abaqus精品學(xué)習(xí)大合集電子版二element-selection

1、ABAQUS/Standard 基礎(chǔ)教程Element Selection CriteriaAppendix 1ABAQUS/Standard 基礎(chǔ)教程內(nèi)容提要Elements in ABAQUS Structural Elements (Shells and Beams) vs. Continuum Elements Modeling Bending Using Continuum Elements 用實(shí)體單元模擬彎曲Stress Concentrations 應(yīng)力集中Contact 接觸 pressible Materials 不可壓縮材料Mesh Generation 網(wǎng)格生成Solid

2、 Element Selection SummaryABAQUS/Standard 基礎(chǔ)教程Elements in ABAQUSABAQUS/Standard 基礎(chǔ)教程Elements in ABAQUSABAQUS單元庫(kù)中提供廣泛的單元類型，適應(yīng)不同的結(jié)構(gòu)和幾何特征The wide range of elements in the ABAQUS element library provides flexibility in modeling different geometries and structures. Each element can be characterized by co

3、nsidering the following:單元特性：Family 單元類型Number of nodes 節(jié)點(diǎn)數(shù)Degrees of freedom 自由度數(shù)Formulation 公式Integration 積分ABAQUS/Standard 基礎(chǔ)教程單元類型（Family） A family of finite elements is the broadest category used to classify elements. 同類型單元有很多相同的基本特。Elements in the same family share many basic features.同種類單元又有很

4、多變化：There are many variations within a family. Elements in ABAQUSspecial-purpose elements like springs, dashpots, and massescontinuum (solid elements)shell elementsbeam elementsrigid elementsmembrane elementstruss elementsinfinite elementsABAQUS/Standard 基礎(chǔ)教程Elements in ABAQUSNumber of nodes節(jié)點(diǎn)數(shù)(inte

5、rpolation)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. 插值函數(shù)階數(shù)可以為一次或者兩次First-order interpolationSecond-order interpolationABAQUS/Standard 基礎(chǔ)教程Elemen

6、ts in ABAQUS自由度數(shù)目Degrees of freedomThe 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 轉(zhuǎn)角Temperature 溫度Electrical potential 電勢(shì)ABAQUS/Standard 基礎(chǔ)教程公式FormulationThe mathemati

7、cal 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 平面應(yīng)變Plane stress 平面應(yīng)力Hybrid elements 雜交單元 patible-mode elements 非協(xié)調(diào)元Small-strain shells 小應(yīng)變殼元Finite-strain shells 有限應(yīng)變殼元Th

8、ick shells 后殼Thin shells 薄殼Elements in ABAQUSABAQUS/Standard 基礎(chǔ)教程積分Integration單元的剛度和質(zhì)量在單元內(nèi)的采樣點(diǎn)進(jìn)行數(shù)值計(jì)算，這些采樣點(diǎn)叫做“積分點(diǎn)” The stiffness and mass of an element are calculated numerically at sampling points called “integration points” within the element. 數(shù)值積分的算法影響單元的行為The numerical algorithm used to integrate

9、 these variables influences how an element behaves.ABAQUS包括完全積分和減縮積分。ABAQUS includes elements with both “full” and “reduced” integration.Elements in ABAQUSABAQUS/Standard 基礎(chǔ)教程Full integration:完全積分The minimum integration order required for exact integration of the strain energy for an undistorted ele

10、ment with linear material properties.Reduced integration:簡(jiǎn)縮積分The integration rule that is one order less than the full integration rule.Elements in ABAQUSFirst-order interpolationFull integration Second-orderinterpolationReduced integrationABAQUS/Standard 基礎(chǔ)教程Elements in ABAQUSElement naming convent

11、ions: examples 單元命名約定B21: Beam, 2-D, 1st-order interpolationCAX8R: Continuum, AXisymmetric, 8-node, Reduced integrationDC3D4: Diffusion (heat transfer), Continuum, 3-D, 4-nodeS8RT: Shell, 8-node, Reduced integration, TemperatureCPE8PH: Continuum, Plane strain, 8-node, Pore pressure, HybridDC1D2E: Di

12、ffusion (heat transfer), Continuum, 1-D, 2-node, ElectricalABAQUS/Standard 基礎(chǔ)教程Elements in ABAQUSABAQUS/Standard 和 ABAQUS/Explicit單元庫(kù)的對(duì)比 Both programs have essentially the same element families: continuum, shell, beam, etc.ABAQUS/Standard includes elements for many analysis types in addition to stre

13、ss analysis: 熱傳導(dǎo), 固化soils consolidation, 聲場(chǎng)acoustics, etc.Acoustic elements are also available in ABAQUS/Explicit.ABAQUS/Standard includes many more variations within each element family.ABAQUS/Explicit 包括的單元絕大多數(shù)都為一次單元。例外: 二次單元和四面體單元 and 二次 beam elementsMany of the same general element selection gui

14、delines apply to both programs.ABAQUS/Standard 基礎(chǔ)教程Structural Elements (Shells and Beams) vs. Continuum ElementsABAQUS/Standard 基礎(chǔ)教程Structural Elements (Shells and Beams) vs. Continuum Elements實(shí)體單元建立有限元模型通常規(guī)模較大，尤其對(duì)于三維實(shí)體單元如果選用適當(dāng)?shù)慕Y(jié)構(gòu)單元 (shells and beams) 會(huì)得到一個(gè)更經(jīng)濟(jì)的解決方案模擬相同的問題，用結(jié)構(gòu)體單元通常需要的單元數(shù)量比實(shí)體單元少很多要由結(jié)構(gòu)

15、體單元得到合理的結(jié)果需要滿足一定要求： 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 cross sectionThe wavelength of the highest vibration modeABAQUS/St

16、andard 基礎(chǔ)教程Shell elementsShell elements approximate a three-dimensional continuum with a surface model.高效率的模擬面內(nèi)彎曲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 o

17、r submodeling.如果需要三維實(shí)體單元模擬細(xì)節(jié)可以使用子模型Shell model of a hemispherical dome subjected to a projectile impactStructural Elements (Shells and Beams) vs. Continuum Elements3-D continuumsurface modelABAQUS/Standard 基礎(chǔ)教程Structural Elements (Shells and Beams) vs. Continuum ElementsBeam elements用線簡(jiǎn)化三維實(shí)體。Beam el

18、ements approximate a three-dimensional continuum with a line model.高效率模擬彎曲，扭轉(zhuǎn)，軸向力。提供很多不同的截面形狀截面形狀可以通過工程常數(shù)定義line modelframed structure modeled using beam elements3-D continuumABAQUS/Standard 基礎(chǔ)教程Modeling Bending Using Continuum ElementsABAQUS/Standard 基礎(chǔ)教程Modeling Bending Using Continuum ElementsPhys

19、ical characteristics of pure bendingThe assumed behavior of the material that finite elements attempt to model is:純彎狀態(tài)：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

20、 membrane shear strain.Implies that lines parallel to the beam axis lie on a circular arc.xxABAQUS/Standard 基礎(chǔ)教程Modeling Bending Using Continuum ElementsModeling bending using second-order solid elements (CPE8, C3D20R, ) 二次單元模擬Second-order full- and reduced-integration solid elements model bending a

21、ccurately: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 edges can assume a curved shape, the angle between the deformed is

22、oparametric lines remains equal to 90o (implies xy=0).isoparametric linesABAQUS/Standard 基礎(chǔ)教程Modeling Bending Using Continuum ElementsModeling bending using first-order fully integrated solid elements (CPS4, CPE4, C3D8)These elements detect shear strains at the integration points. Nonphysical; prese

23、nt 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 remain straight, the angle between the deformed isoparametric lines is not equal to 90o (implies

24、).Integration pointDo not use these elements in regions dominated by bending!ABAQUS/Standard 基礎(chǔ)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 the

25、se 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 (有應(yīng)變形但是沒有應(yīng)變能的現(xiàn)象 called “hourglassing”).Change in length is zero (implies no strain is detected at the integration point).Bending behavior

26、 for a single first-order reduced-integration element.ABAQUS/Standard 基礎(chǔ)教程Modeling Bending Using Continuum ElementsHourglassing 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 s

27、trains are measured correctly.The thickness and shear strains are zero.Cheap and effective elements.Hourglassing can propagate easily through a mesh of first-order reduced-integration elements, causing unreliable results.Four elements through the thicknessNo hourglassingABAQUS/Standard 基礎(chǔ)教程Modeling

28、Bending Using Continuum ElementsDetecting and controlling hourglassingHourglassing 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.

29、Verify that the artificial energy used to control hourglassing is small ( 0.475).RubberMetals at large 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

30、 of an elastic-plastic material with volumetric lockingcorrect behavior of an elastic-plastic materialExample of the effect of volumetric lockingABAQUS/Standard 基礎(chǔ)教程 pressible MaterialsThe cause of volumetric locking is that each integration points volume must remain almost constant, overconstrainin

31、g 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. 每個(gè)單元平均只有1個(gè)有三個(gè)自由度的節(jié)點(diǎn)The volume at each integration point must remain fixed. Fully integrated hexahedra use 8 integrat

32、ion 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. 每個(gè)單元有8個(gè)約束，以至于產(chǎn)生體積鎖死。The mesh is overconstrainedit “l(fā)ocks.”Volumetric locking is most pronounced in fully integrated elements. Reduced-

33、integration elements have fewer volumetric constraints.Reduced integration effectively eliminates volumetric locking in many problems with nearly pressible material.ABAQUS/Standard 基礎(chǔ)教程 pressible MaterialsFully pressible materials modeled with solid elements must use the “hybrid” formulation (elemen

34、ts 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 more variables into the problem to alleviate the volumetr

35、ic 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 基礎(chǔ)教程Hybrid elements are only necessary for:以不可壓縮材料為主的網(wǎng)格，如橡膠材料。All meshes with

36、strictly pressible materials, such as rubber.精密的網(wǎng)格，使用減縮積分仍然有l(wèi)ocking的網(wǎng)格，比如彈塑性材料完全進(jìn)入塑性階段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 range.即使使用了hybrid單元一次三角形或者四面體單元仍然有

37、過度約束。因此建議這類單元使用的比例要小，可以作為六面體單元的“填充物”使用。Even with hybrid elements a mesh of first-order triangles and tetrahedra is overconstrained when modeling fully pressible materials. Hence, these elements are mended only for use as “fillers” in quadrilateral or brick-type meshes with such material. pressible M

38、aterialsABAQUS/Standard 基礎(chǔ)教程Mesh GenerationABAQUS/Standard 基礎(chǔ)教程Mesh GenerationQuad/Hex vs. Tri/Tet ElementsOf particular importance when generating a mesh is the decision regarding whether to use quad/hex or tri/tet elements.Quad/hex elements should be used wherever possible.They give the best resul

39、ts 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 elementsABAQUS/Standard 基礎(chǔ)教程Mesh GenerationFirst-order tri/tet elements (CPE3, CPS3, CAX3,

40、 C3D4, C3D6) are poor elements; they have the following problems:Poor convergence rate. They typically require very fine meshes to produce good results. Volumetric locking with pressible or nearly pressible materials, even using the “hybrid” formulation.These elements should be used only as fillers

41、in regions far from any areas where accurate results are needed.ABAQUS/Standard 基礎(chǔ)教程Equivalent nodal forces created by uniform 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 co

42、ntact. Under uniform pressure the contact forces are significantly different at the corner and midside nodes.For small-displacement problems without contact these elements provide reasonable results.ABAQUS/Standard 基礎(chǔ)教程Mesh GenerationModified second-order tri/tet elements (C3D10M, etc.) alleviate th

43、e problems of other tri/tet elements.Good convergence rateclose to convergence rate of second-order quad/hex elements.Minimal shear or volumetric locking. Can be used to model pressible or nearly pressible materials in the hybrid formulation (C3D10MH). These elements are robust during finite deforma

44、tion.Uniform contact pressure allows these elements to model contact accurately.Use them!ABAQUS/Standard 基礎(chǔ)教程Mesh GenerationMesh refinement and convergenceUse a sufficiently refined mesh to ensure that the results from your ABAQUS simulation are adequate.Coarse meshes tend to yield inaccurate result

45、s.The computer resources required to run your 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 predi

46、ct regions of high gradients before generating the mesh.Use hand calculations, experience, etc.Alternatively, you can use coarse mesh results to identify high gradient regions.ABAQUS/Standard 基礎(chǔ)教程Mesh GenerationSome mendations:Minimize mesh distortion as much as possible.A minimum of four quadratic

47、elements per 90o should be used around a circular hole.A minimum of four elements should be used through the thickness of a structure if first-order, reduced-integration solid elements are used to model bending. Other guidelines can be developed based on experience with a given class of problem. ABAQUS/Standard 基礎(chǔ)教程Mesh GenerationIt is good practice to perform a mesh convergence study.Simulate the problem using progressively finer meshes, and compare the results.The mesh density can be changed very easily using ABAQUS/CAE since the definition of the analy