研究非圆截面弹性杆的解析方法.docx

《研究非圆截面弹性杆的解析方法.docx》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、TheanalyticalanalysisoftheasymmetricelasticrodWANGWei,CHENTao(DepartmentofMechanics,SchoolofEngineering,TianjinUniversity,Tianjin300072,China)Abstract:Theanalyticalequationoftheasymmetricelasticrodgovernedbytheordinarydifferentialequationisobtained.WereconstructtheKirchh

2、offequationswiththecomplexcoordinatesandintroduceanoveltransformationparameter.Theychangetheinitialnon-circularcharacterofthecrosssectionintoanearlycrosssectioncase,andapproximatelyresulttheDuffingtypeordinarydifferentialequations・Perturbationmethodsbasingontheseequation

3、spermitourexpectationtoexploretheintrinsicpropertiesofDNAdoublehelixwithintheframeworkofanalyticalresearchnotmerelythenumericalsimulations,suchasstructuralinhomogeneityandperiodicallyvaryingofbendingrigidities.Keywords:Elasticrod;Kirchhoffequation;DNAdoublehelix0Introduc

4、tionTheelasticrodsprovideidealizedmodelswithwhichtocharacterizetheelasticbehaviorofdifferentfilamentarystructurebothmacroscopicallyandmicrocosmically,suchasflexiblecables,antennas,shafts,pipes,proteins,andDNAdoublehelix.Theavailableapproachtoresearchtheseflexiblestructur

5、esistoassumethattheyarcmadeofanclasticmaterialobeyingtheappropriatelawsofelasticity.Thatcomesthewell-knownKirchhoffmodelforrods[i,%whichdescribesthestationarystatesofelasticfilamentswithintheapproximationoflinearelasticitytheorybyasystemofsixcoupledordinarydifferentialeq

6、uations(ODE).Seemann[3]investigatedthedeformationofashorthelixincontactwitharigidcylinderbasingonthemathematicaltheoryofKirchhoffandLove.VanderHeijdenandco-workersconsideredtheequilibriumconfigurationsofalongrodconstrainedtolieinaplanesubjecttoendconditionsconstitutingaw

7、rench[4].CustodioandVazpresentedformulationsandasolutionfortheresponseofumbilicalcablesandflexiblepipessubjectedtocomplexexternalconditions(5j.AnothervaluableapplicationdomainistowardtheDNAdoublehelix・BecausecharacterizingtheelasticbehaviorofDNAmoleculeisofcmcialimportan

8、ceinunderstandingitsbiologicalfunctions,andtheanaloguewiththethinclasticrodhasattractedaremarkabletende