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Chapter 2: Planning Your ApproachGo to the Next ChapterGo to the Previous ChapterGo to the Table of Contents for This ManualGo to the Guides Master IndexChapter 1 * Chapter 2 * Chapter 3 * Chapter 4 * Chapter 5 * Chapter 6 * Chapter 7 * Chapter 8 * Chapter 9 *Chapter 10 * Chapter 11 * Chapter 12 * Chapter 13 * Chapter 14

2.1 The Importance of PlanningAs you begin your model generation, you will (consciously or unconsciously) make a number of decisionsthat determine how you will mathematically simulate the physical system: What are the objectives of youranalysis? Will you model all, or just a portion, of the physical system? How much detail will you include inyour model? What kinds of elements will you use? How dense should your finite element mesh be? Ingeneral, you will attempt to balance computational expense (CPU time, etc.) against precision of results asyou answer these questions. The decisions you make in the planning stage of your analysis will largelygovern the success or failure of your analysis efforts.

2.2 Determine Your ObjectivesThis first step of your analysis relies not on the capabilities of the ANSYS program, but relies instead on yourown education, experience, and professional judgment. Only you can determine what the objectives of youranalysis must be. The objectives you establish at the start will influence the remainder of your choices as yougenerate the model.

2.3 Choose a Model Type (2-D, 3-D, etc.)Your finite element model may be categorized as being 2-dimensional or 3-dimensional, and as beingcomposed of point elements, line elements, area elements, or solid elements. Of course, you can intermixdifferent kinds of elements as required (taking care to maintain the appropriate compatibility among degreesof freedom). For example, you might model a stiffened shell structure using 3-D shell elements to representthe skin and 3-D beam elements to represent the ribs. Your choice of model dimensionality and element typewill often determine which method of model generation will be most practical for your problem.LINE models can represent 2-D or 3-D beam or pipe structures, as well as 2-D models of 3-D axisymmetricshell structures. Solid modeling usually does not offer much benefit for generating line models; they are moreoften created by direct generation methods.2-D SOLID analysis models are used for thin planar structures (plane stress), "infinitely long" structureshaving a constant cross section (plane strain), or axisymmetric solid structures. Although many 2-D analysis

MODELING: Chapter 2: Planning Your Approach (UP19980818) http://www.ansys.stuba.sk/html/guide_55/g-mod/GMOD2.htm

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models are relatively easy to create by direct generation methods, they are usually easier to create with solidmodeling.3-D SHELL models are used for thin structures in 3-D space. Although some 3-D shell analysis models arerelatively easy to create by direct generation methods, they are usually easier to create with solid modeling.3-D SOLID analysis models are used for thick structures in 3-D space that have neither a constant crosssection nor an axis of symmetry. Creating a 3-D solid analysis model by direct generation methods usuallyrequires considerable effort. Solid modeling will nearly always make the job easier.

2.4 Choose Between Linear and Higher OrderElementsThe ANSYS program's element library includes two basic types of area and volume elements: linear (with orwithout extra shapes), and quadratic. These basic element types are represented schematically in Figure 2-1.Let's examine some of the considerations involved in choosing between these two basic element types:Figure 2-1 Basic area and volume types available in the ANSYS program(a) Linear isoparametric(b) Linear isoparametric with extra shapes(c) Quadratic

2.4.1 Linear Elements (No Midside Nodes)For structural analyses, these corner noded elements with extra shape functions will often yield an accuratesolution in a reasonable amount of computer time. When using these elements, it is important to avoid theirdegenerate forms in critical regions. That is, avoid using the triangular form of 2-D linear elements and thewedge or tetrahedral forms of 3-D linear elements in high results-gradient regions, or other regions of specialinterest. You should also take care to avoid using excessively distorted linear elements. In nonlinearstructural analyses, you will usually obtain better accuracy at less expense if you use a fine mesh of theselinear elements rather than a comparable coarse mesh of quadratic elements.Figure 2-2 "Comparable" grids of (a) linear and (b) quadratic elements

When modeling a curved shell, you must choose between using curved (that is, quadratic) or flat (linear) shellelements. Each choice has its advantages and disadvantages. For most practical cases, the majority of


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problems can be solved to a high degree of accuracy in a minimum amount of computer time with flatelements. You must take care, however, to ensure that you use enough flat elements to model the curvedsurface adequately. Obviously, the smaller the element, the better the accuracy. It is recommended that the3-D flat shell elements not extend over more than a 15° arc. Conical shell (axisymmetric line) elementsshould be limited to a 10° arc (or 5° if near the Y axis).For most non-structural analyses (thermal, magnetic, etc.), the linear elements are nearly as good as thehigher order elements, and are less expensive to use. Degenerate elements (triangles and tetrahedra) usuallyproduce accurate results in non-structural analyses.

2.4.2 Quadratic Elements (Midside Nodes)For linear structural analyses with degenerate element shapes (that is, triangular 2-D elements and wedge ortetrahedral 3-D elements), the quadratic elements will usually yield better results at less expense than will thelinear elements. However, in order to use these elements correctly, you need to be aware of a few peculiartraits that they exhibit:

Distributed loads and edge pressures are not allocated to the element nodes according to "commonsense," as they are in the linear elements. (See Figure 2-3.) Reaction forces from midside nodeelements exhibit the same nonintuitive interpretation.3-D thermal elements with midside nodes subject to convection loading inherently distribute the heatflow such that it flows in one direction at the midside node and in the other direction at the cornernodes.For structural elements, a temperature defined at a midside node that falls outside the temperaturerange of the two adjacent corner nodes is redefined as the average temperature of these corner nodes.Since the mass at the midside nodes is also greater than at the corner nodes, it is usually better to pickmaster degrees of freedom (for reduced analyses) at the midside nodes.

Figure 2-3 (a) Equivalent nodal allocation of a unit uniform surface load on 2-D elements, (b)Equivalent nodal allocations of a unit uniform surface load on 3-D elements, (c) Equivalent nodalallocations of a uniform surface load on triangular 3-D elements.

In dynamic analyses where wave propagation is of interest, midside node elements are notrecommended because of the nonuniform mass distribution.Do not define general contact surfaces at, or connect gap elements to, edges with midside nodes.Similarly, for thermal problems, do not apply radiation links or nonlinear convection surfaces to edges


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with midside nodes. (Meshing of solid models provides ways to omit certain midside nodes.)Figure 2-4 Avoid midside nodes at gaps and contact surfaces

When constraining degrees of freedom at an element edge (or face), all nodes on the edge, includingthe midside nodes, must be constrained.The corner node of an element should only be connected to the corner node, and not the midside nodeof an adjacent element. Adjacent elements should have connected (or common) midside nodes.

Figure 2-5 Avoid midside-to-corner node connections between elements

For elements having midside nodes, it is generally preferred that each such node be located at thestraight-line position halfway between the corresponding corner nodes. There are, however, situationswhere other locations may be more desirable:

Nodes following curved geometric boundaries will usually produce more accurate analysisresults-and all ANSYS meshers place them there by default.Even internal edges in some meshes may have to curve to prevent elements from becominginverted or otherwise overly distorted. ANSYS meshers sometimes produce this type ofcurvature.It is possible to mimic a crack-tip singularity with "quarter point" elements, with midside nodesdeliberately placed off-center. You can produce this type of specialized area mesh in ANSYS byusing the KSCON command (Main Menu>Preprocessor>-Meshing-Size Cntrls>-ConcentratKPs-Create).

Midside node positions are checked by the element shape test described below. (For information aboutcontrolling element shape checking, see Chapter 7 of this manual.)

All solid and shell elements except three-noded triangles and four-noded tetrahedra are tested foruniformity of the mapping between "real" 3-D space and the element's own "natural" coordinatespace. A large Jacobian ratio indicates excessive element distortion, which may or may not becaused by poorly located midside nodes. For details about Jacobian ratio tests, refer to thesection on element shape testing in the ANSYS Theory Reference.

If you do not assign a location for a midside node, the program will automatically place that nodemidway between the two corner nodes, based on a linear Cartesian interpolation. Nodes located in thismanner will also have their nodal coordinate system rotation angles linearly interpolated.Connecting elements should have the same number of nodes along the common side. When mixingelement types it may be necessary to remove the midside node from an element. For example, node Nof the 8-node element shown below should be removed (or given a zero node number when theelement is created [E]) when the element is connected to a 4-node element.


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Figure 2-6 Avoid mismatched midside nodes at element interconnections

Note-The program will automatically remove midside nodes along the common sides of linear and quadraticelements in the following situation: one area (or volume) is meshed [AMESH, VMESH, FVMESH] withlinear elements, then an adjacent area (or volume) is meshed with quadratic elements. Midside nodes will notbe removed if the order of meshing is reversed (quadratic elements followed by linear elements).

A removed midside node implies that the edge is and remains straight, resulting in a correspondingincrease in the stiffness. It is recommended that elements with removed nodes be used only intransition regions and not where simpler linear elements with added shape functions will do. If needed,nodes may be added or removed after an element has been generated, using one of the followingmethods:

Command(s):EMID

GUI:Main Menu>Preprocessor>Move / Modify>Add Mid NodesMain Menu>Preprocessor>Move / Modify>Remove Mid NdCommand(s):

EMODIFGUI:Main Menu>Preprocessor>Move / Modify>Modify Nodes

A quadratic element has no more integration points than a linear element. For this reason, linearelements will usually be preferred for nonlinear analyses.One-element meshes of higher-order quadrilateral elements such as PLANE82 and SHELL93 mayproduce a singularity due to zero energy deformation.In postprocessing, the program uses only corner nodes for section and hidden line displays. Similarly,nodal stress data for printout and postprocessing are available only for the corner nodes.In graphics displays, midside node elements, which actually use a curved edge in the elementformulation, are displayed with straight-line segments (unless PowerGraphics is used). Models willtherefore look "cruder" than they actually are.

2.5 Limitations on Joining Different ElementsYou must be careful when you directly join elements that have differing degrees of freedom (DOFs), becausethere will be inconsistencies at the interface. When elements are not consistent with each other, the solution


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may not transfer appropriate forces or moments between different elements.To be consistent, two elements must have the same DOFs; for example, they must both have the samenumber and type of displacement DOFs and the same number and type of rotational DOFs. Furthermore, theDOFs must overlay (be tied to) each other; that is, they must be continuous across the element boundaries atthe interface.Consider three examples of the use of inconsistent elements:

Elements having a different number of DOFs are inconsistent. SHELL63 and BEAM4 elements havethree displacement and three rotational DOFs per node. SOLID45 elements have three displacementDOFs per node, but lack rotational DOFs. If a SOLID45 element is joined to either a SHELL63 orBEAM4 element, the nodal forces corresponding to displacement DOFs will be transmitted to the solidelement. However, the nodal moments corresponding to the rotational DOFs of the SHELL63 andBEAM4 elements will not be transmitted to the SOLID45 element.Elements having the same number of DOFs may nevertheless be inconsistent. BEAM3 (2-D elasticbeam) elements and SHELL41 (membrane shell) elements each have three DOFs per node. However,the shell element has three displacement DOFs (UX, UY and UZ), while the beam element has onlytwo (UX and UY). Therefore, the UZ result will reflect the stiffness of the shell element, only.Furthermore, the shell element does not have the rotational DOF (ROTZ) that the beam element has.The nodal moment corresponding to the beam element's rotational DOF will not be transmitted to theshell element. The interface will behave as if the beam was "pinned."Both 3-D beam elements and 3-D shell elements have 6 DOFs per node. However, the ROTZ degree offreedom of the shell element (the drilling mode) is associated with the in-plane rotational stiffness. Thisis normally a fictitious stiffness; that is, it is not the result of a mathematical calculation of the truestiffness. Thus, the ROTZ degree of freedom of the shell element is not a true DOF. (The exception iswhen the Allman Rotational Stiffness is activated for SHELL43 or SHELL63 elements(KEYOPT(3)=2 for both).) Therefore, it is not consistent to connect only one node of a 3-D beamelement to a 3-D shell element such that a rotational DOF of the beam element corresponds to theROTZ of the shell element. You should not join beams to shells in this manner.

Similar inconsistencies may exist between other elements with differing number and/or types of DOFs.An additional limitation exists even when the joined elements have consistent DOFs. A potential forerroneous results exists when SOLID72 or SOLID73 elements are joined to other element types andinsufficient rigid body motion constraints are placed on the SOLID72 or SOLID73 elements. The potentialproblem exists even when the other element types have 6 DOFs, as do SOLID72 and SOLID73 elements.The following limitations are noted in the descriptions of the SOLID72 and SOLID73 elements in the ANSYSElements Reference manual:

You should specify the rigid body motion constraints on the nodes of the SOLID72 or SOLID73elements, because specifying the restraints on the other elements instead of on these solids could leadto erroneous results.You should also specify constraints in each of the three rotational directions for at least one of thenodes.

These types of problems may not invalidate the analysis, but you should at least be aware of the conditions atthe interface between two different element types.


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2.6 Find Ways to Take Advantage of SymmetryMany objects have some kind of symmetry, be it repetitive symmetry (such as evenly spaced cooling fins ona long pipe), reflective symmetry (such as a molded plastic container), or axisymmetry (such as a light bulb).When an object is symmetric in all respects (geometry, loads, constraints, and material properties), you canoften take advantage of that fact to reduce the size and scope of your model.Figure 2-7 Examples of symmetry

2.6.1 Some Comments on Axisymmetric StructuresAny structure that displays geometric symmetry about a central axis (such as a shell or solid of revolution) isan axisymmetric structure. Examples would include straight pipes, cones, circular plates, domes, and so forth.Models of axisymmetric 3-D structures may be represented in equivalent 2-D form. You may expect thatresults from a 2-D axisymmetric analysis will be more accurate than those from an equivalent 3-D analysis.By definition, a fully axisymmetric model can only be subjected to axisymmetric loads. In many situations,however, axisymmetric structures will experience non-axisymmetric loads. You must use a special type ofelement, known as an axisymmetric harmonic element, to create a 2-D model of an axisymmetric structurewith non-axisymmetric loads. See Section 2.8 of the ANSYS Elements Reference for details.2.6.1.1 Some Special Requirements for Axisymmetric ModelsSpecial requirements for axisymmetric models include:

The axis of symmetry must coincide with the global Cartesian Y-axis.Negative nodal X-coordinates are not permitted.The global Cartesian Y-direction represents the axial direction, the global Cartesian X-directionrepresents the radial direction, and the global Cartesian Z-direction corresponds to the circumferentialdirection.Your model should be assembled using appropriate element types:

For axisymmetric models, use applicable 2-D solids with KEYOPT(3)=1, and/or axisymmetricshells. In addition, various link, contact, combination, and surface elements can be included in a


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model that also contains axisymmetric solids or shells. (The program will not realize that these"other" elements are axisymmetric unless axisymmetric solids or shells are present.) If theANSYS Elements Reference does not discuss axisymmetric applications for a particular elementtype, do not use that element type in an axisymmetric analysis.For axisymmetric harmonic models, use only axisymmetric harmonic elements.

SHELL51 and SHELL61 elements cannot lie on the global Y-axis.For models containing 2-D solid elements in which shear effects are important, at least two elementsthrough the thickness should be used.

2.6.1.2 Some Further Hints and RestrictionsIf your structure contains a hole along the axis of symmetry, don't forget to provide the proper spacingbetween the Y-axis and the 2-D axisymmetric model. (See Figure 2-8.) See Chapter 2 of the ANSYS BasicAnalysis Procedures Guide for a discussion of axisymmetric loads.Figure 2-8 An X-direction offset represents an axisymmetric hole

2.7 Decide How Much Detail to IncludeSmall details that are unimportant to the analysis should not be included in the solid model, since they willonly make your model more complicated than necessary. However, for some structures, "small" details suchas fillets or holes can be locations of maximum stress, and might be quite important, depending on youranalysis objectives. You must have an adequate understanding of your structure's expected behavior in orderto make competent decisions concerning how much detail to include in your model.In some cases, only a few minor details will disrupt a structure's symmetry. You can sometimes ignore thesedetails (or, conversely, treat them as being symmetric) in order to gain the benefits of using a smallersymmetric model. You must weigh the gain in model simplification against the cost in reduced accuracywhen deciding whether or not to deliberately ignore unsymmetric features of an otherwise symmetricstructure.

2.8 Determine the Appropriate Mesh DensityA question that frequently arises in a finite element analysis is, "How fine should the element mesh be inorder to obtain reasonably good results?" Unfortunately, no one can give you a definitive answer to thisquestion; you must resolve this issue for yourself. Some of the techniques you might employ to resolve thisquestion include:


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Use adaptive meshing to generate a mesh that meets acceptable energy error estimate criteria. (Thistechnique is available only for linear static structural or steady state thermal problems. Your judgementas to what constitutes an "acceptable" error level will depend on your analysis requirements.) Adaptivemeshing requires solid modeling.Compare the results of a preliminary analysis with independently derived experimental or knownaccurate analytical results. Refine the mesh in regions where the discrepancy between known andcalculated results is too great. (For all area meshes and for volume meshes composed of tetrahedra, youcan refine the mesh locally with the NREFINE, EREFINE, KREFINE, LREFINE, and AREFINEcommands (Main Menu> Preprocessor>-Meshing-Modify Mesh>-Refine At-entity type).)Perform an initial analysis using what seems to you to be a "reasonable" mesh. Reanalyze the problemusing twice as many elements in critical regions, and compare the two solutions. If the two meshes givenearly the same results, then the mesh is probably adequate. If the two meshes yield substantiallydifferent results, then further mesh refinement might be required. You should keep refining your meshuntil you obtain nearly identical results for succeeding meshes.If mesh-refinement testing reveals that only a portion of your model requires a finer mesh, you can usesubmodeling to "zoom in" on critical regions.

Mesh density is extremely important. If your mesh is too coarse, your results can contain serious errors. Ifyour mesh is too fine, you will waste computer resources, experience excessively long run times, and yourmodel may be too large to run on your computer system. To avoid such problems, always address the issue ofmesh density before you begin your model generation.

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