diffusion(heattransfer), Continuum,3-D,4-nodeS8RT:Shell,8-node,Reducedintegration,TemperatureCPE8PH:Continuum,Planestrain,8-node,Porepressure,HybridDC1D2E:Diffusion(heattransfer),Continuum,1-D,2-node,ElectricalABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.12Elements in ABAQUSABAQUS/Standard 和和 ABAQUS/Explicit单元库的对比单元库的对比 Bothprogramshaveessentiallythesameelementfamilies:continuum,shell,beam,etc.ABAQUS/Standardincludeselementsformanyanalysistypesmanyanalysistypesinadditiontostressanalysis:热传导,固化soilsconsolidation,声场acoustics,etc.AcousticelementsarealsoavailableinABAQUS/Explicit.ABAQUS/Standardincludesmanymorevariationswithineachelementfamily.ABAQUS/Explicit包括的单元绝大多数都为一次单元。例外:二次单元和四面体单元and二次beamelementsManyofthesamegeneralelementselectionguidelinesapplytobothprograms.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京办事处.Structural Elements (Shells and Beams) vs. Continuum ElementsABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.14Structural Elements (Shells and Beams) vs. Continuum Elements实体单元建立有限元模型通常规模较大，尤其对于三维实体单元如果选用适当的结构单元(shellsandbeams)会得到一个更经济的解决方案模拟相同的问题，用结构体单元通常需要的单元数量比实体单元少很多要由结构体单元得到合理的结果需要满足一定要求：theshellthicknessorthebeamcross-sectiondimensionsshouldbelessthan1/10ofatypicalglobalstructuraldimension,suchas:ThedistancebetweensupportsorpointloadsThedistancebetweengrosschangesincrosssectionThewavelengthofthehighestvibrationmodeABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.15Shell elementsShellelementsapproximateathree-dimensionalcontinuumwithasurfacemodel.高效率的模拟面内弯曲Modelbendingandin-planedeformationsefficiently.Ifadetailedanalysisofaregionisneeded,alocalthree-dimensionalcontinuummodelcanbeincludedusingmulti-pointconstraintsorsubmodeling.如果需要三维实体单元模拟细节可以使用子模型ShellmodelofahemisphericaldomesubjectedtoaprojectileimpactStructural Elements (Shells and Beams) vs. Continuum Elements3-DcontinuumsurfacemodelABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.16Structural Elements (Shells and Beams) vs. Continuum ElementsBeam elements用线简化三维实体。Beamelementsapproximateathree-dimensionalcontinuumwithalinemodel.高效率模拟弯曲，扭转，轴向力。提供很多不同的截面形状截面形状可以通过工程常数定义linemodelframedstructuremodeledusingbeamelements3-DcontinuumABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京办事处.Modeling Bending Using Continuum ElementsABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.18Modeling Bending Using Continuum ElementsPhysical characteristics of pure bendingTheassumedbehaviorofthematerialthatfiniteelementsattempttomodelis:纯弯状态：Planecross-sectionsremainplanethroughoutthedeformation.保持平面Theaxialstrainxxvarieslinearlythroughthethickness.Thestraininthethicknessdirectionyyiszeroif=0.Nomembraneshearstrain.Impliesthatlinesparalleltothebeamaxislieonacirculararc.xxABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.19Modeling Bending Using Continuum ElementsModeling bending using second-order solid elements (CPE8, C3D20R, ) 二次单元模拟二次单元模拟Second-orderfull-andreduced-integrationsolidelementsmodelbendingaccurately:Theaxialstrainequalsthechangeinlengthoftheinitiallyhorizontallines.Thethicknessstrainiszero.Theshearstrainiszero.Linesthatareinitiallyverticaldonotchangelength(impliesyy=0).Becausetheelementedgescanassumeacurvedshape,theanglebetweenthedeformedisoparametriclinesremainsequalto90o(impliesxy=0).isoparametriclinesABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.20Modeling Bending Using Continuum ElementsModeling bending using first-order fully integrated solid elements (CPS4, CPE4, C3D8)Theseelementsdetectshearstrainsattheintegrationpoints.Nonphysical;presentsolelybecauseoftheelementformulationused.Overlystiffbehaviorresultsfromenergygoingintoshearingtheelementratherthanbendingit(called“shearlocking”).Becausetheelementedgesmustremainstraight,theanglebetweenthedeformedisoparametriclinesisnotequalto90o(implies).IntegrationpointDo not use these elements in regions dominated by bending!ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.21Modeling Bending Using Continuum ElementsModeling bending using first-order reduced-integration elements (CPE4R, )Theseelementseliminateshearlocking.However,hourglassingisaconcernwhenusingtheseelements.Onlyoneintegrationpointatthecentroid.Asingleelementthroughthethicknessdoesnotdetectstraininbending.Deformationisazero-energymode(有应变形但是没有应变能的现象called“hourglassing”).Changeinlengthiszero(impliesnostrainisdetectedattheintegrationpoint).Bendingbehaviorforasinglefirst-orderreduced-integrationelement.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.22Modeling Bending Using Continuum ElementsHourglassing is not a problem if you use multiple elementsat least four through the thickness.Eachelementcaptureseithercompressiveortensileaxialstrains,butnotboth.Theaxialstrainsaremeasuredcorrectly.Thethicknessandshearstrainsarezero.Cheapandeffectiveelements.Hourglassingcanpropagateeasilythroughameshoffirst-orderreduced-integrationelements,causingunreliableresults.FourelementsthroughthethicknessNohourglassingABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.23Modeling Bending Using Continuum ElementsDetecting and controlling hourglassingHourglassingcanusuallybeseenindeformedshapeplots.Example:Coarseandmediummeshesofasimplysupportedbeamwithacenterpointload.ABAQUShasbuilt-inhourglasscontrolsthatlimittheproblemscausedbyhourglassing.Verifythattheartificialenergyusedtocontrolhourglassingissmall(0.475).RubberMetalsatlargeplasticstrainsConventionalfiniteelementmeshesoftenexhibitoverlystiffbehaviorduetovolumetric locking,whichismostseverewhenthesematerialsarehighlyconfined.overlystiffbehaviorofanelastic-plasticmaterialwithvolumetriclockingcorrectbehaviorofanelastic-plasticmaterialExampleoftheeffectofvolumetriclockingABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.39Incompressible MaterialsThecauseofvolumetriclockingisthateachintegrationpointsvolumemustremainalmostconstant,overconstrainingthekinematicallyadmissibledisplacementfield.Forexample,inarefinedthree-dimensionalmeshof8-nodehexahedra,thereisonaverage1nodewith3degreesoffreedomperelement.每个单元平均只有1个有三个自由度的节点Thevolumeateachintegrationpointmustremainfixed.Fullyintegratedhexahedrause8integrationpointsperelement;thus,inthisexamplewehaveasmanyas8constraintsperelement,butonly3degreesoffreedomareavailabletosatisfytheseconstraints.每个单元有8个约束，以至于产生体积锁死。Themeshisoverconstrainedit“locks.”Volumetriclockingismostpronouncedinfullyintegratedelements.Reduced-integrationelementshavefewervolumetricconstraints.Reducedintegrationeffectivelyeliminatesvolumetriclockinginmanyproblemswithnearlyincompressiblematerial.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.40Incompressible MaterialsFullyincompressiblematerialsmodeledwithsolidelementsmustusethe“hybrid”formulation(elementswhosenamesendwiththeletter“H”).Inthisformulationthepressurestressistreatedasanindependentlyinterpolatedbasicsolutionvariable,coupledtothedisplacementsolutionthroughtheconstitutivetheory.Hybridelementsintroducemorevariablesintotheproblemtoalleviatethevolumetriclockingproblem.Theextravariablesalsomakethemmoreexpensive.TheABAQUSelementlibraryincludeshybridversionsofallcontinuumelements(exceptplanestresselements,wheretheyarenotneeded).ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.41Hybridelementsareonlynecessaryfor:以不可压缩材料为主的网格，如橡胶材料。Allmesheswithstrictlyincompressiblematerials,suchasrubber.精密的网格，使用减缩积分仍然有locking的网格，比如弹塑性材料完全进入塑性阶段Refinedmeshesofreduced-integrationelementsthatstillshowvolumetriclockingproblems.Suchproblemsarepossiblewithelastic-plasticmaterialsstrainedfarintotheplasticrange.即使使用了hybrid单元一次三角形或者四面体单元仍然有过度约束。因此建议这类单元使用的比例要小，可以作为六面体单元的“填充物”使用。Evenwithhybridelementsameshoffirst-ordertrianglesandtetrahedraisoverconstrainedwhenmodelingfullyincompressiblematerials.Hence,theseelementsarerecommendedonlyforuseas“fillers”inquadrilateralorbrick-typemesheswithsuchmaterial.Incompressible MaterialsABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京办事处.Mesh GenerationABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.43Mesh GenerationQuad/Hex vs. Tri/Tet ElementsOfparticularimportancewhengeneratingameshisthedecisionregardingwhethertousequad/hexortri/tetelements.Quad/hexelementsshouldbeusedwhereverpossible.Theygivethebestresultsfortheminimumcost.Whenmodelingcomplexgeometries,however,theanalystoftenhaslittlechoicebuttomeshwithtriangularandtetrahedralelements.TurbinebladewithplatformmodeledwithtetrahedralelementsABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.44Mesh GenerationFirst-ordertri/tetelements(CPE3,CPS3,CAX3,C3D4,C3D6)arepoorelements;theyhavethefollowingproblems:Poorconvergencerate.Theytypicallyrequireveryfinemeshestoproducegoodresults.Volumetriclockingwithincompressibleornearlyincompressiblematerials,evenusingthe“hybrid”formulation.Theseelementsshouldbeusedonlyasfillersinregionsfarfromanyareaswhereaccurateresultsareneeded.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.45Equivalentnodalforcescreatedbyuniformpressureonthefaceofaregularsecond-ordertetrahedralelementMesh Generation“Regular”second-ordertri/tetelements(CPE6,CPS6,CAX6,C3D10)cannotbeusedtomodelcontact.Underuniformpressurethecontactforcesaresignificantlydifferentatthecornerandmidsidenodes.Forsmall-displacementproblemswithoutcontacttheseelementsprovidereasonableresults.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.46Mesh GenerationModifiedsecond-ordertri/tetelements(C3D10M,etc.)alleviatetheproblemsofothertri/tetelements.Goodconvergencerateclosetoconvergencerateofsecond-orderquad/hexelements.Minimalshearorvolumetriclocking.Canbeusedtomodelincompressibleornearlyincompressiblematerialsinthehybridformulation(C3D10MH).Theseelementsarerobustduringfinitedeformation.Uniformcontactpressureallowstheseelementstomodelcontactaccurately.Use them!ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.47Mesh GenerationMesh refinement and convergenceUseasufficientlyrefinedmeshtoensurethattheresultsfromyourABAQUSsimulationareadequate.Coarsemeshestendtoyieldinaccurateresults.Thecomputerresourcesrequiredtorunyourjobincreasewiththelevelofmeshrefinement.Itisrarelynecessarytouseauniformlyrefinedmeshthroughoutthestructurebeinganalyzed.Useafinemeshonlyinareasofhighgradientsandacoarsermeshinareasoflowgradients.Youcanoftenpredictregionsofhighgradientsbeforegeneratingthemesh.Usehandcalculations,experience,etc.Alternatively,youcanusecoarsemeshresultstoidentifyhighgradientregions.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.48Mesh GenerationSomerecommendations:Minimizemeshdistortionasmuchaspossible.Aminimumoffourquadraticelementsper90oshouldbeusedaroundacircularhole.Aminimumoffourelementsshouldbeusedthroughthethicknessofastructureiffirst-order,reduced-integrationsolidelementsareusedtomodelbending.Otherguidelinescanbedevelopedbasedonexperiencewithagivenclassofproblem.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.49Mesh GenerationItisgoodpracticetoperformameshconvergencestudy.Simulatetheproblemusingprogressivelyfinermeshes,andcomparetheresults.ThemeshdensitycanbechangedveryeasilyusingABAQUS/CAEsincethedefinitionoftheanalysismodelisbasedonthegeometryofthestructure.Thiswillbediscussedfurtherinthenextlecture.Whentwomeshesyieldnearlyidenticalresults,theresultsaresaidtohave“converged.”Thisprovidesincreasedconfidenceinyourresults.ABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京办事处.Solid Element Selection SummaryABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.51Solid Element Selection SummaryClass of problemBest element choiceAvoid usingGeneral contact between deformable bodiesFirst-order quad/hexSecond-order quad/hexContact with bendingIncompatible modeFirst-order fully integrated quad/hex or second-order quad/hexBending (no contact)Second-order quad/hexFirst-order fully integrated quad/hexStress concentrationSecond-orderFirst-orderNearly incompressible (n n0.475 or large strain plasticity e epl10%)First-order elements or second-order reduced-integration elementsSecond-order fully integratedABAQUS/Standard 基础教程基础教程2003,ABAQUS软件公司北京代表处.A1.52Solid Element Selection SummaryClass of problemBest element choiceAvoid usingCompletely incompressible (rubber n n = 0.5)Hybrid quad/hex, first-order if large deformations are anticipatedBulk metal forming (high mesh distortion)First-order reduced-integration quad/hexSecond-order quad/hexComplicated model geometry (linear material, no contact)Second-order quad/hex if possible (if not overly distorted) or second-order tet/tri (because of meshing difficulties)Complicated model geometry (nonlinear problem or contact)First-order quad/hex if possible (if not overly distorted) or modified second-order tet/tri (because of meshing difficulties)Natural frequency (linear dynamics)Second-orderNonlinear dynamic (impact)First-orderSecond-orderABAQUS/Standard 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