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1、内容提要内容提要(nirntyo)ElementsinABAQUSStructuralElements(ShellsandBeams)vs.ContinuumElementsModelingBendingUsingContinuumElements用实体单元模拟(mn)弯曲StressConcentrations应力集中Contact接触IncompressibleMaterials不可压缩材料MeshGeneration网格生成SolidElementSelectionSummary第1页/共52页第一页，共53页。ElementsinABAQUS第2页/共52页第二页，共53页。Eleme
2、ntsinABAQUSABAQUS单元库中提供广泛(gungfn)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积分第3页/共52页
3、第三页，共53页。单元类型（Family）Afamilyoffiniteelementsisthebroadestcategoryusedtoclassifyelements.同类型单元有很多相同(xintn)的基本特。Elementsinthesamefamilysharemanybasicfeatures.同种类单元又有很多变化：Therearemanyvariationswithinafamily.ElementsinABAQUSspecial-purpose elements like springs, dashpots, and massescontinuum (solid elem
4、ents)shell elementsbeam elementsrigid elementsmembrane elementstruss elementsinfinite elements第4页/共52页第四页，共53页。ElementsinABAQUSNumberofnodes节点( jidin)数(interpolation)Anelementsnumberofnodesdetermineshowthenodaldegreesoffreedomwillbeinterpolatedoverthedomainoftheelement.ABAQUSincludeselementswithboth
5、first-andsecond-orderinterpolation.插值函数阶数可以为一次或者两次First-order interpolationSecond-order interpolation第5页/共52页第五页，共53页。ElementsinABAQUS自由度数目DegreesoffreedomTheprimaryvariablesthatexistatthenodesofanelementarethedegreesoffreedominthefiniteelementanalysis.Examplesofdegreesoffreedomare:Displacements位移Ro
6、tations转角(zhunjio)Temperature 温度Electricalpotential电势第6页/共52页第六页，共53页。公式(gngsh)FormulationThemathematicalformulationusedtodescribethebehaviorofanelementisanotherbroadcategorythatisusedtoclassifyelements.Examplesofdifferentelementformulations:Planestrain平面应变Planestress平面应力Hybridelements杂交单元Incompatib
7、le-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ElementsinABAQUS第7页/共52页第七页，共53页。积分Integration单元的刚度和质量在单元内的采样点进行( jnxng)数值计算，这些采样点叫做“积分点”Thestiffnessandmassofanelementarecalculatednumericallyatsamplingpointscalled“integrationpoints”withintheelement.数值积分的算法
8、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.ElementsinABAQUS第8页/共52页第八页，共53页。Fullintegration:完全(wnqun)积分Theminimumintegrationorderrequiredforexactintegrationofthestrainenergyforan
9、undistortedelementwithlinearmaterialproperties.Reducedintegration:简缩积分Theintegrationrulethatisoneorderlessthanthefullintegrationrule.ElementsinABAQUSFirst-order interpolationFull integration Second-orderinterpolationReduced integration第9页/共52页第九页，共53页。ElementsinABAQUSElementnamingconventions:example
10、s单元命名(mngmng)约定B21: Beam, 2-D, 1st-order interpolationCAX8R: Continuum, AXisymmetric, 8-node, Reduced integrationDC3D4: Diffusion (heat transfer), Continuum, 3-D, 4-nodeS8RT: Shell, 8-node, Reduced integration, TemperatureCPE8PH: Continuum, Plane strain, 8-node, Pore pressure, HybridDC1D2E: Diffusio
11、n (heat transfer), Continuum, 1-D, 2-node, Electrical第10页/共52页第十页，共53页。ElementsinABAQUSABAQUS/Standard和ABAQUS/Explicit单元(dnyun)库的对比Bothprogramshaveessentiallythesameelementfamilies:continuum,shell,beam,etc.ABAQUS/Standardincludeselementsformanyanalysistypesinadditiontostressanalysis:热传导,固化soilsconso
12、lidation,声场acoustics,etc.AcousticelementsarealsoavailableinABAQUS/Explicit.ABAQUS/Standardincludesmanymorevariationswithineachelementfamily.ABAQUS/Explicit包括的单元(dnyun)绝大多数都为一次单元(dnyun)。例外:二次单元(dnyun)和四面体单元(dnyun)and二次beamelementsManyofthesamegeneralelementselectionguidelinesapplytobothprograms.第11页/
13、共52页第十一页，共53页。StructuralElements(ShellsandBeams)vs.ContinuumElements第12页/共52页第十二页，共53页。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(hl)的结果需要满足一定要求：theshellthicknessorthebeamcross-s
14、ectiondimensionsshouldbelessthan1/10ofatypicalglobalstructuraldimension,suchas:ThedistancebetweensupportsorpointloadsThedistancebetweengrosschangesincrosssectionThewavelengthofthehighestvibrationmode第13页/共52页第十三页，共53页。ShellelementsShellelementsapproximateathree-dimensionalcontinuumwithasurfacemodel.
15、高效率的模拟面内弯曲Modelbendingandin-planedeformationsefficiently.Ifadetailedanalysisofaregionisneeded,alocalthree-dimensionalcontinuummodelcanbeincludedusingmulti-pointconstraintsorsubmodeling.如果需要三维实体(sht)单元模拟细节可以使用子模型Shell model of a hemispherical dome subjected to a projectile impactStructuralElements(Sh
16、ellsandBeams)vs.ContinuumElements3-D continuumsurface model第14页/共52页第十四页，共53页。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( jimin)形状截面( jimin)形状可以通过工程常数定义line modelframed structure
17、 modeled using beam elements3-D continuum第15页/共52页第十五页，共53页。ModelingBendingUsingContinuumElements第16页/共52页第十六页，共53页。ModelingBendingUsingContinuumElementsPhysicalcharacteristicsofpurebendingTheassumedbehaviorofthematerialthatfiniteelementsattempttomodelis:纯弯状态(zhungti)：Planecross-sectionsremainplanet
18、hroughoutthedeformation.保持平面Theaxialstrainxxvarieslinearlythroughthethickness.Thestraininthethicknessdirectionyyiszeroif=0.Nomembraneshearstrain.Impliesthatlinesparalleltothebeamaxislieonacirculararc.xx第17页/共52页第十七页，共53页。ModelingBendingUsingContinuumElementsModelingbendingusingsecond-ordersolideleme
19、nts(CPE8,C3D20R,)二次单元(dnyun)模拟Second-orderfull-andreduced-integrationsolidelementsmodelbendingaccurately:Theaxialstrainequalsthechangeinlengthoftheinitiallyhorizontallines.Thethicknessstrainiszero.Theshearstrainiszero.Lines that are initially vertical do not change length (implies yy=0).Because the
20、element edges can assume a curved shape, the angle between the deformed isoparametric lines remains equal to 90o (implies xy=0).isoparametric lines第18页/共52页第十八页，共53页。ModelingBendingUsingContinuumElementsModelingbendingusingfirst-orderfullyintegratedsolidelements(CPS4,CPE4,C3D8)Theseelementsdetectshe
21、arstrainsattheintegrationpoints.Nonphysical;presentsolelybecauseoftheelementformulationused.Overlystiffbehaviorresultsfromenergygoingintoshearingtheelementratherthanbendingit(called“shearlocking”).Because the element edges must remain straight, the angle between the deformed isoparametric lines is n
22、ot equal to 90o (implies ).Integration pointDo not use these elements in regions dominated by bending!第19页/共52页第十九页，共53页。ModelingBendingUsingContinuumElementsModelingbendingusingfirst-orderreduced-integrationelements(CPE4R,)Theseelementseliminateshearlocking.However,hourglassingisaconcernwhenusingth
23、eseelements.Onlyoneintegrationpointatthecentroid.Asingleelementthroughthethicknessdoesnotdetectstraininbending.Deformationisazero-energymode(有应变形(binxng)但是没有应变能的现象called“hourglassing”).Change in length is zero (implies no strain is detected at the integration point).Bending behavior for a single fir
24、st-order reduced-integration element.第20页/共52页第二十页，共53页。ModelingBendingUsingContinuumElementsHourglassingisnotaproblemifyouusemultipleelementsatleastfourthroughthethickness.Eachelementcaptureseithercompressiveortensileaxialstrains,butnotboth.Theaxialstrainsaremeasuredcorrectly.Thethicknessandshearst
25、rainsarezero.Cheapandeffectiveelements.Hourglassing can propagate easily through a mesh of first-order reduced-integration elements, causing unreliable results.Four elements through the thicknessNo hourglassing第21页/共52页第二十一页，共53页。ModelingBendingUsingContinuumElementsDetectingandcontrollinghourglassi
26、ngHourglassingcanusuallybeseenindeformedshapeplots.Example:Coarseandmediummeshesofasimplysupportedbeamwithacenterpointload.ABAQUShasbuilt-inhourglasscontrolsthatlimittheproblemscausedbyhourglassing.Verifythattheartificialenergyusedtocontrolhourglassingissmall(0.475).RubberMetalsatlargeplasticstrains
27、Conventionalfiniteelementmeshesoftenexhibitoverlystiffbehaviorduetovolumetriclocking,whichismostseverewhenthesematerialsarehighlyconfined.overly stiff behavior of an elastic-plastic material with volumetric lockingcorrect behavior of an elastic-plastic materialExample of the effect of volumetric loc
28、king第37页/共52页第三十七页，共53页。IncompressibleMaterialsThecauseofvolumetriclockingisthateachintegrationpointsvolumemustremainalmostconstant,overconstrainingthekinematicallyadmissibledisplacementfield.Forexample,inarefinedthree-dimensionalmeshof8-nodehexahedra,thereisonaverage1nodewith3degreesoffreedomperele
29、ment. 每个单元平均只有1个有三个自由度的节点( jidin)Thevolumeateachintegrationpointmustremainfixed.Fullyintegratedhexahedrause8integrationpointsperelement;thus,inthisexamplewehaveasmanyas8constraintsperelement,butonly3degreesoffreedomareavailable tosatisfytheseconstraints.每个单元有8个约束，以至于产生体积锁死。Themeshisoverconstrainedit
30、“locks.”Volumetriclockingismostpronouncedinfullyintegratedelements.Reduced-integrationelementshavefewervolumetricconstraints.Reducedintegrationeffectivelyeliminatesvolumetriclockinginmanyproblemswithnearlyincompressiblematerial.第38页/共52页第三十八页，共53页。IncompressibleMaterialsFullyincompressiblematerialsm
31、odeledwithsolidelementsmustusethe“hybrid”formulation(elementswhosenamesendwiththeletter“H”).Inthisformulationthepressurestressistreatedasanindependentlyinterpolatedbasicsolutionvariable,coupledtothedisplacementsolutionthroughtheconstitutivetheory.Hybridelementsintroducemorevariablesintotheproblemtoa
32、lleviatethevolumetriclockingproblem.Theextravariablesalsomakethemmoreexpensive.TheABAQUSelementlibraryincludeshybridversionsofallcontinuumelements(exceptplanestresselements,wheretheyarenotneeded).第39页/共52页第三十九页，共53页。Hybridelementsareonlynecessaryfor:以不可压缩材料(cilio)为主的网格，如橡胶材料(cilio)。Allmesheswithstri
33、ctlyincompressiblematerials,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(cilio)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
34、，可以作为六面体单元的“填充物”使用。Evenwithhybridelementsameshoffirst-ordertrianglesandtetrahedraisoverconstrainedwhenmodelingfullyincompressiblematerials.Hence,theseelementsarerecommendedonlyforuseas“fillers”inquadrilateralorbrick-typemesheswithsuchmaterial.IncompressibleMaterials第40页/共52页第四十页，共53页。MeshGeneration第
35、41页/共52页第四十一页，共53页。MeshGenerationQuad/Hexvs.Tri/TetElementsOfparticularimportancewhengeneratingameshisthedecisionregardingwhethertousequad/hexortri/tetelements.Quad/hexelementsshouldbeusedwhereverpossible.Theygivethebestresultsfortheminimumcost.Whenmodelingcomplexgeometries,however,theanalystoftenha
36、slittlechoicebuttomeshwithtriangularandtetrahedralelements.Turbine blade with platform modeled with tetrahedral elements第42页/共52页第四十二页，共53页。MeshGenerationFirst-ordertri/tetelements(CPE3,CPS3,CAX3,C3D4,C3D6)arepoorelements;theyhavethefollowingproblems:Poorconvergencerate.Theytypicallyrequireveryfinem
37、eshestoproducegoodresults.Volumetriclockingwithincompressibleornearlyincompressiblematerials,evenusingthe“hybrid”formulation.Theseelementsshouldbeusedonlyasfillersinregionsfarfromanyareaswhereaccurateresultsareneeded.第43页/共52页第四十三页，共53页。Equivalent nodal forces created by uniform pressure on the face
38、 of a regular second-order tetrahedral elementMeshGeneration“Regular”second-ordertri/tetelements(CPE6,CPS6,CAX6,C3D10)cannotbeusedtomodelcontact.Underuniformpressurethecontactforcesaresignificantlydifferentatthecornerandmidsidenodes.Forsmall-displacementproblemswithoutcontacttheseelementsprovidereas
39、onableresults.第44页/共52页第四十四页，共53页。MeshGenerationModifiedsecond-ordertri/tetelements(C3D10M,etc.)alleviatetheproblemsofothertri/tetelements.Goodconvergencerateclosetoconvergencerateofsecond-orderquad/hexelements.Minimalshearorvolumetriclocking.Canbeusedtomodelincompressibleornearlyincompressiblemater
40、ialsinthehybridformulation(C3D10MH).Theseelementsarerobustduringfinitedeformation.Uniformcontactpressureallowstheseelementstomodelcontactaccurately.Usethem!第45页/共52页第四十五页，共53页。MeshGenerationMeshrefinementandconvergenceUseasufficientlyrefinedmeshtoensurethattheresultsfromyourABAQUSsimulationareadequa
41、te.Coarsemeshestendtoyieldinaccurateresults.Thecomputerresourcesrequiredtorunyourjobincreasewiththelevelofmeshrefinement.Itisrarelynecessarytouseauniformlyrefinedmeshthroughoutthestructurebeinganalyzed.Useafinemeshonlyinareasofhighgradientsandacoarsermeshinareasoflowgradients.Youcanoftenpredictregio
42、nsofhighgradientsbeforegeneratingthemesh.Usehandcalculations,experience,etc.Alternatively,youcanusecoarsemeshresultstoidentifyhighgradientregions.第46页/共52页第四十六页，共53页。MeshGenerationSomerecommendations:Minimizemeshdistortionasmuchaspossible.Aminimumoffourquadraticelementsper90oshouldbeusedaroundacircu
43、larhole.Aminimumoffourelementsshouldbeusedthroughthethicknessofastructureiffirst-order,reduced-integrationsolidelementsareusedtomodelbending.Otherguidelinescanbedevelopedbasedonexperiencewithagivenclassofproblem.第47页/共52页第四十七页，共53页。MeshGenerationItisgoodpracticetoperformameshconvergencestudy.Simulat
44、etheproblemusingprogressivelyfinermeshes,andcomparetheresults.ThemeshdensitycanbechangedveryeasilyusingABAQUS/CAEsincethedefinitionoftheanalysismodelisbasedonthegeometryofthestructure.Thiswillbediscussedfurtherinthenextlecture.Whentwomeshesyieldnearlyidenticalresults,theresultsaresaidtohave“converge
45、d.”Thisprovidesincreasedconfidenceinyourresults.第48页/共52页第四十八页，共53页。SolidElementSelectionSummary第49页/共52页第四十九页，共53页。SolidElementSelectionSummaryClass of problemBest element choiceAvoid usingGeneral contact between deformable bodiesFirst-order quad/hexSecond-order quad/hexContact with bendingIncompat
46、ible 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 red
47、uced-integration elementsSecond-order fully integrated第50页/共52页第五十页，共53页。SolidElementSelectionSummaryClass 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)Fi
48、rst-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
49、 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-order第51页/共52页第五十一页，共53页。ABAQUS/Standard基础教程谢谢大家(dji)观赏！第52页/共52页第五十二页，共53页。内容(nirng)总结内容提要。Second-orderinterpolation。ABAQUS/Explicit 包括的单元绝大多数都为一次单元。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(gud)约束。谢谢大家观赏第五十三页，共53页。
