ABAQUS 单元类型

Advanced Finite Element Analysis–And ApplicationsDaming Zhang, Ph.D.Associate Professor of Transportation SystemsDepartment of Industrial TechnologyCollege of Agricultural Sciences and TechnologyCalifornia State University, FresnoMay 27, 2009Dr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications1ABAQUS Elements Overview•A wide range of elements available for solving different problems•Five characteristics of an element:–Family–Degree of freedom–Number of nodes–Formulation–Integration•Unique name: T2D2, S4R, C3D8Iused on the *ELEMENT option, TYPE parameterDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications3Degree of Freedom•Degree of Freedom (DOF) are the fundamental variables1Translation in direction 12Translation in direction 23Translation in direction 34Rotation about the 1-axis5Rotation about the 2-axis6Rotation about the 3-axis7Warping in open-section beam elements8Acoustic pressure or pore pressure9Electric potential11Temperature 12+Temperature at other points through the thickness of beams and shells Dr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications5Lecture 4:ABAQUS Element LibraryDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications2Family•Used to distinguish the geometry•Indicated by first letter or letters: S4R, C3D8I, CINPE4Dr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications4Number of Nodes•Determines the interpolation orderfirst order, second order, …•Clearly identified in the name: C3D8, S8R•Beam family indicating order of interpolation: B31, B32Dr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications61

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Formulation•Refers to the mathematical theoryLagrangian:material descriptionEulerian:Spatial description•Shell family has 3 classes:General purposethin-onlythick-only•Alternative formulations (end of element name)Hybrid formulation: C3D8H, B31HIncompatible formulation: C3D8IDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications7Continuum Elements (1)•Used to model the widest variety of components•Element names begin with “C”•Next two indicate the dimensionality: 3D, PE, PS, AX•The last shows the degree of freedom•3D continuum elements:hexa, penta, tetra•2D continuum elements:plane strainplane stressaxisymmetric•shape: quadrilateralor triangularDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications9Shell Elements (1)•Used to model structure with one dimension small•Element name begins with: S, SAX, SAXA•The first number indicates the number of nodes•If the last character is “5”, the element doesn’t use the rotational DOF around normal of middle plane•Quadrilateral or triangular; Linear or quadratic elements•Three different formulationsDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications11Integration•Gaussian Quadrature to integrate quantities over the volume of each element•Full or Reduced integrationUse “R” at the end of element name to distinguish the reduced-integration elements: CAX4, CAX4R•Will significantly affect the accuracyDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications8Continuum Elements (2)•2D continuum elements must be defined in 1-2 planeNode order should be counterclockwiseElement normals must all pointed at same direction•Degree of freedom: translational DOFs•Element properties: *SOLID SECTION•Formulation & Integration: Incompatible, Hybrid, Reduced•Output variable: default in global coordinate system*ORIENTATION to define local coordinate systemDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications10Shell Elements (2)•Degree of freedom: default 6 DOF, but also 5 DOF: S4R5Axisymmetric shells have 3DOF:1Translation in the r-direction.2Translation in the z-direction.6Rotation in the r-z plane.•*SHELL GENERAL SECTION: you define the properties*SHELL SECTION: ABAQUS calculates section properties•Formulation & Integration: complicated, check before use•Output variable: defined in the local material directionsLie on the surface of each shell elementAxes rotate with the element’s deformation in large-displacement simulationsDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications122

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Beam Elements•Used to model structure with one dimension is quite large•Element name begins with: B (e.g. B31)•The first number indicates the dimensionality•The third character indicates the interpolation order•Degree of freedom: default 6 DOF, 2D beams have 3 DOFOpen-section beams (e.g. B31OS) have DOF 7 for warping•*BEAM GENERAL SECTION: you define the properties*BEAM SECTION: ABAQUS calculates section properties•Formulation & Integration: Hybrid for very slender beams;B21, B31, B22, B32: shear deformable, and finite axial strain; B23 and B33 are not; Open section: B31OS, B32OS•Output variable: axial stress (s11), shear stress (s12)Dr. Daming Zhang -Cal State Univ Fresno13Advanced Finite Element Analysis -And ApplicationsRigid Elements•Element name begins with: R (e.g. R3D4, R3D3)•The next two characters indicates the dimensionality•The final character indicates the number of nodes•The nodes have no independent degrees of freedom•The nodes defining rigid elements can have loads applied to them or can be connected to other elementsbut they cannot have any boundary conditions•*RIGID BODY defines the rigid body reference node•Pay attention to the ‘sides’ of the rigid body elements•Formulation & Integration: none•Output: motion onlyDr. Daming Zhang -Cal State Univ Fresno15Advanced Finite Element Analysis -And ApplicationsFull Integration•The accuracy of Gaussian Quadrature is (2n-1) for n=4•The Element Stiffness Matrix is calculated by:[k]em=∫V[B]T[D][B]dV•Fully integrated linear elements use two integration points in each direction•Fully integrated quadratic elements use three integration points in each directionDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications17Truss Elements•Model rods that can carry only tensile or compressive loads•Element name begins with: T (e.g. T2D3, T3D2)•The next two characters indicates the dimensionality•The final character indicates the number of nodes•Degree of freedom: has only translational DOFs•*SOLID SECTION: specify the material propertiesThe cross-sectional area is given on the data line•Formulation & Integration: Hybrid for very rigid links•Output variable: Axial stress and strainDr. Daming Zhang -Cal State Univ Fresno14Advanced Finite Element Analysis -And ApplicationsContinuum Elements Overview•The biggest family with over 20 just for 3D models•3D: Hexa, Penta, Tetra; 2D: triangles and quadrilaterals•Linear and quadratic versions for each of these shapes•Full-and reduced-integration elements for hexa and quad•Standard or hybrid element formulation•For linear hexa or quad: incompatible mode formulation•For quadratic tria or tetra: \"modified\" formulation•The accuracy of your simulation will depend strongly on the type of element you use in your modelDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications16Full Integration Example•Use a cantilever beam to show the accuracy of analysisDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications183

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Shear Locking•Happened on fully integrated, first-order, solid elementscauses the elements to be too stiff in bending•Deformation of material subjected to bending moment M•Deformation of a fully integrated, linear elementDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications19Reduced Integration Results•Linear reduced-integration elements tend to be too flexibleBut fine mesh will produce acceptable results•Deformation of a linear element with reduced integration Dr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications21Hybrid Elements•Hybrid elements have the letter \"H\" in their names•Hybrid elements are used when the material behavior is incompressible (Poisson's ratio = 0.5)•The volume cannot change if thematerial is incompressible•The pressure stress cannot becomputed from the displacementsof the nodes•Hybrid elements include an additional degree of freedom that determines the pressure stress in the element directlyDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications23Reduced Integration•Only quadrilateral and hexahedral elements can use a reduced-integration scheme•use one fewer integration point in each direction than the fully integrated elementsDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications20Incompatible mode elements•An attempt to overcome the problems of shear locking in fully integrated first-order elements•Additional degrees of freedom enhance the element's deformation gradients as linear variation•can produce results in bending problems that are comparable to quadratic elements but at significantly lower computational cost•The mesh distortion should be minimized as much as possible to improve the accuracy of the resultsDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications22Selecting Continuum Elements•Use quadratic, reduced-integration elements (CAX8R, CPE8R, CPS8R, C3D20R, etc.) for general analysis work•Use quadratic, fully integrated elements (CAX8, CPE8, CPS8, C3D20, etc.) locally where stress concentrations may exist•Use a fine mesh of linear, reduced-integration elements (CAX4R, CPE4R, CPS4R, C3D8R, etc.) for large-strain analysis•For contact problems use a fine mesh of linear, reduced-integration elements or incompatible elements (CAX4I, CPE4I, CPS4I, C3D8I, etc.)•Minimize the mesh distortion as much as possible•In three dimensions use hexahedral (brick-shaped) elements wherever possible; Use C3D6 and C3D4 only when necessary•modified quadratic tetrahedral element (C3D10M) is robust for large-deformation and contact problems and exhibits minimal shear and volumetric lockingDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications244

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Thank YouDr. Daming Zhang -Cal State Univ FresnoAdvanced Finite Element Analysis -And Applications255