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1、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SolidElementSelectionSummaryABA
2、QUS/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
3、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。Element
4、sinthesamefamilysharemanybasicfeatures.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
5、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-orderinterpolatio
6、nABAQUS/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/Standar
7、d 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
8、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Thenu
9、mericalalgorithmusedtointegratethesevariablesinfluenceshowanelementbehaves.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 integ
10、ration 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/Sta
11、ndard 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:Cont
12、inuum,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.ABAQ
13、US/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beam
14、elementsManyofthesamegeneralelementselectionguidelinesapplytobothprograms.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
15、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:ThedistancebetweensupportsorpointloadsThedistancebetweengrosschangesincross
16、sectionThewavelengthofthehighestvibrationmodeABAQUS/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-dimensionalconti
17、nuummodelcanbeincludedusingmulti-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 (Sh
18、ells 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 Continu
19、um 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Theaxialstrainxxvarieslinear
20、lythroughthethickness.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, C3D20
21、R, ) 二次单元模拟二次单元模拟Second-orderfull-andreduced-integrationsolidelementsmodelbendingaccurately:Theaxialstrainequalsthechangeinlengthoftheinitiallyhorizontallines.Thethicknessstrainiszero.Theshearstrainiszero.Linesthatareinitiallyverticaldonotchangelength(impliesyy=0).Becausetheelementedgescanassumeacur
22、vedshape,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)Theseelementsdetectshe
23、arstrainsattheintegrationpoints.Nonphysical;presentsolelybecauseoftheelementformulationused.Overlystiffbehaviorresultsfromenergygoingintoshearingtheelementratherthanbendingit(called“shearlocking”).Becausetheelementedgesmustremainstraight,theanglebetweenthedeformedisoparametriclinesisnotequalto90o(im
24、plies).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,hourglassing
25、isaconcernwhenusingtheseelements.Onlyoneintegrationpointatthecentroid.Asingleelementthroughthethicknessdoesnotdetectstraininbending.Deformationisazero-energymode(有应变形但是没有应变能的现象called“hourglassing”).Changeinlengthiszero(impliesnostrainisdetectedattheintegrationpoint).Bendingbehaviorforasinglefirst-or
26、derreduced-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.Theaxialstrainsa
27、remeasuredcorrectly.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
28、 Using Continuum ElementsDetecting and controlling hourglassingHourglassingcanusuallybeseenindeformedshapeplots.Example:Coarseandmediummeshesofasimplysupportedbeamwithacenterpointload.ABAQUShasbuilt-inhourglasscontrolsthatlimittheproblemscausedbyhourglassing.Verifythattheartificialenergyusedtocontro
29、lhourglassingissmall(0.475).RubberMetalsatlargeplasticstrainsConventionalfiniteelementmeshesoftenexhibitoverlystiffbehaviorduetovolumetric locking,whichismostseverewhenthesematerialsarehighlyconfined.overlystiffbehaviorofanelastic-plasticmaterialwithvolumetriclockingcorrectbehaviorofanelastic-plasti
30、cmaterialExampleoftheeffectofvolumetriclockingABAQUS/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-dimensio
31、nalmeshof8-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,butonly3degreesoffreedomareavailabletosatisfy
32、theseconstraints.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/St
33、andard 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,coupledtothedisplace
34、mentsolutionthroughtheconstitutivetheory.Hybridelementsintroducemorevariablesintotheproblemtoalleviatethevolumetriclockingproblem.Theextravariablesalsomakethemmoreexpensive.TheABAQUSelementlibraryincludeshybridversionsofallcontinuumelements(exceptplanestresselements,wheretheyarenotneeded).ABAQUS/Sta
35、ndard 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.Suchproblemsarepossiblewith
36、elastic-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”inqu
37、adrilateralorbrick-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 ElementsOfparticularimportancewhengeneratingameshisthedecisionregardingwhethertouseq
38、uad/hexortri/tetelements.Quad/hexelementsshouldbeusedwhereverpossible.Theygivethebestresultsfortheminimumcost.Whenmodelingcomplexgeometries,however,theanalystoftenhaslittlechoicebuttomeshwithtriangularandtetrahedralelements.TurbinebladewithplatformmodeledwithtetrahedralelementsABAQUS/Standard 基础教程基础
39、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“hybri
40、d”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/tetelement
41、s(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-o
42、rdertri/tetelements(C3D10M,etc.)alleviatetheproblemsofothertri/tetelements.Goodconvergencerateclosetoconvergencerateofsecond-orderquad/hexelements.Minimalshearorvolumetriclocking.Canbeusedtomodelincompressibleornearlyincompressiblematerialsinthehybridformulation(C3D10MH).Theseelementsarerobustduring
43、finitedeformation.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.Coarsemeshestendtoyieldina
44、ccurateresults.Thecomputerresourcesrequiredtorunyourjobincreasewiththelevelofmeshrefinement.Itisrarelynecessarytouseauniformlyrefinedmeshthroughoutthestructurebeinganalyzed.Useafinemeshonlyinareasofhighgradientsandacoarsermeshinareasoflowgradients.Youcanoftenpredictregionsofhighgradientsbeforegenera
45、tingthemesh.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.Aminimumoffourquadraticelementsper90oshouldbeusedaroundacir
46、cularhole.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 GenerationItisgoodpracticetoper
47、formameshconvergencestudy.Simulatetheproblemusingprogressivelyfinermeshes,andcomparetheresults.ThemeshdensitycanbechangedveryeasilyusingABAQUS/CAEsincethedefinitionoftheanalysismodelisbasedonthegeometryofthestructure.Thiswillbediscussedfurtherinthenextlecture.Whentwomeshesyieldnearlyidenticalresults
48、,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
49、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 incompr
50、essible (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
51、 (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 distorte
52、d) 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 d
53、ynamic (impact)First-orderSecond-orderABAQUS/Standard 基础教程基础教程进入夏天，少不了一个热字当头，电扇空调陆续登场，每逢此时，总会想起进入夏天，少不了一个热字当头，电扇空调陆续登场，每逢此时，总会想起那一把蒲扇。蒲扇，是记忆中的农村，夏季经常用的一件物品。记忆中的故那一把蒲扇。蒲扇，是记忆中的农村，夏季经常用的一件物品。记忆中的故乡，每逢进入夏天，集市上最常见的便是蒲扇、凉席，不论男女老少，个个手持乡，每逢进入夏天，集市上最常见的便是蒲扇、凉席，不论男女老少，个个手持一把，忽闪忽闪个不停，嘴里叨叨着一把，忽闪忽闪个不停，嘴里叨叨着“怎么这
54、么热怎么这么热”，于是三五成群，聚在大树，于是三五成群，聚在大树下，或站着，或随即坐在石头上，手持那把扇子，边唠嗑边乘凉。孩子们却在周下，或站着，或随即坐在石头上，手持那把扇子，边唠嗑边乘凉。孩子们却在周围跑跑跳跳，热得满头大汗，不时听到围跑跑跳跳，热得满头大汗，不时听到“强子，别跑了，快来我给你扇扇强子，别跑了，快来我给你扇扇”。孩。孩子们才不听这一套，跑个没完，直到累气喘吁吁，这才一跑一踮地围过了，这时子们才不听这一套，跑个没完，直到累气喘吁吁，这才一跑一踮地围过了，这时母亲总是，好似生气的样子，边扇边训，母亲总是，好似生气的样子，边扇边训，“你看热的，跑什么？你看热的，跑什么？”此时这把
55、蒲扇，此时这把蒲扇，是那么凉快，那么的温馨幸福，有母亲的味道！蒲扇是中国传统工艺品，在是那么凉快，那么的温馨幸福，有母亲的味道！蒲扇是中国传统工艺品，在我国已有三千年多年的历史。取材于棕榈树，制作简单，方便携带，且蒲扇的表我国已有三千年多年的历史。取材于棕榈树，制作简单，方便携带，且蒲扇的表面光滑，因而，古人常会在上面作画。古有棕扇、葵扇、蒲扇、蕉扇诸名，实即面光滑，因而，古人常会在上面作画。古有棕扇、葵扇、蒲扇、蕉扇诸名，实即今日的蒲扇，江浙称之为芭蕉扇。六七十年代，人们最常用的就是这种，似圆非今日的蒲扇，江浙称之为芭蕉扇。六七十年代，人们最常用的就是这种，似圆非圆，轻巧又便宜的蒲扇。蒲扇流传至今，我的记忆中，它跨越了半个世纪，圆，轻巧又便宜的蒲扇。蒲扇流传至今，我的记忆中，它跨越了半个世纪，也走过了我们的半个人生的轨迹，携带着特有的念想，一年年，一天天，流向长也走过了我们的半个人生的轨迹，携带着特有的念想，一年年，一天天，流向长长的时间隧道，袅长的时间隧道，袅结束
