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3.2 Edge Meshing Commands

The following commands are available on the Mesh/Edge subpad.

Symbol Command Description
Mesh Edges Creates mesh nodes along edges
Set Edge Element Type Specifies edge element types used throughout the model
Link Edge Meshes
Unlink Edge Meshes
Creates and deletes mesh hard links between edges
Split Meshed Edge Splits an edge at a mesh node
Summarize Edge Mesh Displays mesh grading information
Delete Edge Meshes Deletes existing mesh nodes from edges

The following sections describe the purpose and operation of each of the commands listed above.


3.2.1 Mesh Edges

The Mesh Edges operation (edge mesh, edge modify, edge picklink, and edge pickunlink commands) grades or meshes any or all edges in the model. When you grade an edge, GAMBIT applies the mesh node spacing specifications but does not create mesh nodes on the edge. When you mesh an edge, GAMBIT creates mesh nodes according to the specifications.

To perform a grading or meshing operation, you must specify the following parameters:

Specifying Edges

When you specify one or more edges for a grading or meshing operation, you must specify the following options:

When you soft-link two or more edges, GAMBIT links the edges for meshing purposes so that any grading or meshing specifications applied to one edge can be simultaneously applied to the other edges as well. When you reverse an edge, GAMBIT reverses the sense of the edge; therefore, any directional grading scheme associated with the edge is also reversed.

In addition to the soft-link and reverse options described above, GAMBIT allows you to specify whether or not to impose the grading parameters of the first edge specified in the Edges list on all other parameters in the list (see "Imposing First-Edge Grading and Spacing Parameters," below).

Soft-linking Edges

When you specify more than one edge for a grading or meshing operation, GAMBIT allows you to create soft links between the specified edges. When you grade or mesh an edge that is soft-linked to other edges, you can simultaneously apply the grading or meshing specifications to all of the edges that are soft-linked to the specified edge.

Forming, Maintaining, and Breaking Soft Links

When you specify two or more edges for a grading or meshing operation, you must specify the status of any soft links that involve the edges. The three soft-link status options are as follows:

When you Form soft links between two or more edges, GAMBIT creates a "chain" of links between the specified edges. If you form a soft link involving an edge that is part of an existing soft-link chain, GAMBIT breaks the existing soft link associated with the edge. That is, no single edge is allowed to constitute part of more than one soft-link chain.

When you Maintain soft links, GAMBIT does not form or break any existing soft links associated with the specified edge(s).

When you Break a soft link associated with an edge, GAMBIT removes the edge from the soft-link chain but does not break any other soft links in the chain. That is, any other edges that are part of the soft-link chain remain soft-linked to each other.

Grading or Meshing Soft-link Chains

When you grade or mesh an edge that constitutes part of an existing soft-link chain, GAMBIT allows you to specify whether the grading or meshing specifications apply to all edges that belong to the chain (the Pick with links option). The general rules pertaining to the Pick with links option are as follows.

Reversing Edges

When you mesh an edge using a non-uniform grading scheme, GAMBIT grades or meshes the edge relative to its sense. For example, if you mesh an edge using a First Length scheme (see below) and specify a first interval length of 2, GAMBIT locates the first mesh node at a distance of 2 units from the edge start vertex.

When you specify edges for a grading or meshing operation, GAMBIT allows you to change their respective senses by means of the Reverse command button on the Mesh Edges form. If you reverse the sense of an edge the grading of which is non-uniform, the grading or meshing scheme is also reversed. For example, if you mesh an edge using a First Length grading scheme and specify a first interval length of 2, then click Reverse to reverse the sense of the edge, GAMBIT meshes the edge such that the last mesh node is located at a distance of 2 from the edge end vertex.

If you apply the Reverse option to an edge that is part of a soft-link chain and select the Pick with links option, GAMBIT reverses the sense and, therefore, the grading of all edges in the chain.

Imposing First-Edge Grading and Spacing Parameters

When you specify a set of edges for grading and/or meshing, you can also determine whether or not to impose the grading parameters of the first edge specified in the Edges list on all other edges in the list. To impose the first-edge grading parameters on the other specified edges, you must select the Use first edge settings option on the Mesh Edges form. By default, the Use first edge settings option is selected.

Grading Parameters

If you specify a set of edges at least one of which differs from the others with respect to its Grading parameters, the Use first edge settings option produces the following effects on the Grading section of the Mesh Edges form.

Spacing Parameters

The behavior of the Spacing section is identical to that of the Grading section (see above) with respect to the Use first edge settings option.

NOTE: The Grading and Spacing sections of the Mesh Edges form behave independently of each other with respect to the Use first edge settings option.

Specifying the Grading Scheme

GAMBIT provides the following types of edge mesh grading schemes.

The first six schemes listed above are non-symmetric schemes—that is, they can produce grading patterns that are not necessarily symmetric about the center of the edge. The last two schemes are symmetric schemes—that is, they are constrained to produce grading patterns that are symmetric about the center of the edge.

NOTE: When you grade or mesh an edge that is connected to one or more edges that are already graded or meshed, GAMBIT provides the means to ensure that the new grading is similar to the existing grading(s) in the region surrounding the connecting vertex. This specification is accomplished by means of the MESH.EDGE.FLEXIBLE_GRADING default variable.
  • If you set the variable to 0 (default), GAMBIT applies the settings specified on the Mesh Edges form without regard to the existing grading/meshing parameters(s) on the already graded or meshed edges.
  • If you set the variable to 1, GAMBIT ignores the settings specified on the Mesh Edges form and grades the edge such that its first interval length in the region adjacent to the connecting vertex is similar to that on the already meshed or graded edge(s) to which it is connected. If the edge is connected to graded/meshed edges at both endpoint vertices, GAMBIT uses a single-sided grading scheme the first and last interval lengths of which are similar to the lengths of the intervals on the edges to which it is connected (on each end). If the edge is connected to multiple graded or meshed edges at a single vertex, GAMBIT averages the lengths on the graded/meshed edges in the region surrounding the connecting vertex to determine the appropriate first interval length on the ungraded edge.

Non-Symmetric Grading Schemes

For each of the non-symmetric grading schemes, GAMBIT positions mesh nodes along the edge such that the ratio of any two succeeding interval lengths is constant. That is,

where and are the lengths of intervals i and i+1, respectively, and R is a fixed value (see Figure 3-20). For any given number of intervals (n), the grading schemes differ from each other only with respect to the manner in which GAMBIT determines the value of the interval length ratio, R.

Figure 3-20: Edge mesh grading parameters

NOTE: When you mesh an edge, GAMBIT positions the mesh nodes based, in part, on the edge element type as currently specified on the Set Edge Element Type form (see "Set Edge Element Type," below).
  • If you specify 2-node edge elements, GAMBIT creates mesh nodes only at the endpoints of the edge mesh intervals.
  • If you specify 3-node edge elements, GAMBIT creates an additional mesh node at the center of each mesh interval.
For example, if you specify the 3-node edge element type and grade an edge such that it includes five mesh intervals, GAMBIT creates 11 mesh nodes on the edge. Six of the mesh nodes define the endpoints of the mesh intervals; the other five are located at the centers of the intervals.

The mesh node locations presented throughout this section are based on the 2-node edge element type.

Grading Scheme Input Parameters

For all non-symmetric grading schemes other than the Exponent scheme, the interval length ratio, R, is a function of the following parameters:

For the Exponent scheme, R is a function of L, n, and a user-specified input parameter, x.

The following table lists the formulas that GAMBIT uses to determine the interval length ratios (R) for each of the non-symmetric grading schemes. The table also lists the pertinent input parameters and the corresponding titles of the input fields on the Mesh Edges form.

Scheme Formula Parameter Field Title
Successive Ratio None R Ratio
First Length Length
Last Length Length
First Last Ratio Ratio
Last First Ratio Ratio
Exponent x Ratio

As an example of the differences between input parameters for the non-symmetric grading schemes, consider the straight, graded edge shown in Figure 3-21. The edge possesses a length of 15 units (L = 15) and is to be graded such that it contains four intervals (n = 4), each of which is twice as long as the previous interval (R = 2).

Figure 3-21: Edge grading example

The grading parameters required by each of the non-symmetric schemes to create the grading shown in Figure 3-21 are as follows.

Scheme Ratio Length
Successive Ratio 2  
First Length   1
Last Length   8
First Last Ratio 0.125  
Last First Ratio 8  
Exponent 0.6848  

Double-Sided Grading

When you grade or mesh an edge using any non-symmetric scheme other than the Last Length or Exponent schemes, GAMBIT allows you to specify whether the grading scheme is single-sided or double-sided. (NOTE: To apply an Expo­nent scheme to two segments of a single edge, use the Bi-exponent sym­metric grading scheme (see below).) Double-sided grading differs from single-sided grading in that the edge is divided into two separate segments for grading purposes, and each segment is graded according to its own grading parameter. (NOTE: GAMBIT does not allow you to specify differ­ent grading schemes for each segment.)

Center of Grading

When you specify double-sided grading, GAMBIT positions either a node or an interval at the center of grading for the edge. The form of the grading center (node or interval) depends on the total number of edge intervals (n) as follows (see Figure 3-22).

Figure 3-22: Double-sided grading—location of grading center

The location of the center node (n even) or the location and size of the center interval (n odd) is determined according to the following rules.

As an example of the effect of interval number on double-sided grading, consider the edge shown in Figure 3-23. The edge possesses a length of 8 units and is to be graded such that R1 = 1.5 and R2 = 1.0.

Figure 3-23: Double-sided grading scheme-example

Figure 3-24 and Figure 3-25 show the effect of specifying 7 and 8 intervals, respectively, on the grading of the edge shown in Figure 3-23.

Figure 3-24: Double-sided grading scheme, n = 7

Figure 3-25: Double-sided grading scheme, n = 8

The following table lists the interval lengths for the double-sided grading schemes shown in Figure 3-24 and Figure 3-25.

Interval Figure 3-24
n = 7
Figure 3-25
n = 8
1 0.44 0.37
2 0.66 0.56
3 0.99 0.83
4 1.48 1.25
5 1.48 1.25
6 1.48 1.25
7 1.48 1.25
8   1.25

Note that, if you specify seven intervals for the edge (n = 7), GAMBIT grades the edge such that the length of the center interval satisfies the grading ratios for both edge segments (see Figure 3-24). That is,

and

If you specify eight intervals for the edge (n = 8), GAMBIT grades the edge such that the lengths of the intervals on either side of the center node are equal (see Figure 3-25). That is,

and

Double-Sided Grading Input Parameters

When you grade or mesh an edge by means of a double-sided grading scheme, you must specify grading parameters for both segments of the edge. The following table lists double-sided grading input parameters as they appear on the Mesh Edges form for each of the available grading schemes. (For descriptions of the parameters, see Figure 3-22.)

Scheme Parameter Field Title
Successive Ratio

Ratio 1

Ratio 2

First Length

Length 1

Length 2

First Last Ratio

Ratio 1

Ratio 2

Last First Ratio

Ratio 1

Ratio 2

As an example of the specification of double-sided grading input parameters, consider the examples shown in Figure 3-24 and Figure 3-25, above. The following tables list the parameters that are required to create the grading schemes shown in the figures.

Double-sided grading input parameters, Figure 3-24 (n = 7):

Scheme Ratio 1 Ratio 2 Length 1 Length 2
Successive Ratio 1.5 1    
First Length     0.44 1.48
First Last Ratio 0.297 1    
Last First Ratio 3.36 1    

Double-sided grading input parameters, Figure 3-25 (n = 8):

Scheme Ratio 1 Ratio 2 Length 1 Length 2
Successive Ratio 1.5 1    
First Length     0.37 1.25
First Last Ratio 0.297 1    
Last First Ratio 3.36 1    

Symmetric Grading Schemes

GAMBIT provides two symmetric grading schemes for edge meshing:

Both schemes grade a given edge such that mesh node placement is symmetric about the center of the edge. The schemes differ from each other in the manner in which GAMBIT determines the mesh node spacing along the edge.

Bi-Exponent Scheme

The Bi-exponent scheme divides the edge into two segments of equal length and applies the Exponent grading scheme separately to each segment. The Exponent input parameter, x—specified by means of the Ratio field on the Mesh Edges form-produces the following grading characteristics for the Bi-exponent scheme.

x Grading Characteristic
< 0.5 Mesh nodes are densest near the center of grading and least dense near the endpoints of the edge.
= 0.5 Mesh nodes are evenly spaced along the entire edge.
> 0.5 Mesh nodes are densest near the endpoints of the edge and least dense near the center of grading.

Bell Shaped Scheme

The Bell Shaped scheme grades the edge such that the mesh node density obeys a normal distribution centered at the geometric center of the edge. The user-specified input parameter for the Bell Shaped scheme-specified by means of the Ratio field on the Mesh Edges form-produces grading characteristics identical to those shown above for the Bi-exponent scheme.

Specifying Node Spacing

The interval length ratio, R, is a function of both the edge length, L, and the number of intervals, n (see above). GAMBIT provides three different ways to specify the number of intervals on an edge.

Interval Count

When you select the Interval count option, you must input the actual number of mesh intervals to be placed on the edge. GAMBIT grades or meshes the edge with enough nodes to result in the specified number of intervals. That is,

where m is the total number of mesh nodes on the edge, including the endpoints. For example, if you specify an interval count of 6 (n = 6), GAMBIT grades or meshes the edge with 7 nodes (m = 7), thereby creating 6 intervals on the edge.

Interval Size

When you select the Interval size option, you must input an interval length. GAMBIT uses the interval length to determine the total number of intervals on the edge according to the following equation:

where n is the number of intervals on the edge, L is the edge length, and d is the interval size (user input). If n is a non-integer, GAMBIT rounds to the nearest whole number to determine the number of intervals on the edge.

Shortest Edge (%)

When you select the Shortest edge (%) option, you must input an interval size value expressed as a percentage of edge length. GAMBIT calculates the global interval size (d) for the current edge-meshing operation as follows:

where x is the Shortest edge (%) input value, and is the length of the shortest edge currently existing in the entire model. (NOTE: When you select the Shortest edge (%) option, GAMBIT highlights the graphics window display of the shortest edge.)

GAMBIT uses the resulting value of d to calculate the total numbers of intervals for all edges specified for the current edge-meshing operation. For example, if the shortest edge in the model is 10 units in length, and you mesh an edge that is 30 units long and specify the Shortest edge (%) option with x = 20 (%), GAMBIT calculates the number of intervals, n, on the meshed edge as follows:

Therefore, GAMBIT creates 15 intervals on the meshed edge.

Specifying Edge Meshing Options

GAMBIT provides the following edge meshing options:

If you select the Mesh option, GAMBIT creates mesh nodes when it applies the grading specifications listed on the Mesh Edges form. If you Apply the currently specified parameters without selecting the Mesh option, GAMBIT applies the node distribution parameters to the edge(s) but does not create mesh nodes.

If you select the Remove old mesh option, GAMBIT deletes any currently existing mesh and/or grading information from the specified edge(s).

If you select the Ignore size functions option, GAMBIT ignores any existing size-function specifications that would otherwise affect the edge mesh.

NOTE: If you attempt to grade or mesh an edge that serves directly as an attachment entity for an existing size function or is part of a higher-topology entity that serves as an attachment entity for a size function, GAMBIT suspends the temporary display of edge mesh nodes until the background grid is generated. For example, if you attach a size function to a brick-shaped volume and attempt to grade or mesh one of the volume edges before meshing the volume, GAMBIT suspends the temporary display of mesh nodes for the edge. However, if you mesh one of the other edges before attempting to grade or mesh the edge (thereby generating the background grid for the size function), GAMBIT enables the temporary display of mesh nodes for the edge.

To enable the temporary display of the mesh nodes and assign the specified grading parameters to an edge such as that described above, you must select the Ignore size functions option on the Mesh Edges form.

Using the Mesh Edges Form

To open the Mesh Edges form (see below), click the Create Mesh command button on the Mesh/Edge subpad.

The Mesh Edges form contains the following options and specifications.

Edge and Soft-link Specifications

Edges specifies one or more edges to which the currently specified grading and/or meshing operations apply.
Pick with links specifies that all edges hard-linked or soft-linked to the picked edge(s) are graded and/or meshed according to the currently specified grading scheme.
Reverse reverses the sense and grading of all specified edges.

NOTE: If the Pick with links option is selected (see above), the Reverse command button reverses the sense of all edges selected by means of the Edges list box as well as all edges linked to those edges.

Soft link
Form
Break
Maintain
specifies whether soft links are formed, broken, or maintained during the edge meshing process.
  • Form—forms soft links between all specified edges
  • Break—breaks existing soft links associated with the specified edges
  • Maintain—maintains all current soft links
Use first edge settings imposes the grading and spacing parameters of the first edge specified in the Edges list on all other edges in the list.
Grading
Apply specifies that the currently displayed grading specifications are applied to all picked edges.
Default

resets grading specifications to their default values.

Type
Successive Ratio
First Length
Last Length
First Last Ratio
Last First Ratio
Exponent
Bi-exponent
Bell Shaped
specifies the grading scheme (see "Specifying the Grading Scheme," above).
Invert converts currently specified grading-scheme lengths or ratios into their reciprocal values. For example, if you specify Successive Ratio grading with a First Ratio of 2.5, the Invert command button converts the First Ratio to 0.4. That is,

Double sided

specifies that all specified edges are graded according to a double-sided scheme. (NOTE: This option is not available for the Last Length, Exponent, Bi-exponent, or Bell Shaped schemes.)

Grading Parameters

The middle section of the Mesh Edges form contains slide bars that allow you to specify grading parameters. GAMBIT displays only those slide bars that are applicable to the currently specified grading scheme. The following subsections describe the parameters associated with the slide bars for each of the five grading types. For a detailed description of the parameters associated with each type of grading, see "Grading Scheme Input Parameters," above.

Successive-Ratio Parameters

Ratio (single-sided) specifies the ratio of successive interval lengths (R) along all specified edges.
Ratio 1 (double-sided) specifies the ratio of successive interval lengths (R) along the segments of all specified edges nearest to their respective start vertices.
Ratio 2 (double-sided) specifies the value of R along the segments of all specified edges nearest to their respective end vertices.

First-Length Parameters

Length (single-sided) specifies the length of the first interval on all specified edges ().
Length 1 (double-sided) specifies the length of the first interval on the segments of the specified edges nearest to their respective start vertices ().
Length 2 (double-sided) specifies the length of the first interval on the segments of the edges nearest to their respective end vertices ().

Last-Length Parameters

Length specifies the length of the last interval on all specified edges ( ).

First-Last Ratio Parameters

Ratio (single-sided) specifies the ratio of the first interval length to the last interval length on the specified edges ( ).
Ratio 1 (double-sided) specifies the ratio of the first interval length to the last interval length on the segments of the specified edges nearest to their respective start vertices ( ).
Ratio 2 (double-sided) specifies the ratio of the first interval length to the last interval length on the segments of the specified edges nearest to their respective end vertices (

Last-First Ratio Parameters

Ratio (single-sided) specifies the ratio of the last interval length to the first interval length on the specified edges ().
Ratio 1 (double-sided) specifies the ratio of the last interval length to the first interval length on the segments of the specified edges nearest to their respective start vertices ().
Ratio 2 (double-sided) specifies the ratio of the last interval length to the first interval length on the segments of the specified edges nearest to their respective end vertices ( ).

Exponent Parameter

Ratio specifies the input parameter, x, that determines the ratio (R) of successive interval lengths for the Exponent grading scheme (see above).

Bi-exponent Parameter

Ratio specifies the input parameter, x, that determines the ratio (R) of successive interval lengths for the Bi-exponent grading scheme (see above).

Bell Shaped Parameter

Ratio specifies the input parameter, x, that determines the shape of the mesh node distribution for the Bell Shaped grading scheme.

Mesh Node Spacing Parameters

Spacing
Apply specifies that the currently displayed spacing parameters are applied to all specified edges.
Default resets mesh node spacing specifications to their default values.
Interval size
Interval count
Shortest edge (%)
specifies the method used to determine the total number of mesh nodes on any edge. The three available methods are as follows:
  • Interval size—specifies the size of intervals (constant ratio grading only)
  • Interval count—specifies the number of intervals along the edge
  • Shortest edge (%)—specifies that the interval size represents a percentage of the length of the shortest edge in the list of specified edges
Value specifies a numerical value associated with the method used to determine the total number of intervals on any edge.

Grading and Meshing Options

Options
Mesh specifies that the edges are to be meshed. If you do not specify the Mesh option, GAMBIT grades but does not create mesh nodes on the edges.
Remove old mesh specifies that any existing mesh nodes and/or elements are removed from the edges.
Ignore size functions specifies that GAMBIT ignores any existing size-function specifications that would otherwise affect the edge mesh.


3.2.2 Set Edge Element Type

The Set Edge Element Type operation (default set command for the MESH.NODES.EDGE default variable) specifies the number of edge nodes upon which all face and volume meshes are based.

The edge element type determines the number of edge mesh nodes corresponding to face and volume elements in the model. There are two edge element type options:

When you specify the 2 node option, GAMBIT creates meshes such that every edge node constitutes one endpoint of an mesh edge element and, therefore, one corner of a mesh face or volume element. When you specify the 3 node option, GAMBIT creates an additional mesh node in the center of each edge mesh element. As a result, only two out of every three edge mesh nodes constitute corners of mesh face or volume elements.

Figure 3-26 shows the effect of edge element type on quadrilateral face mesh elements. In Figure 3-26(a), the edge element type is specified as 2 node, therefore, each edge mesh node constitutes one corner of a face element. In Figure 3-26(b), the edge element type is specified as 3 node, therefore, only two out of every three edge mesh nodes constitute corners of face elements.

Figure 3-26: 2 node and 3 node edge element types

The Effect on Face and Volume Element Types

When you change the edge element type specification, GAMBIT automatically changes all corresponding face and volume element types. Likewise, when you change the face or volume element types, GAMBIT automatically changes the edge element type. The following table summarizes the general correspondence between GAMBIT edge, face, and volume element types.

Edge Face Volume
Nodes Shape Nodes Shape Nodes
2 Triangle

Quadrilateral

3

4

Tetrahedral

Hexahedral

Wedge

Pyramid

4

8

6

5

3 Triangle

Quadrilateral

6

9

Hexahedral

Tetrahedral

Wedge

Pyramid

27

10

18

13

For a description of the face and volume element types listed above, see "Set Face Element Type" and "Set Volume Element Type," below.

Using the Set Edge Element Type Form

To open the Set Edge Element Type form (see below), click the Set Edge Element Type command button on the Mesh/Edge subpad.

The Set Edge Element Type form contains the following options.

2 node specifies that the mesh is based on two-node edge mesh elements.
3 node specifies that the mesh is based on three-node edge mesh elements.


3.2.3 Link/Unlink Edge Meshes

The Link/Unlink Edge Meshes command button allows you to perform the following operations.

Symbol Command Description
Link Edge Meshes Creates hard links between edges
Unlink Edge Meshes Deletes hard links between edges

The following sections describe the procedures and specifications required to execute the operations listed above.


Link Edge Meshes

The Link Edge Meshes operation (edge link command) creates a hard link between edges. When you create hard links between edges in a set, GAMBIT associates the edges with each other such that any meshing or splitting operation applied to one or more of the edges is similarly applied to all edges in the set. For example, if you grade or mesh an edge that is hard-linked to another edge, GAMBIT grades or meshes both edges according to the grading scheme and parameters applied to the specified edge. Likewise, if you split an edge that is hard-linked to another edge, GAMBIT splits both edges.

NOTE: When you select an edge for the Link Edge Meshes operation, GAM­BIT automatically highlights the graphic display of any edges to which the edge is currently linked.

Linking Edge Endpoint Vertices

When you hard-link a set of edges, GAMBIT automatically creates hard links between the endpoint vertices of the edges. The vertex links are created such that the start endpoint vertices of all edges in the set are hard-linked to each other, and the end endpoint vertices of all edges in the set are hard-linked to each other.

GAMBIT does not allow you to hard-link two edges if their endpoint vertices are already linked to each other by means of an existing hard link. As an example of this restriction, consider the set of connected edges shown in Figure 3-27.

Figure 3-27: Edge hard-link restriction—example

If you create a hard link between edge.1 and edge.4 (Link 1), GAMBIT does not allow you to also create a hard link between edge.2 and edge.3 (Link 2), because vertex.1 and vertex.2 are already linked to vertex. 3 and vertex.4, respectively.

Reversing the Grading Orientation

When you select an edge for hard-linking, GAMBIT allows you to reverse the orientation of the grading on the edge relative to its start and end vertices. To reverse the grading orientation of an edge, Shift-middle-click the edge in the graphics window when selecting it for hard-linking. (NOTE: If you reverse the grading orientation, GAMBIT does not change the sense of the edge.)

As an example of the effect of reversing the grading orientation, consider the two hard-linked edges shown in Figure 3-28, one of which is meshed using a successive-ratio grading scheme with a first ratio of 2.

Figure 3-28: Linked edge meshes—effect of reverse orientation

If you do not reverse the grading orientation, the grading scheme for edge.1 is exactly duplicated on edge.2 (see Figure 3-28(a)). If you do reverse the grading scheme, the grading scheme on edge.2 is exactly reversed relative to that of edge.1 (see Figure 3-28(b)).

Specifying the Periodic Option

The Link Edge Meshes command includes a Periodic option that allows you to specify that the specified edges are periodically linked. Periodically linked edges are constrained such that they must behave identically to each other with respect to any virtual edge-split and vertex-move operations.

As an example of the effect of periodic linking, consider the square, planar face shown in Figure 3-29, two edges (edge.1 and edge.3) of which are hard-linked to each other.

Figure 3-29: Virtual splitting of two hard linked edges

If you perform a virtual split of edge.1 at the split point shown in Figure 3-29(a), GAMBIT splits both edges to create the geometric entities shown in Figure 3-29(b). (NOTE: In this example, the hard link was created such that the grading orientations of edge.1 and edge.3 point in the same direction, therefore v_edge.5 and v_edge.7 are equal in length. If the grading orientations had opposed each other when the link was created, v_edge.8 would be equal in length to v_edge.5, and v_edge.7 would be equal in length to v_edge.6).

If you move v_vertex.5 in Figure 3-29 by means of the Slide Virtual Vertex command (see Section 2.2.2), the final state of v_vertex.6 depends on two factors:

Specifically, the rules governing the vertex move can be summarized as follows (see Figure 3-30):

Periodic link Move with links option Move v_vertex.6 Figure 3-30
Yes On Yes (a)
Yes Off Yes (a)
No On Yes (a)
No Off No (b)

For example, if edge.1 and edge.3 are periodically linked, GAMBIT moves v_vertex.6 regardless of the state of the Move with links option. Likewise, if you specify the Move with links option, GAMBIT moves v_vertex.6 regardless of whether the link between edge.1 and edge.3 is periodic.

Figure 3-30: v_vertex.6 move states—Periodic and Move with links options

Using the Link Edge Meshes Form

To open the Link Edge Meshes form (see below), click the Link command button on the Mesh/Edge subpad.

The Link Edge Meshes form contains the following specifications.

Edges specifies the edges to be hard-linked.
Periodic specifies that the edges are to be periodically linked.


Unlink Edge Meshes

The Unlink Edge Meshes operation (edge unlink command) deletes existing hard links associated with one or more edges. When you unlink an edge, GAMBIT deletes the link(s) between the specified edge and the edge to which it is hard-linked.

NOTE: When you select an edge for the Unlink Edge Meshes operation, GAM­BIT automatically highlights the graphic display of any edges to which the edge is currently linked.

Using the Unlink Edge Meshes Form

To open the Unlink Edge Meshes form (see below), click the Unlink command button on the Mesh/Edge subpad.

The Unlink Edge Meshes form contains the following specifications.

Edge specifies the edge(s) for which the hard link is to be deleted.
Lower topology specifies that all vertex hard links that are associated with the specified edge are deleted along with the corresponding edge hard links.


3.2.4 Split Meshed Edge

The Split Meshed Edge operation (edge split meshnode command) splits a real or non-real edge at a mesh node.

When you split an edge at a mesh node, GAMBIT splits the edge into two virtual edges that share a common virtual endpoint vertex. The common vertex is located at the position of the specified node.

When you specify the edge to be split, GAMBIT displays its existing mesh in the graphics window. To specify the exact mesh node at which the edge is to be split, either pick the node in the graphics window (using the mouse) or select the mesh node by means of the Mesh Node pick-list form.

Using the Split Meshed Edge Form

To open the Split Meshed Edge form (see below), click the Split Edge command button on the Mesh/Edge subpad.

The Split Meshed Edge form contains the following specifications.

Edge specifies the edge to be split.
Split With
Node specifies the node at which the edge is to be split.


3.2.5 Summarize Edge Mesh

The Summarize Edge Mesh operation (edge msummarize command) displays edge mesh information in the Transcript window and allows you to highlight specific mesh nodes and/or edge mesh elements in the graphics window. The command requires three input parameters:

Specifying the Component Type

To summarize edge mesh information in the Transcript window, you must specify the type of mesh components to be included in the summary. Each edge mesh includes two component types:

The type of edge mesh summary information displayed in the Transcript window depends on the component type (see "Edge Mesh Summary Information," below).

Selecting Specific Components

GAMBIT provides two methods for selecting specific components (elements or nodes) to be included in the edge mesh summary:

In most cases, it is preferable to pick the components in the graphics window, rather than selecting them by means of a pick list, because the component labels (element or node numbers) are not known prior to component selection.

To pick the components in the graphics window:

  1. Select the appropriate Component option (Elements or Nodes).
  2. Click (to activate) the appropriate (Elements or Nodes) pick-list field.
  3. Shift-left-click in the graphics window to select each element or node to be included in the summary.
To select the components by means of a pick list:
  1. Select the appropriate Component option (Elements or Nodes).
  2. Click the appropriate (Elements or Nodes) pick-list button to open the Mesh Edge List (Multiple) or Mesh Node List (Multiple) form.
  3. On the Mesh Edge List (Multiple) or Mesh Node List (Multiple) form, click the All–> pushbutton to populate the list with all elements or nodes associated with the specified edge.
  4. In the Mesh Edge List (Multiple) or Mesh Node List (Multiple) list, select (highlight) the elements or nodes to be excluded from the summary.
  5. Click the <– – – pushbutton to remove the selected (highlighted) elements or nodes from the list.
NOTE: The Mesh Edge List (Multiple) and Mesh Node List (Multiple) forms do not include the Available list field that is included on most pick-list forms because of the number of items that might need to be included in the list field. A fully meshed model can contain tens of thousands of edge mesh elements or nodes, each of which constitutes an Available component. If the Mesh Edge List (Multiple) or Mesh Node List (Multiple) form included an Available list field, GAMBIT would need to compile the Available list before opening the form, thereby delaying the appearance of the form on the GUI.

When you specify any component (element or node) to be included in the edge mesh summary, GAMBIT highlights the component in the graphics window. If you select the Element labels and/or Node labels options, GAMBIT also displays the element and/or node numbers associated with the specified components (see Figure 3-31).

Figure 3-31: Edge mesh element and node numbering display

Edge Mesh Summary Information

As noted above, the type of edge mesh summary information displayed in the Transcript window depends on the type of component being summarized. For example, element summaries include node connectivity information, which is not available in node summaries.

Elements Summary Information

If you select the Elements option, the edge mesh summary includes the following information for each specified element.

NOTE: For edge mesh summary information, the element type is always "edge" and the number (count) of nodes associated with each element is always "2".

For example, if you select an Elements summary for the edge and highlighted elements shown in Figure 3-31, above, GAMBIT displays the following information in the Transcript window.

Total nodes: 6
Total elements: 3
 Element     Type         Count        Connectivity
----------- --------- ------------ ----------------------
      1       edge          2:             1    3
      3       edge          2:             4    5
      4       edge          2:             5    6
In this case, the summary indicates that element 3 is an edge mesh element connected to nodes 4 and 5.

Nodes Summary Information
If you select the Nodes option, the edge mesh summary includes the following information for each specified node. For example, if you select a Nodes summary for the edge and highlighted nodes shown in Figure 3-31, above, GAMBIT displays the following information in the Transcript window.
Total nodes: 6
Total elements: 3
Coordinate System: c_sys.1

   Node        x          y         z        Owner
----------- --------- ---------- --------- -------------
      1       5.0000     5.0000   -5.0000   vertex.4
      3       5.0000     3.0000   -5.0000   edge.3
      4       5.0000     1.0000   -5.0000   edge.3
      5       5.0000    -1.0000   -5.0000   edge.3
      6       5.0000     3.0000   -5.0000   edge.3
In this case, the summary indicates that node 1 is located at the position (5, 5, -5) and is associated with ("owned by") vertex.4.

Using the Summarize Edge Mesh Form

To open the Summarize Edge Mesh form (see below), click the Summarize command button on the Mesh/Edge subpad.

The Summarize Edge Mesh form contains the following options and specifications.

Edge specifies the edge for which summary information is to be displayed.
Component
Elements displays summary information for specified elements.
All
Pick
specifies whether the edge mesh summary information includes all elements or only selected elements.
Pick specifies the elements for which mesh sum­mary information is to be displayed.
Element labels displays labels (numbers) in the graphics window for all specified elements.
Node labels displays labels (numbers) in the graphics window for all nodes associated with the specified elements.
Nodes displays summary information for specified nodes.
All
Pick
specifies whether the edge mesh summary information includes all nodes or only selected nodes.
Pick specifies the nodes for which edge mesh sum­mary information is to be displayed.
Node labels displays labels (numbers) in the graphics window for all specified nodes.


3.2.6 Delete Edge Meshes

The Delete Edge Meshes operation (edge delete onlymesh command) deletes the mesh (and, optionally, mesh grading information) on one or more edges.

Using the Delete Edge Meshes Form

To open the Delete Edge Meshes form (see below), click the Delete command button on the Mesh/Edge subpad.

The Delete Edge Meshes form contains the following specifications.

Edges specifies the edge(s) from which the mesh is to be deleted.
All
Pick
  • All specifies all edges in the model.
  • Pick specifies edges selected by means of the Edges list box.
Reset to default values resets the grading parameters associated with the specified edge(s) to their default values.


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