验证例题25.pdf

1Example 25 Title Thick cylinder subjected to an internal pressure load Description Compute the displacements and stresses of a cylinder modeled with plane strain elements and axisymmetric elements due to an internal pressure load.Structural geometry Verification Example 2 Structural analysis model consisted of axisymmetric elements(EX25-1)Structural analysis model consisted of plane strain elements(EX25-2)Example 25 3MODEL Analysis Type 2-D static analysis(X-Z plane)Unit System Input :m,N Output :mm,N Dimension Outer radius a =0.2m Inner radius b =0.1m Element Axisymmetric element and plane strain element Material Modulus of elasticity E =2.1 1011 Pa Characteristics of element Possible to model only in X-Z plane,and cannot be used in conjunction with other elements.Axisymmetric elements;Analysis per unit radian(1 Radian)of the cylinder Plane Strain elements ;Analysis per unit thickness Boundary Condition Axisymmetric elements ;Nodes 1 22 :Constrain Dz.Plain Strain elements ;Nodes 1 11 :Constrain Dz.Nodes 199 209 :Constrain Dx.Load Case Axisymmetric elements;Pressure load,1.0 108 Pa is applied to the element.Plane Strain elements ;Pressure load,1.0 108 Pa is applied to the inner edge of the innermost elements.Verification Example 4Results Displacements(Axisymmetric elements):EX25-1 Stresses(Axisymmetric elements):EX25-1 Example 25 5 Displacements(Plane strain elements):EX25-2 Stresses(Plane strain elements):EX25-2 Verification Example 6Comparison of Results Unit:mm,N/mm2 Division TheoreticalNISA II MIDAS/GenAxisymmetric element 0.0793650.079299 0.079299Inner radial displacement Plain strain element 0.0793650.079259 0.079259Axisymmetric element 0.0634920.063459 0.063459Outer radial displacement Plain strain element 0.0634920.063439 0.063459Axisymmetric element 154.271154.423 154.423Circumferential stress(r=0.105)Plain strain element 154.271154.346 154.423Axisymmetric element 68.39768.385 68.385Circumferential stress(r=0.195)Plain strain element 68.39768.363 68.386 Theoretical equations:Displacement;Inner radial displacement )(2222+=babaEpb Outer radial displacement )2(222baabEp=Stress:Circumferential stress )()(222222barrapb+=Radial stress )()(222222barrapb=Where,p:Inner pressure a:Outer radius b:Inner radius r:Distance from the center References Warren C.Young “Roarks Formulas for Stress&Strain.6 Edition”McGraw-Hill NISA II,Verification Manual Problem 2.5”,Version 90.0