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1、BasicsofMechanicsofMicropolarShellsVictorEremeyevandHolmAltenbachAbstractThechapterisdevotedtotheintroductiontothenonlineartheoryofmicropolarshellscalledalsosix-parametricshelltheory.Withinthetheoryashellisdescribedasadeformabledirectedmaterialsurfaceeachpointofwhichhassixdegr
2、eesoffreedom(DOF),i.e.threetranslationalandthreerotationalDOF.Inotherwordstheshellkinematicscoincideswiththekinematicsofatwo-dimensional(2D)micropolarorCosseratbody.Herewepresentthebasicequationsofthemicropolarshelltheoryincludingvariationalstatements,compatibilityconditions,e
3、tc.1IntroductionTheoryofplatesandshellsisoneoftheoldestbranchesofmechanics.FirstscientiÞcpublicationsintheÞeldbelongtoEulerwhopublishedpaperin1767,tothepaperbyJ.Bernoulliin1789,seethebibliographycollectedbyJemielita(2001)andtheÞrstchapterinthisbook.Nowadaystherearetheoriesofpl
4、atesandshellsrelatedwiththenamesbyKirchhoff,Love,Cosserat,Timoshenko,Reissner,Mindlin,Koiter,Naghdi,Donnell,Vekuaandmanyothers.So,manymodelsmaybeconsideredasreÞnementorextensionoftheclassicalKirchhoff-Lovetheoryofshells.Nowadays,variousreÞned2Dtheoriesareimplementedincommercia
5、lFEMsoftwareandwidelyusedincontemporaryengineeringpractice.Nevertheless,thereÞnementofplateandshellV.Eremeyev(B)DepartmentofMechanicalEngineeringandAvionics,RzeszwUniversityofTechnology,Podkarpacie,Rzeszw,Polande-mail:veremeyev@prz.edu.plV.EremeyevSouthScientiÞcCenterofRussian
6、AcademyofScience,RostovonDon,RussiaV.EremeyevDepartmentofMathematics,MechanicsandComputerScience,SouthFederalUniversity,RostovonDon,RussiaH.AltenbachChairofEngineeringMechanics,FacultyofMechanicalEngineering,Otto-von-Guericke-UniversityMagdeburg,Magdeburg,Germanye-mail:holm.al
7、tenbach@ovgu.de©CISMInternationalCentreforMechanicalSciences201763H.AltenbachandV.Eremeyev(eds.),Shell-likeStructures,CISMInternationalCentreforMechanicalSciences572,DOI10.1007/978-3-319-42277-0_264V.EremeyevandH.Altenbachtheoriesarestillrequiredinvariousdirections,seebriefdis
8、cussionbyEremeyevandPietraszkiewicz(2014).Inparticular,thefol
