Introduction
This tutorial illustrates a number of tools and methods that can fine-tune a mesh or repair imported geome-try. To demonstrate these, four examples are presented. The first is of a sheet metal part (“Automesh Tu-torial 5a.IGS”) with poor geometry definition. The second is a detailed 3 dimensional model (“Automesh Tutorial 5b.SAT”) that includes a number of features that are unnecessary for analysis purposes. The third example focuses on the meshing of a single face of the model used in the second example. The last example demonstrates the use of the Surface Automeshing tool’s custom settings and vertex attributes for local mesh control.
Example 1
The geometry of a sheet metal part (Figure 1), is composed of two separate faces. The figure displays the wireframe, vertices and free edges of this geometry. Note that the geometry is invalid for analysis purposes as there are free edges between the two faces (the free edges along the perimeter of the model are expected as this is a surface-only model). In addition, there are a number of vertices that are not necessary for meshing.
The geometry is cleaned using the default settings.
Figure 1. Geometry of the Sheet Metal Part example
The cleaned geometry is shown in Figure 2 with free edges existing only along the perimeter of the sheet metal part. Note that intermediate vertices have been removed. This geometry is ready to be meshed. Figure 3 shows the part meshed with a relative Maximum Edge Length of 4%.
A visual inspection of this mesh shows that a line of high aspect ratio elements borders the edge that connects the two faces. The accuracy of such elements will not be very high. These elements are due to the very nar-row face. This can be eliminated by cleaning the face such that the thin region that joins the two larger re-gions is removed. This procedure will then convert the lower face into two separate faces. Performing such
Figure 2. Cleaned geometry
Figure 3. Meshed part
a clean requires knowing the width of the narrow portion. In this example, the width is equal to the shortest edge near the chamfer of the same face. Figure 4 shows the Entity Inspector displaying the length of this edge.
The length of the shortest edge is 6.35. To remove these edges along with the narrow region, the geometry should be cleaned with a Minimum Edge Length that is greater than this value. Figure 5 shows the result of the geometry cleaned with an absolute Minimum Edge Length of 7.0. It can be seen that the resulting clean-ing operation has split the sclean-ingle face into two.
Figure 4. Entity Inspector displaying edge length
Figure 5. Cleaned geometry with the narrow region removed
Meshing the geometry of Figure 5 using the same settings used in the previous automesh, results in the mesh of Figure 6. This mesh does not suffer from the inclusion of high aspect ratio elements and would be pre-ferred for analysis. It is important to note that if you intend to mesh this part at a mesh size near to 6.35 (the shortest edge size of the uncleaned geometry), you should not perform the defeaturing shown here.
Example 2
Figure 7 displays the solid CAD model of an embossed bracket with 3 holes. When imported, it displays as shown in Figure 8. The imported geometry shows two additional cylinders. These are holes in the original model that have been ‘plugged’ with solid cylinders. For analysis, such plugged holes must be corrected.
More importantly, the embossing is unnecessary for analysis purposes and should also be removed, otherwise an unnecessarily large mesh would be generated.
Figure 6. Meshed geometry
The cylinders representing the bores of the plugged holes can be removed by first ensuring that the Toggle Face Select button is on and then selecting the entities and pressing the Delete key. The circles that define the ends of the holes on the bracket face, on the other hand, are not as straightforward to remove. An attempt to select these will instead select the entire face to which these circles are connected. By right-clicking the Toggle Face Select button on the main menu bar, two icons will appear denoting whether geometry faces are to be selected or only geometry loops are to be selected. The latter option can be used to select circles or other internal loops (cavities) that may be part of a larger face. Removal of the remaining circles in the model then involves setting the Toggle Select Loop button on, selecting these circles and pressing Delete. Fig-ure 9 shows only these circles being selected.
Figure 7. Bracket CAD model
Figure 8. Imported Bracket geometry
The embossing may be removed manually by selecting each face that comprises the embossing. This is a slow process that can be expedited by using the Select Connected Entities tool. However, the embossing geometry is connected to the bracket geometry, which would mean that selecting all entities connected to a face on the embossing would select the entire geometry. Because the Select Connected Entities function can apply to only entities that are drawn, this problem can be avoided by not displaying the face that the embossing is connect-ed to. To hide this face, first select it and then click Hide Selectconnect-ed. Figure 10 shows the result of such an action.
Figure 9. Circular ends of the plugged holes selected with Toggle Loop Select on
Figure 10. Geometry with selected faces hidden
The Select Connected Entities function can then be used on only the embossing. After clicking the Select Con-nected Entities toggle, a dialog appears prompting you to select a Master Entity of a specified Entity Type.
Note that by default the Select Connected Entities tool does not consider hidden entities, which in this example is what is required. Upon selecting a single face of one of the letters of the embossing click Apply to select all visible entities connected to it. This action selects the entire letter. Press Delete to remove these selected entities. Figure 11 shows the Select Connected Entities dialog along with a letter of the embossing selected with the tool.
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Once all the letters of the embossing have been removed, the faces of the bracket that were hidden can be displayed again by clicking the Show Selected Entities toggle. Viewing the face that the embossing was con-nected to will then reveal the outlines of the removed embossing, as shown in Figure 12. Removal of these can be performed after selecting these entities with the Toggle Loop Select function. Figure 13 shows the com-pleted model.
Figure 11. Select Connected Entities tool used to select the embossing
Example 3
To focus on the fine-tuning of generating a surface mesh, only the front face of the previous example will be used for this example. This then involves the removal of all other faces, which can be done by selecting the front face and then inverting that selection by clicking the Select All button. Figure 14 shows the result of
Figure 12. Outlines left after the removal of the embossing
Figure 13. Completed model without extraneous features
this action. Press Delete when the selection has been made. Figure 15 is a plan view of the remaining front face with vertices displayed.
The result of using the Surface Automeshing tool with the default settings is shown in Figure 16. From the figure, it is clear that there is a clustering of elements about the top left chamfer. To see why this is the case, the meshing operation can be undone by clicking the Undo button and displaying the geometry by clicking the Show Geometry toggle. Focusing on this area reveals a number of closely spaced vertices (Figure 17).
Figure 14. All but front face selected
Figure 15. Front face
The close spacing of the vertices has a significant effect on the resulting mesh. This is because the Surface Automeshing tool will always position a node at every vertex. This then means that a clustering of elements will be created around the region. The extra vertices can be removed and the curvature of the geometry in Figure 15 retained by using the Clean Geometry tool with an appropriate Merging Angle setting. The Merging Angle determines at what interior angle (defined by the tangents of two edges) a vertex gets removed. If the interior edge angle at a vertex is greater than the Merging Angle, that vertex is removed. This function is useful for removing unnecessary vertices that are positioned along straight or near-straight edges. Applying
Figure 16. Meshed face
Figure 17. Top left corner of the face
the Clean Geometry tool with a Merging Angle of 140° results in the geometry and vertices as shown in Figure 18. This operation has eliminated all 4 vertices positioned along the chamfer.
The Surface Automeshing operation can then be reapplied to the geometry. The resulting mesh is as shown in Figure 19.
Figure 18. Cleaned geometry
Figure 19. Meshed geometry
The result of an automeshing operation can be fine tuned by using the Custom Settings in the Surface Au-tomeshing dialog (Figure 20). The following will offer an overview of the four extra settings.
The Length ratio setting can be used to specify the minimum edge length that can be created by any one ele-ment (with exception of eleele-ments that connect closely spaced vertices as seen in Figure 16). By default the Length ratio is set to 0.1, which means that the minimum element size created will be limited to 10% of that specified by the Maximum Edge Length setting. To highlight the use of this setting the face of Figure 18 is remeshed with a Maximum Edge Length of 10% and a Length ratio of 0.01. This setting should allow for relatively large and relatively small elements to be created in the one mesh. Figure 21 shows the result of this setting. Here, the curvature of the circular holes is well defined with small elements, which quickly grow into larger elements with distance away from the holes.
The change in element size across faces of a geometry can be controlled with the Maximum Increase setting.
This defines the percentage difference in edge length that is allowed between neighbouring elements. In-Figure 20. Custom Settings dialog
Figure 21. Result of Maximum Edge Length of 10% and Length ratio set to 0.01
creasing this value gives a faster transition in element size from small geometric features to large. Reducing this value maintains a more gradual transition between element sizes. A small Maximum Increase value will produce a better quality mesh, but will introduce more elements. Figure 22 shows the result of repeating the last meshing operation with a Maximum Increase of 8%. The effect of this setting is pronounced when compared to Figure 21. The much more stable gradation of element size has produced more elements overall resulting in a better defined mesh which is most obvious around the centre circle.
Note that it is possible and valid to enter a Maximum Increase of zero. Such a value means that the increase in edge length between neighbouring elements is zero. Therefore the entire mesh will be composed of ele-ments of a size dictated by the smallest edge length or feature in the model.
The Edges per circle setting determines the minimum number of elements to be placed around a circle and, effectively any curved edges. For this example with no closely spaced vertices defining the geometry, the Edg-es per circle setting is the one factor that has forced some elements down to a size that approachEdg-es that defined by the Length ratio. If a circle is so small that to put the minimum number specified means that the edge length of those elements will be smaller than that defined by the Length ratio, then the number created around that circle will be less than the minimum specified. Instead only the maximum number of elements of the minimum size that can fit around that circle will be created. The minimum value that can be assigned to the Edges per circle setting is 8. Figures 23 and 24 show the result of repeating the last operation with Edges per circle set to 8 and 34, respectively.
Figure 22. Mesh with Maximum Increase of 8%
The fourth parameter that is part of the Custom Settings determines on which edges the Edges per circle setting should be applied. By default this value is set to 0.0, meaning that the Edges per circle setting is applicable to all edges. However, if this value is set to a value that is greater than the circumference of a particular circle, that circle will not necessarily be assigned the specified minimum number of edges. For example, Figure 25 is the result of repeating the last meshing operation with the fourth setting (...on edges longer than) set to 10mm, which is larger than the edge length (circumference) of the two smaller circles.
Figure 23. Mesh with Edges per circle set to 8
Figure 24. Mesh with Edges per circle set to 34
The Edges per circle and ...on edges longer than settings are not limited in their application to only circles; these settings apply to any edge with curvature. An edge with curvature has a radius of curvature. Based on the radius of curvature, a circumference is derived. This circumference is compared to the ...on edges longer than setting. If it is greater than that value, the edge is assigned a portion of the elements defined by the Edges per circle value, corresponding to the ratio of the edge length and the circumference of a circle with the same curvature. For example if an edge has a length of 10mm and is shaped as a quarter arc of a circle, it is con-sidered as a circle of length (circumference) 40mm. An ...on edges longer than setting of less than 40mm will assign the minimum number of elements to that edge.
The custom settings in the Surface Mesh dialog are not the only way to control or fine tune a mesh. Much more control is afforded through the use of the Mesh Size attribute and the creation of new vertices. The use of attributes applied to geometric entities such as vertices was discussed in Tutorial 1. The following de-scribes how the Mesh Size attribute and creation of new vertices can be used to change the local mesh density.
Consider that at the bottom left portion of the geometry a support is to be modelled via a number of contact elements. This would then require a locally dense mesh. A locally dense mesh can be enforced by adding a number of vertices that can be used to delimit the region. Create two vertices along the bottom of the left straight edge via the following procedure:
1
Click CREATE, Vertex;2
Select the left straight edge of the geometry;3
Use the slider tool or specify an absolute or relative edge position in the dialog (Figure 26);4
Click Apply.Figure 25. Mesh with ...on edges longer than set to 10mm
After the two vertices have been created, the mesh size that is to be enforced at the region delimited by the vertices can be assigned. The mesh size that is specified is the edge length of elements that will surround the vertex and is given as an absolute value in the current length unit. In this case, a 1mm edge length is desired.
If two neighbouring vertices are assigned a mesh size, then the edge between the two vertices will be linearly interpolated between the vertices. In the case where there is no neighbouring vertex with an assigned mesh size, the mesh size will return to what is ordinarily stipulated by the Auto or Custom settings. The rate of change will follow a geometric progression based on the Maximum Increase value.
To specify a 1mm mesh size along the edge between the two vertices, follow the steps below:
1
Click ATTRIBUTES, Vertex, Mesh Size;2
Select the two newly created vertices;3
Specify a mesh size of 1mm in the dialog (Figure 27);4
Click Apply.Figure 26. Creation of a vertex
The geometry can then be meshed. Figure 28 shows the result (with vertices) when using the Auto setting with a 10% relative edge length. The effect of the two additional vertices is clear.
Figure 27. Vertex Mesh Size attribute
Figure 28. Locally enforced mesh density
Note that the two additional vertices are positioned along a straight edge and do not specify any additional geometric information – their removal would not affect the geometry. Hence, if the Clean Geometry tool was to be used, these vertices would be removed. This can be prevented by changing the vertex type attribute to Fixed Type. To change the Type of a vertex, carry out the following steps:
1
Click ATTRIBUTES, Vertex, Type;2
Select the vertices to be changed;3
Select the type in the dialog (Figure 29);4
Click Apply.To further demonstrate the control provided by the use of the mesh size attribute, additional attributes can be assigned. In this case, the small hole on the right is assigned a relatively fine mesh density, along with a small portion of the right side of the centre hole. To achieve this, create a vertex at the right side of the centre hole. Next assign both this vertex and the vertex at the small hole on the right, a mesh size of 0.25mm. Fig-ure 30 shows the meshed result. Note that the entire small hole inherits this fine mesh size, whereas only a small portion of the larger hole inherits the finer mesh size. This is because the small hole contains only one vertex and the mesh size attribute is therefore applied to the entire edge. You can avoid this if necessary, simply by creating another vertex on the circle, somewhere diametrically opposite the first vertex. This new vertex is not assigned an attribute and hence the mesh is not constrained between the two vertices.
Figure 29. Vertex Type dialog
Example 4
The following figures are intended to further illustrate the use of the Vertex Mesh Size attribute. A square face of edge length 1.5 units is imported. The face is then meshed at 10% and 30% relative edge length, with and without specifying a vertex mesh size at one or both of the top vertices. When a vertex mesh size is spec-ified, it’s value is set to 0.05 units.
Figure 30. Locally enforced mesh density at right side and centre hole
Figure 31. The face
Figure 32. Meshed at 30%
Figure 33. Meshed at 10%
Figure 34. Meshed at 30% with one vertex set to 0.05
Figure 35. Meshed at 10% with one vertex set to 0.05
Figure 36. Meshed at 30% with both vertices set to 0.05
Figure 37. Meshed at 10% with both vertices set to 0.05.