beam188单元.docx

beam188单元.docx

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beam188单元

BEAM188

3-D2-NodeBeam

MPMESTPRPRNDSDSS<><><><>PPVTEMEMFS

ProductRestrictions

BEAM188ElementDescription

BEAM188issuitableforanalyzingslendertomoderatelystubby/thickbeamstructures.TheelementisbasedonTimoshenkobeamtheorywhichincludesshear-deformationeffects.Theelementprovidesoptionsforunrestrainedwarpingandrestrainedwarpingofcross-sections.

Beam188单元适合于分析从细长到中等粗短的梁结构，该单元基于铁木辛哥梁结构理论，并考虑了剪切变形的影响。

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Theelementisalinear,quadratic,orcubictwo-nodebeamelementin3-D.BEAM188hassixorsevendegreesoffreedomateachnode.Theseincludetranslationsinthex,y,andzdirectionsandrotationsaboutthex,y,andzdirections.Aseventhdegreeoffreedom（warpingmagnitude）isoptional.Thiselementiswell-suitedforlinear,largerotation,and/orlargestrainnonlinearapplications.

Beam188是三维线性（2节点）或者二次梁单元。

每个节点有六个或者七个自由度，自由度的个数取决于KEYOPT

（1）的值。

当KEYOPT

（1）＝0（缺省）时，每个节点有六个自由度；节点坐标系的x、y、z方向的平动和绕x、y、z轴的转动。

当KEYOPT

（1）=1时，每个节点有七个自由度，这时引入了第七个自由度（横截面的翘曲）。

这个单元非常适合线性、大角度转动和/并非线性大应变问题。

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Theelementincludesstressstiffnessterms,bydefault,inanyanalysiswithlargedeflection.Theprovidedstress-stiffnesstermsenabletheelementstoanalyzeflexural,lateral,andtorsionalstabilityproblems（usingeigenvaluebuckling,orcollapsestudieswitharclengthmethodsornonlinearstabilization）.

Elasticity,plasticity,creepandothernonlinearmaterialmodelsaresupported.Across-sectionassociatedwiththiselementtypecanbeabuilt-upsectionreferencingmorethanonematerial.

Figure 188.1:

 BEAM188Geometry

BEAM188ElementTechnologyandUsageRecommendations

BEAM188isbasedonTimoshenkobeamtheory,whichisafirst-ordershear-deformationtheory:

transverse-shearstrainisconstantthroughthecross-section（thatis,cross-sectionsremainplaneandundistortedafterdeformation）.

Theelementcanbeusedforslenderorstoutbeams.Duetothelimitationsoffirst-ordershear-deformationtheory,slendertomoderatelythickbeamscanbeanalyzed.Usetheslendernessratioofabeamstructure（GAL2/（EI））tojudgetheapplicabilityoftheelement,where:

G

Shearmodulus

A

Areaofthecross-section

L

Lengthofthemember（nottheelementlength）

EI

Flexuralrigidity

Calculatetheratiousingsomeglobaldistancemeasures,ratherthanbasingituponindividualelementdimensions.Thefollowingillustrationshowsanestimateoftransverse-sheardeformationinacantileverbeamsubjectedtoatipload.Althoughtheresultscannotbeextrapolatedtoanyotherapplication,theexampleserveswellasageneralguideline.Aslendernessratiogreaterthan30isrecommended.

Figure 188.2:

 Transverse-ShearDeformationEstimation

SlendernessRatio（GAL2/（EI））

 δTimoshenko/δEuler-Bernoulli

25

1.120

50

1.060

100

1.030

1000

1.003

Theelementsupportsanelasticrelationshipbetweentransverse-shearforcesandtransverse-shearstrains.Youcanoverridedefaultvaluesoftransverse-shearstiffnessesviatheSECCONTROLScommand.

BEAM188doesnotusehigher-ordertheoriestoaccountforvariationindistributionofshearstresses.UseANSYSsolidelementsifsucheffectsmustbeconsidered.

BEAM188supports“restrainedwarping”analysisbymakingavailableaseventhdegreeoffreedomateachbeamnode.Bydefault,BEAM188elementsassumethatthewarpingofacross-sectionissmallenoughthatitcanbeneglected（KEYOPT

（1）=0）.YoucanactivatethewarpingdegreeoffreedombyusingKEYOPT

（1）=1.Withthewarpingdegreeoffreedomactivated,eachnodehassevendegreesoffreedom:

UX,UY,UZ,ROTX,ROTY,ROTZ,andWARP.WithKEYOPT

（1）=1,bimomentandbicurvatureareoutput.

WhenKEYOPT（3）=0（linear,default）,BEAM188isbasedonlinearshapefunctions.Itusesonepointofintegrationalongthelength;therefore,allelementsolutionquantitiesareconstantalongthelength.Forexample,whenSMISCquantitiesarerequestedatnodesIandJ,thecentroidalvaluesarereportedforbothendnodes.Thisoptionisrecommendediftheelementisusedasstiffeneranditisnecessarytomaintaincompatibilitywithafirst-ordershellelement（suchasSHELL181）.Onlyconstantbendingmomentscanberepresentedexactlywiththisoption.Meshrefinementisgenerallyrequiredintypicalapplications.

WhenKEYOPT（3）=2（quadratic）,BEAM188hasaninternalnodeintheinterpolationscheme,effectivelymakingthisabeamelementbasedonquadraticshapefunctions.Twopointsofintegrationareused,resultinginlinearvariationofelementsolutionquantitiesalongthelength.Linearlyvaryingbendingmomentsarerepresentedexactly.

WhenKEYOPT（3）=3（cubic）,BEAM188hastwointernalnodesandadoptscubicshapefunctions.Quadraticallyvarying