1Example25TitleThickcylindersubjectedtoaninternalpressureloadDescriptionComputethedisplacementsandstressesofacylindermodeledwithplanestrainelementsandaxisymmetricelementsduetoaninternalpressureload.StructuralgeometryVerificationExample2Structuralanalysismodelconsistedofaxisymmetricelements(EX25-1)Structuralanalysismodelconsistedofplanestrainelements(EX25-2)Example253MODELAnalysisType2-Dstaticanalysis(X-Zplane)UnitSystemInput:m,NOutput:mm,NDimensionOuterradiusa=0.2mInnerradiusb=0.1mElementAxisymmetricelementandplanestrainelementMaterialModulusofelasticityE=2.1×1011PaCharacteristicsofelementPossibletomodelonlyinX-Zplane,andcannotbeusedinconjunctionwithotherelements.Axisymmetricelements;Analysisperunitradian(1Radian)ofthecylinderPlaneStrainelements;AnalysisperunitthicknessBoundaryConditionAxisymmetricelements;Nodes1~22:ConstrainDz.PlainStrainelements;Nodes1~11:ConstrainDz.Nodes199~209:ConstrainDx.LoadCaseAxisymmetricelements;Pressureload,1.0×108Paisappliedtotheelement.PlaneStrainelements;Pressureload,1.0×108Paisappliedtotheinneredgeoftheinnermostelements.VerificationExample4ResultsDisplacements(Axisymmetricelements):EX25-1Stresses(Axisymmetricelements):EX25-1Example255Displacements(Planestrainelements):EX25-2Stresses(Planestrainelements):EX25-2VerificationExample6ComparisonofResultsUnit:mm,N/mm2DivisionTheoreticalNISAIIMIDAS/GenAxisymmetricelement0.0793650.0792990.079299InnerradialdisplacementPlainstrainelement0.0793650.0792590.079259Axisymmetricelement0.0634920.0634590.063459OuterradialdisplacementPlainstrainelement0.0634920.0634390.063459Axisymmetricelement154.271154.423154.423Circumferentialstress(r=0.105)Plainstrainelement154.271154.346154.423Axisymmetricelement68.39768.38568.385Circumferentialstress(r=0.195)Plainstrainelement68.39768.36368.386※Theoreticalequations:Displacement;Innerradialdisplacement)(2222υδ+−+=babaEpbOuterradialdisplacement)2(222baabEp−=δStress:Circumferentialstress)()(222222barrapb−+=σRadialstress)()(222222barrapb−−−=σWhere,p:Innerpressurea:Outerradiusb:Innerradiusr:DistancefromthecenterReferencesWarrenC.Young“Roark'sFormulasforStress&Strain.6Edition”McGraw-Hill"NISAII,VerificationManualProblem2.5”,Version90.0
