2002-co-rotational beam elements in instability problems

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1、Co-rotationalbeamelementsininstabilityproblemsbyJean-MarcBattiniDepartmentofMechanicsJanuary2002TechnicalReportsfromRoyalInstituteofTechnologyDepartmentofMechanicsSE-10044Stockholm,SwedenAkademiskavhandlingsommedtillst˚andavKungligaTekniskaH¨ogskolaniStock-holmframl¨a

2、ggestilloffentliggranskningf¨oravl¨aggandeavteknologiedoktorsexamenfredagenden18:ejanuari2002kl13.00iKollegiesalen,Administrationsbyggnaden,KungligaTekniskaH¨ogskolan,Valhallav¨agen79,Stockholm.
cJean-MarcBattini2002ToAmraiiiAbstractThepurposeoftheworkpresentedinthisth

3、esisistoimplementco-rotationalbeamelementsandbranch-switchingproceduresinordertoanalyseelasticandelasto-plasticinstabilityproblems.Forthe2Dbeamelements,theco-rotationalframeworkistakenfromCrisfield[23].Themainobjectiveistocomparethreedifferentlocalelasto-plasticelements

4、.The3Dco-rotationalformulationisbasedontheworkofPacosteandEriksson[73],withnewitemsconcerningtheparameterisationofthefiniterotations,thedefinitionofthelocalframe,theinclusionofwarpingeffectsthroughtheintroductionofaseventhnodaldegreeoffreedomandtheconsiderationofrigidlin

5、ks.Differenttypesoflocalformulationsareconsidered,includingornotwarpingeffects.Itisshownthatatleastsomedegreeofnon-linearitymustbeintroducedinthelocalstraindefinitioninordertoobtaincorrectresultsforcertainclassesofproblems.Withinthepresentapproachanycross-sectioncanbemod

6、elled,andparticularly,thecentroidandshearcenterarenotnecessarilycoincident.PlasticityisintroducedviaavonMisesmaterialwithisotropichardening.Numer-icalintegrationoverthecross-sectionisperformed.Ateachintegrationpoint,theconstitutiveequationsaresolvedbyincludinginteract

7、ionbetweenthenormalandshearstresses.Concerninginstabilities,anewnumericalmethodforthedirectcomputationofelas-ticcriticalpointsisproposed.ThisisbasedonaminimalaugmentationprocedureasdevelopedbyEriksson[32–34].Inelasto-plasticity,aliteraturesurvey,mainlycon-cernedwithth

8、eoreticalaspectsisfirstpresented.Theobjectiveistogetacompletecomprehensionofthephenomenaandtogiveabasisforthetwobranch-switch