ANSYS Mechanical APDL Modeling and Meshing soundofheaven.info - Ebook download as PDF File .pdf), Text File .txt) or read book online. ANSYS Workbench - Meshing The order of the meshing process can be controlled manually > Direct then mesh rest of model with . Manual Source. Overview of the Meshing Process in ANSYS Workbench. plication is launched from a Mesh component system or a Mechanical Model component system.

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ANSYS Modeling and Meshing Guide. ANSYS Release ANSYS, Inc. Southpointe. Technology Drive. Canonsburg, PA [email protected] com. trademarks of ANSYS, Inc. or its subsidiaries in the United States or other countries. ICEM CFD Mechanical APDL ANSYS Mechanical APDL Basic Analysis. Topics in This Manual. Topics in Other ANSYS Manuals. Conventions This Manual Uses. The ANSYS Product Family. 1 Overview of Model Generation.

Area and Volume Types p. Solid Modeling Figure 5. As you create a primitive. Mesh the area that is to be extruded. For some models. Relationships Among Display Screen.

Area and Volume Types p. In nonlinear structural analyses. These basic element types are represented schematically in Figure 2. Let's examine some of the considerations involved in choosing between these two basic element types: When using these elements. Creating a 3-D solid analysis model by direct generation methods usually requires considerable effort.

Comparable Grids p. Each choice has its advantages and disadvantages. When modeling a curved shell. Figure 2. Solid modeling will nearly always make the job easier. You should also take care to avoid using excessively distorted linear elements. You must take care. For most practical cases. Area and Volume Types a b c 2. Equivalent Nodal Allocations p.

Degenerate elements triangles and tetrahedra usually produce accurate results in non-structural analyses. Quadratic Elements Midside Nodes For linear structural analyses with degenerate element shapes that is.

Equivalent nodal allocations of a unit uniform surface load are shown in Figure 2. When selecting master degrees of freedom in a substructure or CMS generation. Where nodal-based contact is necessary on surfaces with midside nodes. See Figure 2. This caution does not apply to the surface-to-surface. Similarly for thermal problems. Reaction forces from midside-node elements exhibit the same nonintuitive interpretation.

The following scenarios are depicted: A large Jacobian ratio indicates excessive element distortion. Adjacent elements should have connected or common midside nodes. ANSYS meshers sometimes produce this type of curvature. Meshing of solid models provides ways to omit certain midside nodes. There are. For information about controlling element shape checking. For details about Jacobian ratio tests.

Midside nodes will not be removed if the order of meshing is reversed quadratic elements followed by linear elements. For this reason. It is recommended that elements with removed nodes be used only in transition regions and not where simpler linear elements with added shape functions will do. Models will therefore look "cruder" than they actually are. Nodes located in this manner will also have their nodal coordinate system rotation angles linearly interpolated.

When mixing element types it may be necessary to remove the midside node from an element. If needed. Command s: To be consistent. When an object is symmetric in all respects geometry.

Planning Your Approach 2. Such problems may not invalidate your analysis. Limitations on Joining Different Elements You must be careful when you directly join elements that have differing degrees of freedom DOFs.

The ROTZ degree of freedom of the shell element the drilling mode is associated with the inplane rotational stiffness. Consider three examples of the use of inconsistent elements: This is normally a fictitious stiffness. It is therefore inconsistent to connect only one node of a 3-D beam element to a 3-D shell element such that a rotational DOF of the beam element corresponds to the ROTZ of the shell element.

When elements are not consistent with each other. The program will not realize that these "other" elements are axisymmetric unless axisymmetric solids or shells are present. In many situations. Some Comments on Axisymmetric Structures Any structure that displays geometric symmetry about a central axis such as a shell or solid of revolution is an axisymmetric structure. By definition. If the Element Reference does not discuss axisymmetric applications for a particular element type.

Examples would include straight pipes. In addition. Some Special Requirements for Axisymmetric Models Special requirements for axisymmetric models include: You may expect that results from a 2-D axisymmetric analysis will be more accurate than those from an equivalent 3-D analysis.

You must use a special type of element. Models of axisymmetric 3-D structures may be represented in equivalent 2-D form. For all area meshes and for volume meshes composed of tetrahedra. You must have an adequate understanding of your structure's expected behavior in order to make competent decisions concerning how much detail to include in your model.

This technique is available only for linear static structural or steady state thermal problems. Determining the Appropriate Mesh Density A question that frequently arises in a finite element analysis is. Adaptive meshing requires solid modeling. See Loading in the Basic Analysis Guide for a discussion of axisymmetric loads. Some of the techniques you might employ to resolve this question include: Some Further Hints and Restrictions If your structure contains a hole along the axis of symmetry.

Your judgement as to what constitutes an "acceptable" error level will depend on your analysis requirements. You can sometimes ignore these details or. Refine the mesh in regions where the discrepancy between known and calculated results is too great. You must weigh the gain in model simplification against the cost in reduced accuracy when deciding whether or not to deliberately ignore unsymmetric features of an otherwise symmetric structure. In some cases.

Determining How Much Detail to Include Small details that are unimportant to the analysis should not be included in the solid model. You should keep refining your mesh until you obtain nearly identical results for succeeding meshes. Mesh density is extremely important. If your mesh is too fine. To avoid such problems. If the two meshes give nearly the same results. Reanalyze the problem using twice as many elements in critical regions.

If the two meshes yield substantially different results. If your mesh is too coarse. Global and Local Coordinate Systems Global and local coordinate systems are used to locate geometry items. Chapter 3: Nodal Coordinate Systems 3. You can input the geometry in any of three predefined global coordinate systems. The following coordinate system topics are available: Global Coordinate Systems A global coordinate system can be thought of as an absolute reference frame. Global and Local Coordinate Systems 3.

See Figure 3. Three predefined global systems are available: Display Coordinate System 3. They are identified by their coordinate system C. When you define a node or a keypoint. The working plane. Element Coordinate Systems 3. The Results Coordinate System 3. Global Coordinate Systems p. For some models. All three of these systems are right-handed and. See Using Working Planes p. When a local coordinate system is defined.

Y components coordinate system 5 C. Such user defined coordinate systems. Euler Rotation Angles p. CS GUI: Z components coordinate system 1 C. Z components coordinate system 0 C. Coordinate Systems Figure 3. To delete a local system.

As you create a local system. Local Coordinate Systems In many cases. Figure 3. Coordinate System Types p.

Note Solid modeling operations in a toroidal coordinate system are not recommended. Note that you may define local cylindrical and spherical coordinate systems in either circular or elliptical configuration. Euler Rotation Angles Release Areas or volumes generated may not be what you expect. Some surfaces of constant 18 Release Each time you define a local coordinate system.

Surfaces Specifying a constant value for a single coordinate implies a surface. If you want to activate one of the global coordinate systems or some other previously defined coordinate system. Z for cylindrical and R. Implied surfaces are used with various operations. You should make the appropriate mental substitutions if the active coordinate system is not Cartesian R. Note When you define a keypoint or a node. The Active Coordinate System You may define as many coordinate systems as you like.

Coordinate System Types 3. The choice of active coordinate system is determined as follows: That same coordinate system will remain active in all subsequent phases until you change it explicitly. Surfaces of Constant Value Release Note that for surfaces in elliptical coordinate systems.

These surfaces may be located in either global or local coordinate systems to allow for any desired orientation. Global and Local Coordinate Systems value C are illustrated in the following figures. A fill operation from C to D will pass through B. Meshed Surfaces of Constant Value 3. A fill operation defined from A to C will pass through B. To move the singularity point. A fill operation from A to D will pass through E.

For a specified cylindrical coordinate system. Closed Surfaces and Surface Singularities Open surfaces are assumed to be infinite. Singularity Points p. Nodal Coordinate Systems Figure 3. You can change the display coordinate system used in such listings by one of the following methods: Unless you desire a specific effect in your displays. A curved line between two keypoints will take the shortest path in the angular direction. Each node has its own nodal coordinate system.

As a result. Nodal Coordinate Systems While global and local coordinate systems locate geometry items. Display Coordinate System By default. Note that solid model lines will not be affected by these singularity locations.

You can rotate the nodal coordinate system at any node to a desired orientation using one of the following methods: Data Interpreted in the Nodal Coordinate System Input data that are interpreted in the nodal coordinate system include component values of the following: N GUI: You can define the rotation angles at the time the node is created 1627.

Since you will usually not know these rotation angles explicitly. Coordinate Systems was defined. For area and volume elements. The default orientations for most elements' coordinate systems fit the following patterns: Element Coordinate Systems Every element has its own coordinate system.

For some elements. All element coordinate systems are right-handed orthogonal systems. Use one of the following methods to change the results coordinate system: If you then list. Coordinate Systems 3. These data are stored in the database and on the results file in either the nodal coordinate system for the primary. You can change the active results coordinate system to another system such as the global cylindrical system or a local coordinate system.

The following topics are available to help you create and use a working plane: Moving the Working Plane 4. Working Plane Enhancements 4. Defining a New Working Plane 4. Creating a Working Plane 4. Relationships Among Display Screen. Rotating the Working Plane 4. Creating a new working plane eliminates your existing working plane.

Chapter 4: Using Working Planes Although your cursor appears as a point on your screen. Recreating a Previously-defined Working Plane Release In order to be able to pick a point with your cursor. The following working plane topics are available: You can define only one working plane at a time. Another way to think of the interaction between your cursor and your working plane is to picture your cursor as a point that moves around on your working plane.

To learn how to force the active coordinate system to track the working plane. Working Plane. The working plane is separate from the coordinate systems. This imaginary plane is called a working plane. Figure 4. Controlling the Display and Style of the Working Plane 4. Creating a Working Plane By default. The working plane need not be parallel to your display screen. Defining a New Working Plane You can define a new working plane by using any of these methods: Moving the Working Plane You can move a working plane to a new location that is.

Using Working Planes 4. Snap Increment 4. If you do not know the rotation angles explicitly. Retrieval Tolerance Release To rotate the working plane. Rotating the Working Plane You can rotate your working plane to a new orientation in two ways: Display Grid 4. Recreating a Previously-defined Working Plane Although you cannot actually "save" a working plane. Working Plane Enhancements Command s: Snap Increment It is difficult. Retrieval Tolerance An existing entity that you want to pick might lie close to.

This grid is not related in any way to your snap points. You can visualize the snap increment as creating a pattern of square boxes. Stated mathematically. The same snap increment is used for both x and y coordinates.

Once a snap increment is defined. Display Grid You can create a square display grid to help you visualize the location and orientation of your working plane. Any locational pick you make will "snap" to the center of its box. Coordinate Type There are two types of working planes that you can choose from: Cartesian and polar. Working Plane Tracking 4. Coordinate Type 4. In order to pick with precision. The grid spacing. Discussion up to this point has concentrated on Cartesian working planes but polar working planes may be used if 28 Release This tolerance.

Polar Working Plane Grid p. When you change or move the working plane. This can be frustrating if you are using a combination of picking based on the working plane. Working Plane Tracking If you've used working planes in conjunction with coordinate systems to define your geometry. For instance. Working Plane Enhancements your geometry is easily described in polar radius. Picking with a polar working plane works the same way as picking on a Cartesian working plane. Polar Working Plane Grid 4.

Cartesian and in the same location as the working plane. The coordinate system is also updated if you change the type of working plane that you are using. The command CSYS. WP 30 Release You moved your plane. Using Working Planes Figure 4. To revisit the example discussed above. WP before you moved the plane. Figure 5. Solid Model Loads 5. An Overview of Solid Modeling Operations The points that define the vertices of your model are called keypoints and are the "lowest-order" solid model entities.

As you create a primitive. With careful planning and alternative strategies. Primitives 5. Chapter 5: Solid Modeling The purpose of using a solid model is to relieve you of the time-consuming task of building a complicated finite element model by direct generation. Sculpting Your Model with Boolean Operations 5. Updating after Boolean Operations 5. Moving and Copying Solid Model Entities 5. Some solid modeling and meshing operations can help you to speed up the creation of your final analysis model The solid modeling features of ANSYS are known to have robustness issues.

Considerations and Cautions for Solid Modeling 5. If your modeling effort begins with the "higher" primitive entities. Mass and Inertia Calculations 5. An Overview of Solid Modeling Operations 5. The followng solid modeling topics are available: Scaling Solid Model Entities 5. Using Boolean operators: You can "sculpt" your solid model using intersections. Solid Modeling model. Booleans allow you to work directly with higher solid model entities to create complex shapes.

Remember that geometric primitives are built within the working plane while bottom up techniques are defined against the active coordinate system.

Top Down Constructions Primitives Note Solid modeling operations in a toroidal coordinate system are not recommended. Boolean operators. If you are mixing techniques. Sometimes a model can be constructed more efficiently by dragging. Both bottom up and top down creations can be used in Boolean operations. You might also find it more convenient to place geometric primitives in their proper location by moving them.

By taking care to meet certain requirements. A complicated area or volume that appears repetitively in your model need only be constructed once. Once you have completed the solid model. Free and Mapped Meshes Moving and copying nodes and elements: Automatic meshing is a huge improvement over direct generation of nodes and elements. If your model contains repetitive features.

Copying an Area Meshing: Your ultimate objective in building a solid model is to mesh that model with nodes and elements. After you have revised your solid model. Copying a mesh in this manner will generally be faster than separately meshing repeated features. Solid Modeling region. As an alternative to clearing. Revising your model clearing and deleting: Before you can revise your model. A lower order entity cannot be deleted if it is attached to a higher-order entity.

The hierarchy of modeling entities is as listed below: Copying a Meshed Area Solid model loads: If an entity is attached to any loads. Once the solid model is cleared. Revising a Meshed Solid Model 5. Basic Solid Model Entities Release Basic Solid Model Entities p. You can then define lines. Notice that there is a hierarchy in these entities: To define individual keypoints. You do not always have to explicitly define all entities in ascending order to create higher-order entities: Keypoints are defined within the currently active coordinate system.

Keypoints When building your model from the bottom up. The intermediate entities will then be generated automatically as needed. See the Command Reference for more information on the individual commands. In bottom up construction. Caution Solid modeling operations in a toroidal coordinate system are not recommended. Solid Modeling Keypoints are the vertices. A keypoint can also be redefined using the K command. You can maintain keypoints using the methods listed in the following table.

Modifying the coordinates will automatically clear any meshed region attached to the specified keypoint. Hard points have their own suite of commands and GUI controls. Mapped meshing is not supported when hard points are used. If you issue any commands that update the geometry of an entity. Solid Modeling 5. Hard point information cannot be written to the IGES file. Hard Points Hard points are actually a special type of keypoints. You can define hard points on existing lines or areas. Most of the keypoint commands.

You cannot manipulate hard points with commands to copy. To create hard points. Hard points do not modify either the geometry or topology of your model. The Jobname. If you delete an entity that has associated hard points.

In both cases. DB option. You can use hard points to apply loads or obtain data from arbitrary points on lines and areas within your model. Lines are required if you want to generate line elements such as beams or to create areas from lines. You do not always need to define all lines explicitly. You can maintain hard points using the methods described in the table below. As with keypoints. If you need to explicitly define a line.

Lines Lines are mainly used to represent the edges of an object. Both of these guidelines 40 Release Drag Operation Suggestions p. Also the entity plane should be as close to parallel to the drag path plane as possible. Creating Your Solid Model from the Bottom Up can be met if the entities to be dragged are in the drag path plane.

Drag path plane orthogonal to start of drag path For those commands that create a "straight" line. Drag Operation Suggestions Drag path d Entities to be dragged. The drag path plane is automatically defined to be orthogonal to and located at the start of the drag path. For a "straight" line in a cylindrical coordinate system. Copy a pattern of lines to generate additional lines using any of the methods described in the following table. The attached areas will be updated.

Areas are required if you wish to use area elements or if you wish to create volumes from areas. Areas Flat areas are used to represent 2-D solid objects such as flat plates or axisymmetric solids.

You can use these three commands to modify unmeshed lines. Curved as well as flat areas are used to represent 3-D surfaces. You can maintain lines using the methods listed in the following table.

Most commands that create areas will also automatically generate the necessary lines and keypoints. Primitives p. Area Command Operations p. Using this process will not generate a new surface when such problems arise you will receive a warning if the process fails. Several geometric primitives and Boolean commands can also be used to generate or modify areas. You might experience difficulties due to the underlying Boolean operations used by this command.

Both of these guidelines can be met if the entities to be dragged are in the drag path plane. Creating Your Solid Model from the Bottom Up You can use any of the methods described in the following table to explicitly define areas.

See When a Boolean Operation Fails p. You might experience difficulties if you attempt to "deflate" an area by a distance that equals or exceeds its least radius of curvature. Area Command Operations You can copy existing areas to generate additional areas using the methods described in the following table. Only unmeshed areas that are not attached to a volume can be redefined or deleted. Solid Modeling Figure 5. Most commands that create volumes will also automatically generate the necessary lower-order entities.

Volumes Volumes are used to represent 3-D objects. Loops Bound an Area p. The "loop" numbers shown refer to the closed strings of lines that define the boundaries of an area. To define volumes. Volume Command Operations To generate additional volumes from existing volumes. Volume Command Operations p. A shell is the volumetric equivalent of a loop.

Specify the desired number of element divisions in the extruded.. Note that only unmeshed volumes can be redefined or deleted. Activate the selection [TYPE]. A volume listing indicates that the volumes are composed of a number of shells.

Follow these steps to extrude your mesh: Mesh the area that is to be extruded. You can get around the concatenated line limitation by first meshing the area s. The carryover of the attributes of the pattern area elements saves you time that would otherwise be required to prepare the 3-D model extrusion of multiple areas with differing attributes. It enables carryover of material attributes. Note that only the area opposite the pattern area will have the same attributes as the pattern area.

In contrast. ANSYS creates the volume and the volume mesh simultaneously. For detailed information about volume sweeping. Primitives In top down construction. Primitives Figure 5. Because primitives are higher-order entities that can be constructed without first defining any keypoints.

You can freely combine bottom up and top down modeling techniques. Solid Modeling associated with it. When you create a primitive. Area primitives must have surface areas greater than zero that is. You can define area primitives using the methods described in the following table.

Creating Area Primitives Any area primitives you create will lie flat on the working plane and will be oriented according to the working plane coordinate system. The interface between two touching primitives will create a seam of discontinuity in the finite element model.

Geometric primitives are created within the working plane. A geometric primitive is a commonly used solid modeling shape such as a sphere or regular prism that can be created with a single ANSYS command. THETA2 on these commands does not define the starting and ending angles of the arc sector.

The following figure illustrates how these commands work: Creating Volume Primitives Volume primitives are positioned relative to the working plane as outlined in their command descriptions. You can define volume primitives using the methods described in the following table. Torus Primitive p.

You can specify the radii in any order. To create the torus shown in Figure 5. See Figure 5. At least two of the values that you specify must be positive values. There is one exception regarding the order of the radii values.

You must specify three values to define the radii of the torus RAD1. Toroidal Sector p. Due to the sizes of the specified radii values relative to one another. To create a torus. The smallest of the values is the inner minor radius. See Creating a Torus or Toroidal Sector p. THETA2 command to create either a torus or a toroidal sector.

If you are using Booleans to modify an existing model. Toroidal Sector Inner minor radius Outer minor radius Major radius 5. You can apply Boolean operations to almost any solid model construction. The only exceptions are that Boolean operations are not valid for entities created by concatenation see Free or Mapped Mesh p. Sculpting Your Model with Boolean Operations Boolean algebra provides a means for combining sets of data. See Solid Model Loads p. Note Boolean operations and other solid modeling operations can be unreliable.

A value of "-1" will allow error messages if a Boolean operation has no effect. Value command. When you perform a Boolean operation on two or more entities.

Note A command input stream created at Revision 5. Boolean Keep Options p. You must clear the mesh from the entity before performing the Boolean operation. Boolean operations cannot be performed on meshed entities. By default. A value of "0" will result in a warning message if a Boolean operation has no effect. Solid Modeling before a Boolean operation in order to cleanly recover from a failure.

A value of "1" will suppress all warning or error messages if a Boolean operation has no effect. The default value of this label is "0". Boolean Keep Options Boolean operations on lower-order entities that are attached to higher-order entities are generally permitted. See Considerations and Cautions for Solid Modeling p. To suppress this warning. Intersect An intersection defines a new set of entities which is common to every original entity included in the operation.

The Boolean intersect commands are as follows: If you are planning to do optimization. The geometry information used for an area consists of the coordinates of its centroid. The topology information used for an area. The label STAT lists the status of present settings. The numbering scheme first assigns numbers beginning with the next available number to those output entities that can be uniquely identified by their topology. The new set can be of the same or lower dimension as the original entities.

Illustrations of Intersection Operations The following figures illustrate the intersection operations listed above: Any remaining entities are then assigned numbers based on their geometry. Entity Numbering After Boolean Operations The numbering scheme assigns numbers to Boolean output entities based on information relating to their topology and geometry. Pairwise Intersect A pairwise intersection defines a new set of entities which is any overlapping set of entities included in the operation.

In other words, a pairwise intersection represents the region of overlap of at least any two of the original entities. For instance, the pairwise intersection of a set of lines can be a keypoint or a set of keypoints , or it can be a line or set of lines.

The Boolean pairwise intersect commands are as follows: Find the pairwise intersection of. Illustrations of Pairwise Intersection Operations Figure 5. Add An addition of entities defines a new entity that includes all parts of the originals. This operation is also known mathematically as a union, joining, or summation. The resulting entity is a single seamless whole, containing no internal divisions. As a practical matter, "added" entities will often not mesh as well as will "overlapped" entities.

Areas added may contain holes within the area; that is, internal loops. The Boolean add commands are as follows: Illustrations of Addition Operations The following figures illustrate the add operations listed above. Subtract If you subtract one entity E2 from another E1 , you will obtain one of two results: Either you will create a new entity or entities E1 - E2 E3 that is of the same dimensionality as E1 and that contains no overlap with E2, or, if the overlap is of a lower dimensionality, you will simply divide E1 into two or more new entities E1 - E2 E3 and E4.

If the command field SEPO on the subtract command is set to blank default , the subtraction of entities can result in lines with a common end point, or areas with a common line boundary, or volumes sharing a common boundary area. If the command field is set to "SEPO", the resulting entities will no longer share common boundaries but have distinct but coincident boundaries.

This latter operation is not valid if the overlap of entities does not divide one of the input entities into at least two distinct lines, areas, or volumes. The Boolean subtract commands and their corresponding GUI paths are as follows: All entity subtraction commands are of the form eSBe. If ALL is used in both minuend and subtrahend fields for subtraction of like entities. The default setting for BOPTN is to delete all entities that are used as inputs to entity subtraction commands.

If these two fields are left blank. You can subtract multiple entities from a single entity. If ALL is used in the minuend field. The KEEP X argument fields of the entity subtraction commands allow you to selectively keep or delete entities.

If ALL is used in the subtrahend field. Value command which demands you either keep or delete all input entities. You can set either entity field value of the subtract operation to ALL. See the descriptions of the LSBL. Illustrations of Subtraction Operations Figure 5. You may also subtract multiple entities from multiple entities.

You can subtract one entity from multiple entities. Working Plane Subtract The working plane can be subtracted from an entity to divide it into two or more entities. For each of these subtract commands. The working plane can be subtracted from lines. You can use any of the methods described in the following table to subtract the working plane from an entity. Sculpting Your Model with Boolean Operations The working plane is often used to cut up an existing model prior to map meshing.

Illustrations of Working Plane Subtraction Operations The following figures illustrate the working plane subtraction operations listed above: The following figure illustrates the classification operation. At present. To perform line-line classification. Classify Classification is similar to subtraction. The Boolean overlap commands and their corresponding GUI paths are as follows: Overlapping is valid only if the overlap region has the same dimensionality as the original entities.

Overlap The overlap commands will join two or more entities to create three or more new entities that encompass all parts of the originals. Illustrations of Overlap Operations The following figures illustrate the overlap operations listed above: The end result is similar to an "add" operation. See the descriptions of the LPTN. Partition The partition commands will join two or more entities to create three or more new entities that encompass all parts of the originals. Illustrations of Partition Operations Figure 5.

The Boolean partition commands are as follows: The end result is similar to an "overlap" operation if the overlap is of the same dimensionality as the original entities. Glue or Merge Glue is similar to overlap. The Boolean glue commands and their corresponding GUI paths are as follows: Illustrations of Glue Operations The following figures illustrate the glue operations listed above: The entities maintain their individuality they are not "added".

Some of the alternative procedures that can sometimes be used in place of Booleans are described below. This releases you from the work of deleting the higher-order entity volume in this case 72 Release Alternatives to Boolean Operations Boolean operations can sometimes be relatively slow and expensive.

A good example would be a model of a block with a number of holes drilled through it. As a general guideline. Updating after Boolean Operations Some Boolean commands will automatically update entities after the Boolean operation is performed on attached lower-order entities. Hollow Spherical Segment Created With One Command It is clear from this example how exercising the full ability of one primitive command can sometimes save the expense of performing several Boolean operations.

Dragging and Rotating: A complicated prismatic or cylindrical volume might be defined just as conveniently. Glue or Merge 5. Alternatives to Boolean Operations 5. Updating after Boolean Operations 5. Moving and Copying Solid Model Entities 5. Generating Entities from a Pattern 5.

Generating Entities by Symmetry Reflection 5. Transferring a Pattern of Entities to a Coordinate System 5. Scaling Solid Model Entities 5. Solid Model Loads 5. Transferring Solid Model Loads 5. Displaying Load Symbols 5. Selecting a Format for the Graphical Display of Numbers 5. Listing Solid Model Loads 5. Mass and Inertia Calculations 5. Considerations and Cautions for Solid Modeling 5.

Representation of Solid Model Entities 5. When a Boolean Operation Fails 5. Graphically Identifying Degeneracies 5. Listing the Keypoints Associated with Degeneracies 5.

Some Suggested Corrective Actions 5. Other Hints 6. Generating the Mesh 7. Free or Mapped Mesh 7. Setting Element Attributes 7. Creating Tables of Element Attributes 7. Assigning Element Attributes Before Meshing 7. Mesh Controls 7. The MeshTool 7. Element Shape 7. Choosing Free or Mapped Meshing 7. Controlling Placement of Midside Nodes 7. Smart Element Sizing for Free Meshing 7. Default Element Sizes for Mapped Meshing 7.

Local Mesh Controls 7. Interior Mesh Controls 7. Creating Transitional Pyramid Elements 7. Doing Layer Meshing 7. Setting Layer Meshing Controls via Commands 7. Listing Layer Mesh Specifications on Lines 7.

Controls Used for Free and Mapped Meshing 7. Free Meshing 7. Mapped Meshing 7. Meshing Your Solid Model 7. Generating a Volume Mesh From Facets 7. Generating a Volume Mesh By Sweeping 7. Generating an Interface Mesh for Gasket Simulations 7. Aborting a Mesh Operation 7.

Element Shape Checking 7. Mesh Validity Checking 7. Changing the Mesh 7. Remeshing the Model 7. Clearing the Mesh 7. Refining the Mesh Locally 7. Meshing Hints 7. Low Sector Boundary 7. Meshing the Sector Volume s 8. Revising Your Model 8. Refining a Mesh Locally 8. How to Refine a Mesh 8. Refinement Commands and Menu Paths 8. Transfer of Attributes and Loads 8. Other Characteristics of Mesh Refinement 8.

Restrictions on Mesh Refinement 8. Moving and Copying Nodes and Elements 8. Keeping Track of Element Faces and Orientations 8. Controlling Area, Line, and Element Normals 8. Revising a Meshed Model: Clearing and Deleting 8. Clearing a Mesh 8. Deleting Solid Model Entities 8. Modifying Solid Model Entities 8. Direct Generation 9. Nodes 9. Elements 9. Prerequisites for Defining Element Attributes 9. Defining Elements 9.

A Note About Overlapping Elements 9. Modifying Elements By Changing Nodes 9. Number Control and Element Reordering Number Control Merging Coincident Items Compressing Item Numbers Setting Starting Numbers Adding Number Offsets Element Reordering