Models and Finite Elements for Thin-Walled Structures

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1、Chapter3ModelsandFiniteElementsforThin-walledStructuresM.Bischoff1,W.A.Wall2,K.-U.Bletzinger1andE.Ramm31Lehrstuhlf¨urStatik,TUM¨unchen,M¨unchen,Germany2Lehrstuhlf¨urNumerischeMechanik,TUM¨unchen,Garching,Germany3Institutf¨urBaustatik,Universit¨atStuttgart,Stutt

2、gart,Germanyeffectofcurvatureisutilizedinshellstructuresallowingto1Introduction59carrytransverseloadinginanoptimalway,adesignprin-2MathematicalandMechanicalFoundations63ciplealreadyknowntotheancientmasterbuilders.Theirconsiderableheuristicknowledgeallowedthemto

3、create3PlatesandShells68remarkablebuildings,liketheRomanPantheon(115126)4DimensionalReductionandStructuralModels70andtheHaghiaSophia(532537)inConstantinople,still5FiniteElementFormulation107existingtoday.ItwasnotbeforetheRenaissancethat6ConcludingRemarks128scie

4、ntistsbegantomathematicallyidealizethestructuralAcknowledgments128response,aprocessthatwedenotenowadaysasmodelingReferences128andsimulation.FurtherReading133Already,LeonardodaVinci(14521519)stated(CodexMadridI)aprinciplethatlateronemergedtoaAppendix134beammodel

5、.Thesubsequentprocess,associatedwithnameslikeGalileo(15641642),Mariotte(16201684),Leibniz(16461716),JakobIBernoulli(16541705),1INTRODUCTIONEuler(17071783),Coulomb(17361806),andNavier(17851836),ledtowhatwecalltodayEulerBernoulli1.1Historicalremarksbeamtheory(Tim

6、oshenko,1953;Szabo,1979).ThisdevelopmentwasdrivenbytheingeniousideastocondenseThin-walledstructureslikeplatesandshellsarethemostthecomplexthree-dimensionalsituationtotheessentialcommonconstructionelementsinnatureandtechnology.ingredientsofstructuralresponselike

7、stretching,bending,Thisisindependentofthespecificscale;theymightbesmalllikecellmembranesandtinymachinepartsorverytorsion,andsoon,andtocastthisintoamanageablelargelikefuselagesandcoolingtowers.Thispreferencetomathematicalformat.Theinclusionoftransverseshearapplyw

8、allsasthinaspossibleisanaturaloptimizationdeformationisattributed(1859)toBresse(18221883)strategytoreducedeadloadandtominimizeconstructionandextended(1921)todynamicsbyTimosh