1、ABAQUS/Standard 基础教程,Element Selection Criteria,Appendix 1,ABAQUS/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 Materials 不可压缩材料 Mesh Generat
2、ion 网格生成 Solid Element Selection Summary,ABAQUS/Standard 基础教程,Elements in ABAQUS,ABAQUS/Standard 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 The wide range of elements in the ABAQUS element library provides flexibility in modeling different geometries and structures. Each element can be
3、 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,ABAQUS/Standard 基础教程,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
4、many basic features. 同种类单元又有很多变化：There are many variations within a family.,Elements in ABAQUS,special-purpose elements like springs, dashpots, and masses,continuum (solid elements),shell elements,beam elements,rigid elements,membrane elements,truss elements,infinite elements,ABAQUS/Standard 基础教程,El
5、ements in ABAQUS,Number 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 both first- and second-order interpolation. 插值函数阶数可以为一次或者两次,ABAQUS/Standard 基础教程,Elements in
6、ABAQUS,自由度数目 Degrees of freedom The 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,ABAQUS/Standard 基础教程,公式 Formulation The math
7、ematical 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 s
8、hells 有限应变壳元 Thick shells 后壳 Thin shells 薄壳,Elements in ABAQUS,ABAQUS/Standard 基础教程,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 algori
9、thm 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 ABAQUS,ABAQUS/Standard 基础教程,Full integration: 完全积分 The minimum integration order required for exact integration of the strain e
10、nergy for an undistorted element with linear material properties. Reduced integration: 简缩积分 The integration rule that is one order less than the full integration rule.,Elements in ABAQUS,ABAQUS/Standard 基础教程,Elements in ABAQUS,Element naming conventions: examples 单元命名约定,B21: Beam, 2-D, 1st-order int
11、erpolation,CAX8R: Continuum, AXisymmetric, 8-node, Reduced integration,DC3D4: Diffusion (heat transfer), Continuum, 3-D, 4-node,S8RT: Shell, 8-node, Reduced integration, Temperature,CPE8PH: Continuum, Plane strain, 8-node, Pore pressure, Hybrid,DC1D2E: Diffusion (heat transfer), Continuum, 1-D, 2-no
12、de, Electrical,ABAQUS/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 addition to stress analysis: 热传导, 固化soils consolidation,
13、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 selection guidelines apply to both programs.,ABAQ
14、US/Standard 基础教程,Structural Elements (Shells and Beams) vs. Continuum Elements,ABAQUS/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 (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 shel
15、l 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 loads The distance between gross changes in cross section The wavelength of the highest vibration mode,ABAQUS/Standard 基础教程,Shell elemen
16、ts 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 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
17、三维实体单元模拟细节可以使用子模型,Shell model of a hemispherical dome subjected to a projectile impact,Structural Elements (Shells and Beams) vs. Continuum Elements,ABAQUS/Standard 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
18、 continuum 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 model,framed structure modeled using beam elements,3-D continuum,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,Physical characteristics of pur
19、e 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 direction yy is zero if =0. No membrane shear strai
20、n. Implies that lines parallel to the beam axis lie on a circular arc.,xx,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,Modeling 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: The
21、axial strain equals the change in length of the initially horizontal lines. The thickness strain is zero. The shear strain is zero.,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,Modeling bending using first-order fully integrated solid elements (CPS4, CPE4, C3D8) These elements dete
22、ct 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”).,Do not use these elements in regions dominated by bending!,ABAQU
23、S/Standard 基础教程,Modeling Bending Using Continuum Elements,Modeling bending using first-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 throu
24、gh 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”).,Change in length is zero (implies no strain is detected at the integration point).,Bending behavior for a single first-order reduced-integration element.,ABAQUS/Standard 基础教程
25、,Modeling Bending Using Continuum Elements,Hourglassing is not 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 zer
26、o. Cheap and effective elements.,Hourglassing can propagate easily through a mesh of first-order reduced-integration elements, causing unreliable results.,Four elements through the thickness,No hourglassing,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,Detecting and controlling hour
27、glassing 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 limit the problems caused by hourglassing. Verify that the artificial energy used to control hourglass
28、ing is small (1%) relative to the internal energy.,Same load and displacement magnification (1000),ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,Use the XY plotting capability in ABAQUS/Viewer to compare the energies graphically.,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum
29、 Elements,Modeling bending using incompatible mode elements (CPS4I, ) Perhaps the most cost-effective solid continuum elements for bending-dominated problems. Compromise in cost between the first- and second-order reduced-integration elements, with many of the advantages of both. Model shear behavio
30、r correctlyno shear strains in pure bending. Model bending with only one element through the thickness. No hourglass modes and work well in plasticity and contact problems. The advantages over reduced-integration first-order elements are reduced if the elements are severely distorted; however, all e
31、lements perform less accurately if severely distorted.,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,Example: Cantilever beam with distorted elements,Parallel distortion,Trapezoidal distortion,ABAQUS/Standard 基础教程,Modeling Bending Using Continuum Elements,Summary,ABAQUS/Standard 基础教
32、程,Stress Concentrations,ABAQUS/Standard 基础教程,Stress Concentrations,二次单元处理应力集中问题，明显优于一次单元 Second-order elements clearly outperform first-order elements in problems with stress concentrations and are ideally suited for the analysis of (stationary) cracks. W无论是完全积分还是减缩积分都可以很好的反映应力集中 Both fully integrat
33、ed and reduced-integration elements work well. 减缩积分效率更高，而且计算结果往往优于完全积分。 Reduced-integration elements tend to be somewhat more efficientresults are often as good or better than full integration at lower computational cost.,ABAQUS/Standard 基础教程,Physical model,Model with first-order elementselement fac
34、es are straight line segments,Model with second-order elements element faces are quadratic curves,Stress Concentrations,二次单元可以以更少的单元更好的反应结构的几何特征 Second-order elements capture geometric features, such as curved edges, with fewer elements than first-order elements.,ABAQUS/Standard 基础教程,Stress Concentr
35、ations,Both first- and second-order quads and bricks become less accurate when their initial shape is distorted. First-order elements are known to be less sensitive to distortion than second-order elements and, thus, are a better choice in problems where significant mesh distortion is expected. Seco
36、nd-order triangles and tetrahedra are less sensitive to initial element shape than most other elements; however, well-shaped elements provide better results.,ABAQUS/Standard 基础教程,elliptical shape,Stress Concentrations,A typical stress concentration problem, a NAFEMS benchmark problem, is shown at ri
37、ght. The analysis results obtained with different element types follow.,P,ABAQUS/Standard 基础教程,Stress Concentrations,First-order elements (including incompatible mode elements) are relatively poor in the study of stress concentration problems. Second-order elements such as CPS6, CPS8, and CPS8R give
38、 much better results.,ABAQUS/Standard 基础教程,Stress Concentrations,Well-shaped, second-order, reduced-integration quadrilaterals and hexahedra can provide high accuracy in stress concentration regions. Distorted elements reduce the accuracy in these regions.,ABAQUS/Standard 基础教程,Contact,ABAQUS/Standar
39、d 基础教程,Contact,Almost all element types are formulated to work well in contact problems, with the following exceptions: Second-order quad/hex elements “Regular” second-order tri/tet elements (as opposed to “modified” tri/tet elements whose names end with the letter “M”) The directions of the consist
40、ent nodal forces resulting from a pressure load are not uniform.,ABAQUS/Standard 基础教程,Incompressible Materials,ABAQUS/Standard 基础教程,Incompressible Materials,Many nonlinear problems involve incompressible materials ( = 0.5) and nearly incompressible materials ( 0.475). Rubber Metals at large plastic
41、strains Conventional finite element meshes often exhibit overly stiff behavior due to volumetric locking, which is most severe when these materials are highly confined.,ABAQUS/Standard 基础教程,Incompressible Materials,The cause of volumetric locking is that each integration points volume must remain al
42、most 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 integration point must remain fixed. Fully int
43、egrated 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.” Volumetric locking is most pronounced in f
44、ully integrated elements. Reduced-integration elements have fewer volumetric constraints. Reduced integration effectively eliminates volumetric locking in many problems with nearly incompressible material.,ABAQUS/Standard 基础教程,Incompressible Materials,Fully incompressible materials modeled with soli
45、d 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 solution through the constitutive theory. Hybrid elements introduce mo
46、re 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 continuum elements (except plane stress elements, where they are not needed).,ABAQUS/Standard 基础教程,Hybrid elements
47、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-integration elements that still show volumetric locking problems. Such problems are possible with elastic-plastic material
48、s 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 “f
49、illers” in quadrilateral or brick-type meshes with such material.,Incompressible Materials,ABAQUS/Standard 基础教程,Mesh Generation,ABAQUS/Standard 基础教程,Mesh Generation,Quad/Hex vs. Tri/Tet Elements Of particular importance when generating a mesh is the decision regarding whether to use quad/hex or tri/
50、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 tetrahedral elements,
