abaqus_lectures182092-element-selection

1、ABAQUS/Standard 基础教程AppeEle2003, ABAQUS软件公司北京办事处.ndix 1ment Selection CriteriaA1.2ABAQUS/Standard 基础教程内容提要 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 Contact 接触 Incompressible Material

2、s 不可压缩材料 Mesh Generation 网格生成 Solid Element Selection Summary2003, ABAQUS软件公司北京代表处.ABAQUS/Standard 基础教程Ele2003, ABAQUS软件公司北京办事处.ments in ABAQUSA1.4ABAQUS/Standard 基础教程Elements in ABAQUSABAQUS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 range of elements in the ABAQUS element library providesflexibility in mo

3、deling 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/Standard 基础教程Elements in ABAQUS 单元类型（Family）A family of finite elements is

4、 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.continuum (solid elements)shell elementsbeam elementsrigid elementsmembrane elementsinfinite elementsspecial-purpose elements

5、like springs, dashpots, and massestruss elements2003, ABAQUS软件公司北京代表处.A1.6ABAQUS/Standard 基础教程Elements in ABAQUSNumber of nodes节点数(interpolation) An elements number of nodes determines how the nodal degrees of freedom will be interpolated over the domain of the element. ABAQUS includes elements with

6、 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Elements in ABAQUS自由度数目Degrees of freedom The primary variables that exist at the nodes of an element are thedegrees of freedom in the finite el

7、ement 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Elements in ABAQUS 公式FormulationThe mathematical formulation used to describe the behavior of an element is another broad category that is

8、 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 有限应变壳元 Thick shells 后壳 Thin shells 薄壳2003, ABAQUS软件公司北京代表处.A1.9ABAQUS/Standard 基础教程Elements i

9、n ABAQUS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 numerical algorithm used to integrate these variables influences how an element behaves. ABAQU

10、S包括完全积分和减缩积分。ABAQUS includes elements with both “full” and “reduced” integration.2003, ABAQUS软件公司北京代表处.A1.10ABAQUS/Standard 基础教程Elements in ABAQUSFull integration:完全积分The minimum integration order required for exact integration of the strain energy for an undistorted element with linear material pro

11、perties.Reduced integration:简缩积分The integration rule that is one order less than the full integration rule.2003, ABAQUS软件公司北京代表处.Full integrationReduced integrationFirst- orderinterpolationSecond- order interpolationA1.11ABAQUS/Standard 基础教程Elements in ABAQUSElement naming conventions: examples 单元命名

12、约定B21: Beam, 2-D,1st-order interpolationS8RT: Shell, 8-node, Reduced integration, TemperatureCAX8R: Continuum, AXisymmetric, 8-node, Reduced integrationCPE8PH: Continuum, Plane strain, 8-node, Pore pressure, HybridDC3D4: Diffusion (heat transfer), Continuum, 3-D, 4-nodeDC1D2E: Diffusion (heat transf

13、er), Continuum, 1-D, 2-node, Electrical2003, ABAQUS软件公司北京代表处.A1.12ABAQUS/Standard 基础教程Elements in ABAQUS ABAQUS/Standard 和 ABAQUS/Explicit单元库的对比 Both programs have essentially the same element families: continuum, shell, beam, etc. ABAQUS/Standard includes elements for many analysis types in additio

14、n 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 each 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 elements Many of the same general element

15、 selection guidelines apply to both programs.2003, ABAQUS软件公司北京代表处.ABAQUS/Standard 基础教程StruBe2003, ABAQUS软件公司北京办事处.ctural Elements (Shells and ams) vs. Continuum ElementsA1.14ABAQUS/Standard 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 (s

16、hells 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 typical global structural dimension, such as:The distance between supports or point loadsThe distance between gross changes in

17、 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Structural Elements (Shells and Beams) vs. Continuum ElementsShell elements Shell elements approximate a three-dimensional continuum with a surface model. 高效率的模拟面内弯曲Model bending and in-plane de

18、formations 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3-D continuumsurface modelShell model of a hemispherical dome subjected to a projectile impact2003, ABAQ

19、US软件公司北京代表处.A1.16ABAQUS/Standard 基础教程Structural Elements (Shells and Beams) vs. Continuum ElementsBeam elements 用线简化三维实体。Beam elements approximate a three- dimensional continuum with a line model.3-D continuumline 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framed structure modeled using beam eleme

20、nts2003, ABAQUS软件公司北京代表处.ABAQUS/Standard 基础教程Mo Elem2003, ABAQUS软件公司北京办事处.deling Bending Using Continuu mentsA1.18ABAQUS/Standard 基础教程Modeling Bending Using Continuum ElementsPhysical characteristics of pure bending The assumed behavior of the material that finite elements attempt to model is:纯弯状态：P

21、lane cross-sections remain plane throughout the deformation. 保持平面The axial strain exx varies linearly through the thickness.The strain in the thickness direction eyy is zero if n=0.No membrane shear strain. Implies that lines parallel to the beam axis lie on a circular arc.exx2003, ABAQUS软件公司北京代表处.A

22、1.19ABAQUS/Standard 基础教程Modeling Bending Using Continuum ElementsModeling bending using second- order solid elements (CPE8, C3D20R, ) 二次单元模拟 Second-order full- and reduced- integration solid elements model bending accurately:Lines that are initially vertical do not change length (implies eyy=0).The

23、axial strain equals the change in length of the initially horizontal lines.The thickness strain is zero. The shear strain is zero.isoparametric linesBecause the element edges can assume a curved shape, the angle between the deformed isoparametric lines remains equal to 90o (implies exy=0).2003, ABAQ

24、US软件公司北京代表处.A1.20ABAQUS/Standard 基础教程Modeling Bending Using Continuum ElementsIntegration pointModeling bending using first- order fully integrated solid elements (CPS4, CPE4, C3D8) These elements detect shear strains at the integration points. Nonphysical; present solely because of the element form

25、ulation used. Overly stiff behavior results from energy going into shearing the element rather than bending it (called “shear locking”).Because the element edges must remain straight, the angle between the deformed isoparametric lines is not equalto 90o (implies e xy 0).Do not use these elements in

26、regions dominated by bending!2003, ABAQUS软件公司北京代表处.A1.21ABAQUS/Standard 基础教程Modeling Bending Using Continuum ElementsModeling bending using first-order reduced-integration elements (CPE4R, ) These elements eliminate shear locking. However, hourglassing is a concern when using these elements.Change i

27、n length is zero (implies no strain is detected at the integration point).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 (有应变形但是没有应变能的现象 called “hourglassing”).Bending behavior for a single first-

28、 order reduced-integration element.2003, ABAQUS软件公司北京代表处.A1.22ABAQUS/Standard 基础教程Modeling Bending Using Continuum ElementsHourglassing can propagate easily through a mesh of first-order reduced- integration elements, causing unreliable results.Hourglassing is not a problem if you use multiple eleme

29、ntsat 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.Four elements through the thicknessNo hourglassing2003, ABAQUS软件公司

30、北京代表处.A1.23ABAQUS/Standard 基础教程Modeling Bending Using Continuum ElementsDetecting and controlling hourglassing Hourglassing can usually be seen 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

31、limit the problems caused by hourglassing. Verify that the artificial energy used to control hourglassing is small ( 0.475). Rubber Metals at large plastic strains Conventional finite element meshes often exhibit overly stiff behavior due to volumetric locking, which is most severe when these materi

32、als are highly confined.overly stiff behavior of an elastic- plastic material with volumetric lockingcorrect behavior of an elastic- plastic materialExample of the effect of volumetric locking2003, ABAQUS软件公司北京代表处.A1.39ABAQUS/Standard 基础教程Incompressible Materials The cause of volumetric locking is t

33、hat each integration points volume must remain almost constant, overconstraining the kinematically admissible displacement field.For example, 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

34、 integration point must remain fixed.Fully integrated hexahedra use 8 integration points per element; thus, in this example we have as many 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

35、.” Volumetric locking is most pronounced in fully integrated elements. Reduced-integration elements have fewer volumetric constraints. Reduced 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Inc

36、ompressible Materials Fully incompressible materials modeled with solid elements must use the “hybrid” formulation (elements whose names end with the letter “H”).In this formulation the pressure stress is treated as an independently interpolated basic solution variable, coupled to the displacement s

37、olution through the constitutive theory.Hybrid elements introduce more variables into the problem to alleviate the volumetric locking problem. The extra variables also make them more expensive.The ABAQUS element library includes hybrid versions of all continuumelements (except plane stress elements,

38、 where they are not needed).2003, ABAQUS软件公司北京代表处.A1.41ABAQUS/Standard 基础教程Incompressible Materials Hybrid elements are only necessary for: 以不可压缩材料为主的网格，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-integra

39、tion elements that still show volumetric locking problems. Such problems are possible with elastic- plastic materials strained far into the plastic range. 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-type meshes with such material.2003, ABAQUS软件公司北京代表处.ABAQUS/Standard 基础教程Me2003, ABA