ABAQUSStandard基础教程实用教案

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1、内容提要内容提要(ni rn t yo) Elements in ABAQUS Structural Elements (Shells and Beams) vs. Continuum Elements Modeling Bending Using Continuum Elements 用实体单元模拟(mn)弯曲 Stress Concentrations 应力集中 Contact 接触 Incompressible Materials 不可压缩材料 Mesh Generation 网格生成 Solid Element Selection Summary第1页/共52页第一页，共53页。NoI

2、mageElements in ABAQUS第2页/共52页第二页，共53页。Elements in ABAQUS ABAQUS单元库中提供广泛(gungfn)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 characterized by considering the following:单元特性： Family

3、 单元类型 Number of nodes 节点数 Degrees of freedom 自由度数 Formulation 公式 Integration 积分第3页/共52页第三页，共53页。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(xin tn)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 variati

4、ons within a family. Elements in ABAQUSspecial-purpose elements like springs, dashpots, and massescontinuum (solid elements)shell elementsbeam elementsrigid elementsmembrane elementstruss elementsinfinite elements第4页/共52页第四页，共53页。Elements in ABAQUS Number of nodes节点( ji din)数(interpolation) An eleme

5、nts 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First-order interpolationSecond-order interpolation第5页/共52页第五页，共53页。Elements in ABAQUS 自由度数目De

6、grees 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(zhunjio) Temperature 温度 Electrical potential 电势第6页/共52页第六页，共53页。公式(gngsh)FormulationThe mathematic

7、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

8、元Thick shells 后壳Thin shells 薄壳Elements in ABAQUS第7页/共52页第七页，共53页。 积分Integration 单元的刚度和质量在单元内的采样点进行( jnxng)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

9、 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第8页/共52页第八页，共53页。 Full integration:完全(wnqun)积分 The minimum integration order required for exact integration of the strain energy for a

10、n 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 ABAQUSFirst-order interpolationFull integration Second-orderinterpolationReduced integration第9页/共52页第九页，共53页。Elements in ABAQUS Eleme

11、nt naming conventions: examples 单元命名(mng mng)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-node, Reduced integration, TemperatureCPE8PH: Continuum, Plane strain, 8-node, Pore

12、pressure, HybridDC1D2E: Diffusion (heat transfer), Continuum, 1-D, 2-node, Electrical第10页/共52页第十页，共53页。Elements in ABAQUS ABAQUS/Standard 和 ABAQUS/Explicit单元(dnyun)库的对比 Both programs have essentially the same element families: continuum, shell, beam, etc. ABAQUS/Standard includes elements for many a

13、nalysis types 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 each element family. ABAQUS/Explicit 包括的单元(dnyun)绝大多数都为一次单元(dnyun)。 例外: 二次单元(dnyun)和四面体单元(dnyun) a

14、nd 二次 beam elements Many of the same general element selection guidelines apply to both programs.第11页/共52页第十一页，共53页。NoImageStructural Elements (Shells and Beams) vs. Continuum Elements第12页/共52页第十二页，共53页。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

15、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(hl)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 loads The distance between gr

16、oss changes in cross section The wavelength of the highest vibration mode第13页/共52页第十三页，共53页。 Shell 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 deformations efficiently. If a detailed analysis of a region is needed, a lo

17、cal three-dimensional continuum model can be included using multi-point constraints or submodeling. 如果需要三维实体(sht)单元模拟细节可以使用子模型Shell model of a hemispherical dome subjected to a projectile impactStructural Elements (Shells and Beams) vs. Continuum Elements3-D continuumsurface model第14页/共52页第十四页，共53页。

18、Structural Elements (Shells and Beams) vs. Continuum Elements Beam elements 用线简化三维实体。Beam elements approximate a three-dimensional 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( jimin)形状 截面( jimin)形状可以通过工程常数定义line modelframed structure modeled using beam elements3-D continuum第15页/共52页第十五页，共

19、53页。NoImageModeling Bending Using Continuum Elements第16页/共52页第十六页，共53页。Modeling Bending Using Continuum ElementsPhysical characteristics of pure bendingThe assumed behavior of the material that finite elements attempt to model is:纯弯状态(zhungti)：Plane cross-sections remain plane throughout the deforma

20、tion. 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 strain.Implies that lines parallel to the beam axis lie on a circular arc.xx第17页/共52页第十七页，共53页。Modeling Bending Using Continuum Elements Modeling bending using

21、 second-order solid elements (CPE8, C3D20R, ) 二次单元(dnyun)模拟 Second-order 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 initia

22、lly vertical do not change length (implies yy=0).Because the element edges can assume a curved shape, the angle between the deformed isoparametric lines remains equal to 90o (implies xy=0).isoparametric lines第18页/共52页第十八页，共53页。Modeling Bending Using Continuum Elements Modeling bending using first-or

23、der fully integrated solid elements (CPS4, 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 l

24、ocking”).Because the element edges must 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!第19页/共52页第十九页，共53页。Modeling Bending Using Continuum Elements Modeling bending usin

25、g 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 through the thickness does not detect strain in bending. Deformation is a zero-energ

26、y mode (有应变形(bin xng)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.第20页/共52页第二十页，共53页。Modeling Bending Using Continuum Elements Hourglassing is not a problem if

27、 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 through a

28、 mesh of first-order reduced-integration elements, causing unreliable results.Four elements through the thicknessNo hourglassing第21页/共52页第二十一页，共53页。Modeling Bending Using Continuum Elements Detecting and controlling hourglassing Hourglassing can usually be seen in deformed shape plots. Example: Coar

29、se 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 large plastic strains Conventional finit

30、e 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 materialExample of the effect of volumetric

31、 locking第37页/共52页第三十七页，共53页。Incompressible MaterialsThe cause of volumetric locking is that 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 av

32、erage1 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( ji din)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 many as 8 constraints per element, but only 3 degrees of freedom ar

33、e 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.Reduced integration effectively eliminates volumetric locking in many

34、 problems with nearly incompressible material.第38页/共52页第三十八页，共53页。Incompressible 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 independent

35、ly 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 locking problem. The extra variables also make them more expensive. The ABAQUS element library includes

36、 hybrid versions of all continuum elements (except plane stress elements, where they are not needed).第39页/共52页第三十九页，共53页。 Hybrid elements are only necessary for: 以不可压缩材料(cilio)为主的网格，如橡胶材料(cilio)。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(cili

37、o)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 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

38、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.Incompressible Materials第40页/共52页第四十页，共53页。NoImageMesh Generation第41页/共52页第四十

39、一页，共53页。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/tet elements. Quad/hex elements should be used wherever possible. They give the best results for the minimum cost. When modeling complex geom

40、etries, however, the analyst often has little choice but to mesh with triangular and tetrahedral elements.Turbine blade with platform modeled with tetrahedral elements第42页/共52页第四十二页，共53页。Mesh Generation First-order tri/tet elements (CPE3, CPS3, CAX3, C3D4, C3D6) are poor elements; they have the foll

41、owing problems: Poor convergence rate. They typically require very fine meshes to produce good results. Volumetric locking 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 ac

42、curate results are needed.第43页/共52页第四十三页，共53页。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 contact. Under uniform pressure the con

43、tact forces are significantly different at the corner and midside nodes. For small-displacement problems without contact these elements provide reasonable results.第44页/共52页第四十四页，共53页。Mesh Generation Modified second-order tri/tet elements (C3D10M, etc.) alleviate the problems of other tri/tet element

44、s. Good convergence rateclose to convergence rate of second-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 p

45、ressure allows these elements to model contact accurately. Use them!第45页/共52页第四十五页，共53页。Mesh Generation Mesh refinement and convergence Use a sufficiently refined mesh to ensure that the results from your ABAQUS simulation are adequate. Coarse meshes tend to yield inaccurate results. The computer re

46、sources 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 predict regions of

47、high gradients before generating the mesh. Use hand calculations, experience, etc. Alternatively, you can use coarse mesh results to identify high gradient regions.第46页/共52页第四十六页，共53页。Mesh Generation Some recommendations: Minimize mesh distortion as much as possible. A minimum of four quadratic elem

48、ents 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. 第47页/共

49、52页第四十七页，共53页。Mesh Generation It 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 analysis model is based on the geometry of t

50、he structure. This will be discussed further in the next lecture. When two meshes yield nearly identical results, the results are said to have “converged.” This provides increased confidence in your results.第48页/共52页第四十八页，共53页。NoImageSolid Element Selection Summary第49页/共52页第四十九页，共53页。Solid Element S

51、election SummaryClass of problemBest element choiceAvoid usingGeneral contact between deformable bodiesFirst-order quad/hexSecond-order quad/hexContact with bendingIncompatible modeFirst-order fully integrated quad/hex or second-order quad/hexBending (no contact)Second-order quad/hexFirst-order full

52、y integrated quad/hexStress concentrationSecond-orderFirst-orderNearly incompressible (n n0.475 or large strain plasticity pl10%)First-order elements or second-order reduced-integration elementsSecond-order fully integrated第50页/共52页第五十页，共53页。Solid Element Selection SummaryClass of problemBest elemen

53、t choiceAvoid usingCompletely incompressible (rubber n n = 0.5)Hybrid quad/hex, first-order if large deformations are anticipatedBulk metal forming (high mesh distortion)First-order reduced-integration quad/hexSecond-order quad/hexComplicated model geometry (linear material, no contact)Second-order

54、quad/hex if possible (if not overly distorted) or second-order tet/tri (because of meshing difficulties)Complicated model geometry (nonlinear problem or contact)First-order quad/hex if possible (if not overly distorted) or modified second-order tet/tri (because of meshing difficulties)Natural frequency (linear dynamics)Second-orderNonlinear dynamic (impact)First-orderSecond-order第51页/共52页第五十一页，共53页。ABAQUS/Standard 基础教程谢谢大家(dji)观赏！第52页/共52页第五十二页，共53页。NoImage内容(nirng)总结内容提要。Second-orderinterpolation。ABAQUS/Explicit 包括的单元绝大多数都为一次单元。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(gud)约束。谢谢大家观赏第五十三页，共53页。