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1、2003, ABAQUS软件公司北京办事处.ABAQUS/Standard 基础教程基础教程Element Selection CriteriaAppendix 12003, ABAQUS软件公司北京代表处.A1.2ABAQUS/Standard 基础教程基础教程内容提要内容提要 Elements in ABAQUS Structural Elements (Shells and Beams) vs. Continuum Elements Modeling Bending Using Continuum Elements 用实体单元模拟弯曲 Stress Concentrations 应力集中
2、 Contact 接触 Incompressible Materials 不可压缩材料 Mesh Generation 网格生成 Solid Element Selection Summary2003, ABAQUS软件公司北京办事处.ABAQUS/Standard 基础教程基础教程Elements in ABAQUS2003, ABAQUS软件公司北京代表处.A1.4ABAQUS/Standard 基础教程基础教程Elements in ABAQUS ABAQUS单元库中提供广泛的单元类型，适应不同的结构和几何特征单元库中提供广泛的单元类型，适应不同的结构和几何特征The wide rang
3、e of elements in the ABAQUS element library provides flexibility in modeling different geometries and structures. Each element can be characterized by considering the following:单元特性： Family 单元类型 Number of nodes 节点数 Degrees of freedom 自由度数 Formulation 公式 Integration 积分2003, ABAQUS软件公司北京代表处.A1.5ABAQUS
4、/Standard 基础教程基础教程单元类型（单元类型（Family） A family of finite elements is the broadest category used to classify elements. 同类型单元有很多相同的基本特。Elements in the same family share many basic features.同种类单元又有很多变化：There are many variations within a family. Elements in ABAQUSspecial-purpose elements like springs, das
5、hpots, and massescontinuum (solid elements)shell elementsbeam elementsrigid elementsmembrane elementstruss elementsinfinite elements2003, ABAQUS软件公司北京代表处.A1.6ABAQUS/Standard 基础教程基础教程Elements in ABAQUS Number of nodes节点数节点数(interpolation)An elements number of nodes determines how the nodal degrees of
6、 freedom will be interpolated over the domain of the element.ABAQUS includes elements with both first- and second-order interpolation. 插值函数阶数可以为一次或者两次First-order interpolationSecond-order interpolation2003, ABAQUS软件公司北京代表处.A1.7ABAQUS/Standard 基础教程基础教程Elements in ABAQUS 自由度数目自由度数目Degrees of freedomTh
7、e primary variables that exist at the nodes of an element are the degrees of freedom in the finite element analysis. Examples of degrees of freedom are: Displacements 位移 Rotations 转角 Temperature 温度 Electrical potential 电势2003, ABAQUS软件公司北京代表处.A1.8ABAQUS/Standard 基础教程基础教程公式公式FormulationThe mathematic
8、al formulation used to describe the behavior of an element is another broad category that is used to classify elements. Examples of different element formulations: Plane strain 平面应变Plane stress 平面应力Hybrid elements 杂交单元Incompatible-mode elements 非协调元Small-strain shells 小应变壳元Finite-strain shells 有限应变壳
9、元Thick shells 后壳Thin shells 薄壳Elements in ABAQUS2003, ABAQUS软件公司北京代表处.A1.9ABAQUS/Standard 基础教程基础教程 积分积分Integration单元的刚度和质量在单元内的采样点进行数值计算，这些采样点叫做“积分点” The stiffness and mass of an element are calculated numerically at sampling points called “integration points” within the element. 数值积分的算法影响单元的行为The n
10、umerical algorithm used to integrate these variables influences how an element behaves.ABAQUS包括完全积分和减缩积分。ABAQUS includes elements with both “full” and “reduced” integration.Elements in ABAQUS2003, ABAQUS软件公司北京代表处.A1.10ABAQUS/Standard 基础教程基础教程 Full integration:完全积分完全积分 The minimum integration order r
11、equired for exact integration of the strain energy for an undistorted element with linear material properties. Reduced integration:简缩积分简缩积分 The integration rule that is one order less than the full integration rule.Elements in ABAQUSFirst-order interpolationFull integration Second-orderinterpolation
12、Reduced integration2003, ABAQUS软件公司北京代表处.A1.11ABAQUS/Standard 基础教程基础教程Elements in ABAQUS Element naming conventions: examples 单元命名约定B21: Beam, 2-D, 1st-order interpolationCAX8R: Continuum, AXisymmetric, 8-node, Reduced integrationDC3D4: Diffusion (heat transfer), Continuum, 3-D, 4-nodeS8RT: Shell, 8
13、-node, Reduced integration, TemperatureCPE8PH: Continuum, Plane strain, 8-node, Pore pressure, HybridDC1D2E: Diffusion (heat transfer), Continuum, 1-D, 2-node, Electrical2003, ABAQUS软件公司北京代表处.A1.12ABAQUS/Standard 基础教程基础教程Elements in ABAQUS ABAQUS/Standard 和和 ABAQUS/Explicit单元库的对比单元库的对比 Both programs
14、 have essentially the same element families: continuum, shell, beam, etc.ABAQUS/Standard includes elements for in addition to stress analysis: 热传导, 固化soils consolidation, 声场acoustics, etc. Acoustic elements are also available in ABAQUS/Explicit.ABAQUS/Standard includes many more variations within ea
15、ch element family.ABAQUS/Explicit 包括的单元绝大多数都为一次单元。 例外: 二次单元和四面体单元 and 二次 beam elementsMany of the same general element selection guidelines apply to both programs.2003, ABAQUS软件公司北京办事处.ABAQUS/Standard 基础教程基础教程Structural Elements (Shells and Beams) vs. Continuum Elements2003, ABAQUS软件公司北京代表处.A1.14ABA
16、QUS/Standard 基础教程基础教程Structural Elements (Shells and Beams) vs. Continuum Elements实体单元建立有限元模型通常规模较大，尤其对于三维实体单元如果选用适当的结构单元 (shells and beams) 会得到一个更经济的解决方案 模拟相同的问题，用结构体单元通常需要的单元数量比实体单元少很多要由结构体单元得到合理的结果需要满足一定要求： the shell thickness or the beam cross-section dimensions should be less than 1/10 of a typ
17、ical global structural dimension, such as: The distance between supports or point loads The distance between gross changes in cross section The wavelength of the highest vibration mode2003, ABAQUS软件公司北京代表处.A1.15ABAQUS/Standard 基础教程基础教程 Shell elementsShell elements approximate a three-dimensional con
18、tinuum with a surface model. 高效率的模拟面内弯曲Model bending and in-plane deformations efficiently.If a detailed analysis of a region is needed, a local three-dimensional continuum model can be included using multi-point constraints or submodeling.如果需要三维实体单元模拟细节可以使用子模型Shell model of a hemispherical dome sub
19、jected to a projectile impactStructural Elements (Shells and Beams) vs. Continuum Elements3-D continuumsurface model2003, ABAQUS软件公司北京代表处.A1.16ABAQUS/Standard 基础教程基础教程Structural Elements (Shells and Beams) vs. Continuum Elements Beam elements用线简化三维实体。Beam elements approximate a three-dimensional con
20、tinuum with a line model. 高效率模拟弯曲，扭转，轴向力。 提供很多不同的截面形状 截面形状可以通过工程常数定义line modelframed structure modeled using beam elements3-D continuum2003, ABAQUS软件公司北京办事处.ABAQUS/Standard 基础教程基础教程Modeling Bending Using Continuum Elements2003, ABAQUS软件公司北京代表处.A1.18ABAQUS/Standard 基础教程基础教程Modeling Bending Using Cont
21、inuum Elements Physical characteristics of pure bending The assumed behavior of the material that finite elements attempt to model is:纯弯状态： Plane cross-sections remain plane throughout the deformation. 保持平面 The axial strain xx varies linearly through the thickness. The strain in the thickness direct
22、ion yy is zero if =0. No membrane shear strain. Implies that lines parallel to the beam axis lie on a circular arc.xx2003, ABAQUS软件公司北京代表处.A1.19ABAQUS/Standard 基础教程基础教程Modeling Bending Using Continuum Elements Modeling bending using second-order solid elements (CPE8, C3D20R, ) 二次单元模拟二次单元模拟Second-ord
23、er full- and reduced-integration solid elements model bending accurately: The axial strain equals the change in length of the initially horizontal lines. The thickness strain is zero. The shear strain is zero.Lines that are initially vertical do not change length (implies yy=0).Because the element e
24、dges can assume a curved shape, the angle between the deformed isoparametric lines remains equal to 90o (implies xy=0).isoparametric lines2003, ABAQUS软件公司北京代表处.A1.20ABAQUS/Standard 基础教程基础教程Modeling Bending Using Continuum Elements Modeling bending using first-order fully integrated solid elements (C
25、PS4, CPE4, C3D8)These elements detect shear strains at the integration points. Nonphysical; present solely because of the element formulation used.Overly stiff behavior results from energy going into shearing the element rather than bending it (called “shear locking”).Because the element edges must
26、remain straight, the angle between the deformed isoparametric lines is not equal to 90o (implies ).0 xyIntegration pointDo not use these elements in regions dominated by bending!2003, ABAQUS软件公司北京代表处.A1.21ABAQUS/Standard 基础教程基础教程Modeling Bending Using Continuum Elements Modeling bending using first-
27、order reduced-integration elements (CPE4R, )These elements eliminate shear locking. However, hourglassing is a concern when using these elements. Only one integration point at the centroid. A single element through the thickness does not detect strain in bending. Deformation is a zero-energy mode (有
28、应变形但是没有应变能的现象 called “hourglassing”).Change in length is zero (implies no strain is detected at the integration point).Bending behavior for a single first-order reduced-integration element.2003, ABAQUS软件公司北京代表处.A1.22ABAQUS/Standard 基础教程基础教程Modeling Bending Using Continuum Elements Hourglassing is no
29、t a problem if you use multiple elementsat least four through the thickness.Each element captures either compressive or tensile axial strains, but not both.The axial strains are measured correctly.The thickness and shear strains are zero.Cheap and effective elements.Hourglassing can propagate easily
30、 through a mesh of first-order reduced-integration elements, causing unreliable results.Four elements through the thicknessNo hourglassing2003, ABAQUS软件公司北京代表处.A1.23ABAQUS/Standard 基础教程基础教程Modeling Bending Using Continuum Elements Detecting and controlling hourglassingHourglassing can usually be see
31、n in deformed shape plots. Example: Coarse and medium meshes of a simply supported beam with a center point load.ABAQUS has built-in hourglass controls that limit the problems caused by hourglassing. Verify that the artificial energy used to control hourglassing is small ( 0.475). Rubber Metals at l
32、arge plastic strains Conventional finite element meshes often exhibit overly stiff behavior due to volumetric locking, which is most severe when these materials are highly confined.overly stiff behavior of an elastic-plastic material with volumetric lockingcorrect behavior of an elastic-plastic mate
33、rialExample of the effect of volumetric locking2003, ABAQUS软件公司北京代表处.A1.39ABAQUS/Standard 基础教程基础教程Incompressible Materials The cause of volumetric locking is that each integration points volume must remain almost constant, overconstraining the kinematically admissible displacement field. For example
34、, in a refined three-dimensional mesh of 8-node hexahedra, there ison average1 node with 3 degrees of freedom per element. 每个单元平均只有1个有三个自由度的节点 The volume at each integration point must remain fixed. Fully integrated hexahedra use 8 integration points per element; thus, in this example we have as man
35、y as 8 constraints per element, but only 3 degrees of freedom are available to satisfy these constraints. 每个单元有8个约束，以至于产生体积锁死。 The mesh is overconstrainedit “locks.” Volumetric locking is most pronounced in fully integrated elements. Reduced-integration elements have fewer volumetric constraints. Re
36、duced integration effectively eliminates volumetric locking in many problems with nearly incompressible material.2003, ABAQUS软件公司北京代表处.A1.40ABAQUS/Standard 基础教程基础教程Incompressible MaterialsFully incompressible materials modeled with solid elements must use the “hybrid” formulation (elements whose nam
37、es end with the letter “H”). In this formulation the pressure stress is treated as an independently interpolated basic solution variable, coupled to the displacement solution through the constitutive theory. Hybrid elements introduce more variables into the problem to alleviate the volumetric lockin
38、g problem. The extra variables also make them more expensive. The ABAQUS element library includes hybrid versions of all continuum elements (except plane stress elements, where they are not needed).2003, ABAQUS软件公司北京代表处.A1.41ABAQUS/Standard 基础教程基础教程Hybrid elements are only necessary for: 以不可压缩材料为主的网
39、格，如橡胶材料。All meshes with strictly incompressible materials, such as rubber. 精密的网格，使用减缩积分仍然有locking的网格，比如弹塑性材料完全进入塑性阶段Refined meshes of reduced-integration elements that still show volumetric locking problems. Such problems are possible with elastic-plastic materials strained far into the plastic rang
40、e.即使使用了hybrid单元一次三角形或者四面体单元仍然有过度约束。因此建议这类单元使用的比例要小，可以作为六面体单元的“填充物”使用。Even with hybrid elements a mesh of first-order triangles and tetrahedra is overconstrained when modeling fully incompressible materials. Hence, these elements are recommended only for use as “fillers” in quadrilateral or brick-typ
41、e meshes with such material.Incompressible Materials2003, ABAQUS软件公司北京办事处.ABAQUS/Standard 基础教程基础教程Mesh Generation2003, ABAQUS软件公司北京代表处.A1.43ABAQUS/Standard 基础教程基础教程Mesh Generation Quad/Hex vs. Tri/Tet ElementsOf particular importance when generating a mesh is the decision regarding whether to use qu
42、ad/hex or tri/tet elements.Quad/hex elements should be used wherever possible. They give the best results for the minimum cost. When modeling complex geometries, however, the analyst often has little choice but to mesh with triangular and tetrahedral elements.Turbine blade with platform modeled with
43、 tetrahedral elements2003, ABAQUS软件公司北京代表处.A1.44ABAQUS/Standard 基础教程基础教程Mesh GenerationFirst-order tri/tet elements (CPE3, CPS3, CAX3, C3D4, C3D6) are poor elements; they have the following problems: Poor convergence rate. They typically require very fine meshes to produce good results. Volumetric l
44、ocking with incompressible or nearly incompressible materials, even using the “hybrid” formulation.These elements should be used only as fillers in regions far from any areas where accurate results are needed.2003, ABAQUS软件公司北京代表处.A1.45ABAQUS/Standard 基础教程基础教程Equivalent nodal forces created by unifo
45、rm pressure on the face of a regular second-order tetrahedral elementMesh Generation“Regular” second-order tri/tet elements (CPE6, CPS6, CAX6, C3D10) cannot be used to model contact. Under uniform pressure the contact forces are significantly different at the corner and midside nodes.For small-displ
46、acement problems without contact these elements provide reasonable results.2003, ABAQUS软件公司北京代表处.A1.46ABAQUS/Standard 基础教程基础教程Mesh GenerationModified second-order tri/tet elements (C3D10M, etc.) alleviate the problems of other tri/tet elements. Good convergence rateclose to convergence rate of secon
47、d-order quad/hex elements. Minimal shear or volumetric locking. Can be used to model incompressible or nearly incompressible materials in the hybrid formulation (C3D10MH). These elements are robust during finite deformation. Uniform contact pressure allows these elements to model contact accurately.
48、 Use them!2003, ABAQUS软件公司北京代表处.A1.47ABAQUS/Standard 基础教程基础教程Mesh Generation Mesh refinement and convergenceUse a sufficiently refined mesh to ensure that the results from your ABAQUS simulation are adequate. Coarse meshes tend to yield inaccurate results. The computer resources required to run your
49、 job increase with the level of mesh refinement.It is rarely necessary to use a uniformly refined mesh throughout the structure being analyzed. Use a fine mesh only in areas of high gradients and a coarser mesh in areas of low gradients.You can often predict regions of high gradients before generati
50、ng the mesh. Use hand calculations, experience, etc. Alternatively, you can use coarse mesh results to identify high gradient regions.2003, ABAQUS软件公司北京代表处.A1.48ABAQUS/Standard 基础教程基础教程Mesh GenerationSome recommendations: Minimize mesh distortion as much as possible. A minimum of four quadratic elem