Abaqus单元选择、压力、接触和网格生成(abaqus软件公司北京代表处)课件

ABAQUS/Standard基础教程ElementSelectionCriteriaAppendix1ABAQUS/Standard基础教程ElementSeABAQUS/Standard基础教程内容提要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基础教程内容提要ElemenABAQUS/Standard基础教程ElementsinABAQUSABAQUS/Standard基础教程ElementsiABAQUS/Standard基础教程ElementsinABAQUSABAQUS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

ThewiderangeofelementsintheABAQUSelementlibraryprovidesflexibilityinmodelingdifferentgeometriesandstructures.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ElementsiABAQUS/Standard基础教程单元类型（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.ElementsinABAQUSspecial-purposeelementslikesprings,dashpots,andmassescontinuum(solidelements)shellelementsbeamelementsrigidelementsmembraneelementstrusselementsinfiniteelementsABAQUS/Standard基础教程单元类型（FamilABAQUS/Standard基础教程ElementsinABAQUSNumberofnodes

节点数(interpolation)Anelement’snumberofnodesdetermineshowthenodaldegreesoffreedomwillbeinterpolatedoverthedomainoftheelement.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ElementsiABAQUS/Standard基础教程ElementsinABAQUS自由度数目

DegreesoffreedomTheprimaryvariablesthatexistatthenodesofanelementarethedegreesoffreedominthefiniteelementanalysis.Examplesofdegreesoffreedomare:Displacements位移Rotations转角Temperature温度Electricalpotential电势ABAQUS/Standard基础教程ElementsiABAQUS/Standard基础教程公式

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ElementsinABAQUSABAQUS/Standard基础教程公式

FormulaABAQUS/Standard基础教程积分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.ElementsinABAQUSABAQUS/Standard基础教程积分IntegratABAQUS/Standard基础教程Fullintegration:

完全积分Theminimumintegrationorderrequiredforexactintegrationofthestrainenergyforanundistortedelementwithlinearmaterialproperties.Reducedintegration:

简缩积分Theintegrationrulethatisoneorderlessthanthefullintegrationrule.ElementsinABAQUSFirst-

orderinterpolationFullintegration

Second-

order

interpolationReducedintegrationABAQUS/Standard基础教程FullintegABAQUS/Standard基础教程ElementsinABAQUSElementnamingconventions: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ElementsiABAQUS/Standard基础教程ElementsinABAQUSABAQUS/Standard和ABAQUS/Explicit单元库的对比

Bothprogramshaveessentiallythesameelementfamilies:continuum,shell,beam,etc.ABAQUS/Standardincludeselementsformanyanalysistypesinadditiontostressanalysis: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ElementsiABAQUS/Standard基础教程StructuralElements(ShellsandBeams)vs.ContinuumElementsABAQUS/Standard基础教程StructuralABAQUS/Standard基础教程StructuralElements(ShellsandBeams)vs.ContinuumElements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StructuralABAQUS/Standard基础教程ShellelementsShellelementsapproximateathree-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ShellmodelofahemisphericaldomesubjectedtoaprojectileimpactStructuralElements(ShellsandBeams)vs.ContinuumElements3-DcontinuumsurfacemodelABAQUS/Standard基础教程ShellelemABAQUS/Standard基础教程StructuralElements(ShellsandBeams)vs.ContinuumElementsBeamelements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StructuralABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsPhysicalcharacteristicsofpurebendingTheassumedbehaviorofthematerialthatfiniteelementsattempttomodelis:

纯弯状态：Planecross-sectionsremainplanethroughoutthedeformation.保持平面Theaxialstrainxxvarieslinearlythroughthethickness.Thestraininthethicknessdirectionyyiszeroif=0.Nomembraneshearstrain.Impliesthatlinesparalleltothebeamaxislieonacirculararc.xxABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsModelingbendingusingsecond-ordersolidelements(CPE8,C3D20R,…)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ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsModelingbendingusingfirst-orderfullyintegratedsolidelements(CPS4,CPE4,C3D8)Theseelementsdetectshearstrainsattheintegrationpoints.Nonphysical;presentsolelybecauseoftheelementformulationused.Overlystiffbehaviorresultsfromenergygoingintoshearingtheelementratherthanbendingit(called“shearlocking”).Becausetheelementedgesmustremainstraight,theanglebetweenthedeformedisoparametriclinesisnotequalto90o(implies).IntegrationpointDonotusetheseelementsinregionsdominatedbybending!ABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsModelingbendingusingfirst-orderreduced-integrationelements(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ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsHourglassingisnotaproblemifyouusemultipleelements—atleastfourthroughthethickness.Eachelementcaptureseithercompressiveortensileaxialstrains,butnotboth.Theaxialstrainsaremeasuredcorrectly.Thethicknessandshearstrainsarezero.Cheapandeffectiveelements.Hourglassingcanpropagateeasilythroughameshoffirst-orderreduced-integrationelements,causingunreliableresults.FourelementsthroughthethicknessNohourglassingABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsDetectingandcontrollinghourglassingHourglassingcanusuallybeseenindeformedshapeplots.Example:Coarseandmediummeshesofasimplysupportedbeamwithacenterpointload.ABAQUShasbuilt-inhourglasscontrolsthatlimittheproblemscausedbyhourglassing.Verifythattheartificialenergyusedtocontrolhourglassingissmall(<1%)relativetotheinternalenergy.Sameloadanddisplacementmagnification(1000×)ABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsUsetheX–YplottingcapabilityinABAQUS/Viewertocomparetheenergiesgraphically.InternalenergyArtificialenergyArtificialenergyInternalenergyTwoelementsthroughthethickness:Ratioofartificialtointernalenergyis2%.Fourelementsthroughthethickness:Ratioofartificialtointernalenergyis0.1%.ABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsModelingbendingusingincompatiblemodeelements(CPS4I,…)Perhapsthemostcost-effectivesolidcontinuumelementsforbending-dominatedproblems.Compromiseincostbetweenthefirst-andsecond-orderreduced-integrationelements,withmanyoftheadvantagesofboth.Modelshearbehaviorcorrectly—noshearstrainsinpurebending.Modelbendingwithonlyoneelementthroughthethickness.Nohourglassmodesandworkwellinplasticityandcontactproblems.Theadvantagesoverreduced-integrationfirst-orderelementsarereducediftheelementsareseverelydistorted;however,allelementsperformlessaccuratelyifseverelydistorted.ABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ModelingBendingUsingContinuumElementsExample:CantileverbeamwithdistortedelementsParalleldistortionTrapezoidaldistortionABAQUS/Standard基础教程ModelingBABAQUS/Standard基础教程ElementtypexxyyxyNotesPhysicalbehavior000Second-order000OKFirst-order,fullintegration000ShearlockingFirst-order,reducedintegration000Hourglassingiftoofewelementsthroughthickness000OKifenoughelementsthroughthethicknessIncompatiblemode000OKifnotoverlydistortedModelingBendingUsingContinuumElementsSummaryABAQUS/Standard基础教程ElementtyABAQUS/Standard基础教程StressConcentrationsABAQUS/Standard基础教程StressConABAQUS/Standard基础教程StressConcentrations二次单元处理应力集中问题，明显优于一次单元

Second-orderelementsclearlyoutperformfirst-orderelementsinproblemswithstressconcentrationsandareideallysuitedfortheanalysisof(stationary)cracks.W无论是完全积分还是减缩积分都可以很好的反映应力集中

Bothfullyintegratedandreduced-integrationelementsworkwell.减缩积分效率更高，而且计算结果往往优于完全积分。

Reduced-integrationelementstendtobesomewhatmoreefficient—resultsareoftenasgoodorbetterthanfullintegrationatlowercomputationalcost.ABAQUS/Standard基础教程StressConABAQUS/Standard基础教程PhysicalmodelModelwithfirst-orderelements—elementfacesarestraightlinesegmentsModelwithsecond-orderelements—

elementfacesarequadraticcurvesStressConcentrations二次单元可以以更少的单元更好的反应结构的几何特征

Second-orderelementscapturegeometricfeatures,suchascurvededges,withfewerelementsthanfirst-orderelements.ABAQUS/Standard基础教程PhysicalmABAQUS/Standard基础教程StressConcentrationsBothfirst-andsecond-orderquadsandbricksbecomelessaccuratewhentheirinitialshapeisdistorted.First-orderelementsareknowntobelesssensitivetodistortionthansecond-orderelementsand,thus,areabetterchoiceinproblemswheresignificantmeshdistortionisexpected.Second-ordertrianglesandtetrahedraarelesssensitivetoinitialelementshapethanmostotherelements;however,well-shapedelementsprovidebetterresults.idealokaybaddistortedundistortedABAQUS/Standard基础教程StressConABAQUS/Standard基础教程ellipticalshapeStressConcentrationsAtypicalstressconcentrationproblem,aNAFEMSbenchmarkproblem,isshownatright.Theanalysisresultsobtainedwithdifferentelementtypesfollow.PABAQUS/Standard基础教程ellipticalABAQUS/Standard基础教程StressConcentrationsFirst-orderelements(includingincompatiblemodeelements)arerelativelypoorinthestudyofstressconcentrationproblems.Second-orderelementssuchasCPS6,CPS8,andCPS8Rgivemuchbetterresults.CoarsemeshFinemeshCPS355.0676.87CPS471.9891.2CPS4I63.4584.37CPS4R43.6760.6CPS696.12101.4CPS891.2100.12CPS8R92.5697.16syyatD(Target=100.0)ElementtypeABAQUS/Standard基础教程StressConABAQUS/Standard基础教程StressConcentrationsWell-shaped,second-order,reduced-integrationquadrilateralsandhexahedracanprovidehighaccuracyinstressconcentrationregions.Distortedelementsreducetheaccuracyintheseregions.ABAQUS/Standard基础教程StressConABAQUS/Standard基础教程ContactABAQUS/Standard基础教程ContactABAQUS/Standard基础教程ContactAlmostallelementtypesareformulatedtoworkwellincontactproblems,withthefollowingexceptions:Second-orderquad/hex

elements“Regular”second-order

tri/tetelements(asopposed

to“modified”tri/tetelements

whosenamesendwiththe

letter“M”)Thedirectionsofthe

consistentnodalforces

resultingfromapressure

loadarenotuniform.ABAQUS/Standard基础教程ContactAlmABAQUS/Standard基础教程IncompressibleMaterialsABAQUS/Standard基础教程IncompressABAQUS/Standard基础教程IncompressibleMaterialsManynonlinearproblemsinvolveincompressiblematerials

(=0.5)andnearlyincompressiblematerials(>0.475).RubberMetalsatlargeplastic

strainsConventionalfiniteelement

meshesoftenexhibitoverly

stiffbehaviorduetovolumetric

locking,whichismostsevere

whenthesematerialsare

highlyconfined.overlystiffbehaviorofanelastic-plasticmaterialwithvolumetriclockingcorrectbehaviorofanelastic-plasticmaterialExampleoftheeffectofvolumetriclockingABAQUS/Standard基础教程IncompressABAQUS/Standard基础教程IncompressibleMaterialsThecauseofvolumetriclockingisthateachintegrationpoint’svolumemustremainalmostconstant,overconstrainingthekinematicallyadmissibledisplacementfield.Forexample,inarefinedthree-dimensionalmeshof8-nodehexahedra,thereis—onaverage—1nodewith3degreesoffreedomperelement.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。Themeshisoverconstrained—it“locks.”Volumetriclockingismostpronouncedinfullyintegratedelements.Reduced-integrationelementshavefewervolumetricconstraints.Reducedintegrationeffectivelyeliminatesvolumetriclockinginmanyproblemswithnearlyincompressiblematerial.ABAQUS/Standard基础教程IncompressABAQUS/Standard基础教程IncompressibleMaterialsFullyincompressiblematerialsmodeledwithsolidelementsmustusethe“hybrid”formulation(elementswhosenamesendwiththeletter

“H”).Inthisformulationthepressurestressistreatedasanindependentlyinterpolatedbasicsolutionvariable,coupledtothedisplacementsolutionthroughtheconstitutivetheory.Hybridelementsintroducemorevariablesintotheproblemtoalleviatethevolumetriclockingproblem.Theextravariablesalsomakethemmoreexpensive.TheABAQUSelementlibraryincludeshybridversionsofallcontinuumelements(exceptplanestresselements,wheretheyarenotneeded).ABAQUS/Standard基础教程IncompressABAQUS/Standard基础教程Hybridelementsareonlynecessaryfor: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.IncompressibleMaterialsABAQUS/Standard基础教程HybrideleABAQUS/Standard基础教程MeshGenerationABAQUS/Standard基础教程MeshGenerABAQUS/Standard基础教程MeshGenerationQuad/Hexvs.Tri/TetElementsOfparticularimportancewhengeneratingameshisthedecisionregardingwhethertousequad/hexortri/tetelements.Quad/hexelementsshouldbeusedwhereverpossible.Theygivethebestresultsfortheminimumcost.Whenmodelingcomplexgeometries,however,theanalystoftenhaslittlechoicebuttomeshwithtriangularandtetrahedralelements.TurbinebladewithplatformmodeledwithtetrahedralelementsABAQUS/Standard基础教程MeshGenerABAQUS/Standard基础教程MeshGenerationFirst-ordertri/tetelements(CPE3,CPS3,CAX3,C3D4,C3D6)arepoorelements;theyhavethefollowingproblems:Poorconvergencerate.Theytypicallyrequireveryfinemeshestoproducegoodresults.Volumetriclockingwithincompressibleornearlyincompressiblematerials,evenusingthe“hybrid”formulation.Theseelementsshouldbeusedonlyasfillersinregionsfarfromanyareaswhereaccurateresultsareneeded.ABAQUS/Standard基础教程MeshGenerABAQUS/Standard基础教程Equivalentnodalforcescreatedbyuniformpressureonthefaceofaregularsecond-ordertetrahedralelementMeshGeneration“Regular”second-ordertri/tetelements(CPE6,CPS6,CAX6,C3D10)cannotbeusedtomodelcontact.Underuniformpressurethecontactforcesaresignificantlydifferentatthecornerandmidsidenodes.Forsmall-displacementproblemswithoutcontacttheseelementsprovidereasonableresults.ABAQUS/Standard基础教程EquivalentABAQUS/Standard基础教程MeshGenerationModifiedsecond-ordertri/tetelements(C3D10M,etc.)alleviatetheproblemsofothertri/tetelements.Goodconvergencerate—closetoconvergencerateofsecond-orderquad/hexelements.Minimalshearorvolumetriclocking.Canbeusedtomodelincompressibleornearlyincompressiblematerialsinthehybridformulation(C3D10MH).Theseelementsarerobustduringfinitedeformation.Uniformcontactpressureallowstheseelementstomodelcontactaccurately.Usethem!ABAQUS/Standard基础教程MeshGenerABAQUS/Standard基础教程MeshGenerationMeshrefinementandconvergenceUseasufficientlyrefinedmeshtoensurethattheresultsfromyourABAQUSsimulationareadequate.Coarsemeshestendtoyieldinaccurateresults.Thecomputerresourcesrequiredtorunyourjobincreasewiththelevelofmeshrefinement.Itisrarelynecessarytouseauniformlyrefinedmeshthroughoutthestructurebeinganalyzed.Useafinemeshonlyinareasofhighgradientsandacoarsermeshinareasoflowgradients.Youcanoftenpredictregionsofhighgradientsbeforegeneratingthemesh.Usehandcalculations,experience,etc.Alternatively,youcanusecoarsemeshresultstoidentifyhighgradientregions.ABAQUS/Standard基础教程MeshGenerABAQUS/Standard基础教程MeshGenerationSomerecommendations:Minimizemeshdistortionasmuchaspossible.Aminimumoffourquadraticelementsper90oshouldbeusedaroundacircularhole.Aminimumoffourelementsshouldbeusedthroughthethicknessofastructureiffirst-order,reduced-integrationsolidelementsareusedtomodelbending.Otherguidelinescanbedevelopedbasedonexperiencewithagivenclassofproblem.ABAQUS/Standard基础教程MeshGenerABAQUS/Standard基础教程MeshGenerationItisgoodpracticetoperformameshconvergencestudy.Simulatetheproblemusingprogressivelyfinermeshes,andcomparetheresults.ThemeshdensitycanbechangedveryeasilyusingABAQUS/CAEsincethedefinitionoftheanalysismodelisbasedonthegeometryofthestructure.Thiswillbediscussedfurtherinthenextlecture.Whentwomeshesyieldnearlyidenticalresults,theresultsaresaidtohave“converged.”Thisprovidesincreasedconfidenceinyourresults.ABAQUS/Standard基础教程MeshGenerABAQUS/Standard基础教程SolidElement

SelectionSummaryABAQUS/Standard基础教程SolidElemABAQUS/Standard基础教程SolidElementSelectionSummaryClassofproblemBestelementchoiceAvoidusingGeneralcontactbetweendeformablebodiesFirst-orderquad/hexSecond-orderquad/hexContactwithbendingIncompatiblemodeFirst-orderfullyintegratedquad/hexorsecond-orderquad/hexBending(nocontact)Second-orderquad/hexFirst-orderfullyintegratedquad/hex StressconcentrationSecond-orderFirst-orderNearlyincompressible(n>0.475orlargestrainplasticityepl>10%)First-orderelementsorsecond-orderreduced-integrationelementsSecond-orderfullyintegratedABAQUS/Standard基础教程SolidElemABAQUS/Standard基础教程SolidElementSelectionSummaryClassofproblemBestelementchoiceAvoidusingCompletelyincompressible(rubbern=0.5)Hybridquad/hex,first-orderiflargedeformationsareanticipatedBulkmetalforming(highmeshdistortion)First-orderreduced-integrationquad/hexSecond-orderquad/hexComplicatedmodelgeometry(linearmaterial,nocontact)Second-orderquad/hexifpossible(ifnotoverlydistorted)orsecond-ordertet/tri(becauseofmeshingdifficulties)Complicatedmodelgeometry(nonlinearproblemorcontact)First-orderquad/hexifpossible(ifnotoverlydistorted)ormodifiedsecond-ordertet/tri(becauseofmeshingdifficulties)Naturalfrequency(lineardynamics)Second-orderNonlineardynamic(impact)First-orderSecond-orderABAQUS/Standard基础教程SolidElem演讲完毕，谢谢观看！演讲完毕，谢谢观看！ABAQUS/Standard基础教程ElementSelectionCriteriaAppendix1ABAQUS/Standard基础教程ElementSeABAQUS/Standard基础教程内容提要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基础教程内容提要ElemenABAQUS/Standard基础教程ElementsinABAQUSABAQUS/Standard基础教程ElementsiABAQUS/Standard基础教程ElementsinABAQUSABAQUS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

ThewiderangeofelementsintheABAQUSelementlibraryprovidesflexibilityinmodelingdifferentgeometriesandstructures.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ElementsiABAQUS/Standard基础教程单元类型（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.ElementsinABAQUSspecial-purposeelementslikesprings,dashpots,andmassescontinuum(solidelements)shellelementsbeamelementsrigidelementsmembraneelementstrusselementsinfiniteelementsABAQUS/Standard基础教程单元类型（FamilABAQUS/Standard基础教程ElementsinABAQUSNumberofnodes

节点数(interpolation)Anelement’snumberofnodesdetermineshowthenodaldegreesoffreedomwillbeinterpolatedoverthedomainoftheelement.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ElementsiABAQUS/Standard基础教程ElementsinABAQUS自由度数目

DegreesoffreedomTheprimaryvariablesthatexistatthenodesofanelementarethedegreesoffreedominthefiniteelementanalysis.Examplesofdegreesoffreedomare:Displacements位移Rotations转角Temperature温度Electricalpotential电势ABAQUS/Standard基础教程ElementsiABAQUS/Standard基础教程公式

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ElementsinABAQUSABAQUS/Standard基础教程公式

FormulaABAQUS/Standard基础教程积分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.ElementsinABAQUSABAQUS/Standard基础教程积分IntegratABAQUS/Standard基础教程Fullintegration:

完全积分Theminimumintegrationorderrequiredforexactintegrationofthestrainenergyforanundistortedelementwithlinearmaterialproperties.Reducedintegration:

简缩积分Theintegrationrulethatisoneorderlessthanthefullintegrationrule.ElementsinABAQUSFirst-

orderinterpolationFullintegration

Second-

order

interpolationReducedintegrationABAQUS/Standard基础教程FullintegABAQUS/Standard基础教程ElementsinABAQUSElementnamingconventions: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ElementsiABAQUS/Standard基础教程ElementsinABAQUSABAQUS/Standard和ABAQUS/Explicit单元库的对比

Bothprogramshaveessen