Checking of solid meshes can rely on the use of tools such as contouring more so than surface meshes. This is because, unlike surface meshes, the internal regions of a solid mesh are difficult to visually inspect. Hence, the use of features such as the histogram become even more helpful.
As with plate elements, brick elements can be contoured with a number of attributes that are relevant to mesh quality checking. These include aspect ratio, internal angles, mixed product and dihedral angles.
Similarly to the aspect ratio for plate elements, brick element aspect ratio is defined as the ratio between the longest and shortest edge of that element. An element with an aspect ratio that is far greater than 1 is usually one of low accuracy. Figure 10 shows the bike hub meshed with Tet4 elements contoured by aspect ratio.
From the histogram, it can be seen that the vast majority of elements have an aspect ratio of less than 3. How-ever, there are some that have high aspect ratios, reaching 12.4. It is important to know where such poor elements are located. If they are on the surface or near an area of interest, then it is advisable to improve the original geometry, or refine the surface mesh to improve the solid mesh. A refinement can involve a manual improvement of the surface mesh near the region where the poor element was found or changing the internal element density in the Solid Automeshing dialog.
It is possible to locate the element with the highest aspect ratio by using the Find tool (Figure 11). The Find tool can be activated by clicking Find within the EDIT menu, or by pressing Ctrl + F. The number of the brick with the highest aspect ratio is shown in the legend of Figure 10 as being 18810. Figure 12 shows this element found within the interior of the axle of the hub.
Figure 10. Brick elements contoured by aspect ratio
The internal angle contour option for bricks is identical to the same option for plates. However, the internal angles through the thickness of the solid are not visible if only the surface is displayed. Hence, mesh checking using this contour type relies on the histogram. Figure 13 shows the hub contoured by internal angle. Based on the information given by the histogram, it can be seen that the majority of elements have reasonable in-ternal angles. However, some elements are composed of either highly acute or obtuse angles. The Select by Region tool can be used to only select elements that are located in regions of interest. The entities that are not selected can then be hidden by using the Hide Unselected toggle. This way, the histogram will only graph data available from the bricks that are displayed. If all bricks (particularly those on the surface) within the regions of interest are of an adequate quality, then the solid mesh is suitable for analysis.
Figure 11. The Find tool
Figure 12. Find tool used to locate element with the highest aspect ratio
The mixed product is an indication of how close to square each corner of an element is. Element corners that are square are given a value of one; conversely, those that are not square are given a value less than one. In the case of tetrahedral meshes, ‘squareness’ of corners is not expected for optimal elements. Instead, tetrahe-dral elements should a have a mixed product that is close to 0.707. Figure 14 shows the histogram for the mixed product contour type for the hub mesh.
The dihedral angle is a measure of the internal angle between two connected faces of a brick. For a tetrahe-dron, the optimum dihedral angle is near 72°, for a hexahedron it is 90°. The dihedral angle ratio is a nor-malised measure of how close to the optimum the worst angle in a brick is. Those that are close to optimal are given a value close to 0. Those that contain an angle that is much larger than the optimum are given a ratio close to 1. Conversely, those with an angle much less than the optimum are given a value close to -1.
Figure 15 shows the hub contoured by dihedral angle ratio. Note that the histogram for the dihedral angle ratio will show a distribution that is concentrated above and below the optimum. In this case, most elements have an angle that is more acute than the optimum.
Figure 13. Solid mesh contoured by internal angle
Figure 14. Histogram for the Mixed Product contour type
After determining that the solid mesh is suitable for analysis, the 1/8 symmetry mesh can be restored to the full model by using the Mirror tool (Figure 16). The mesh can be mirrored about the model’s planes of sym-metry which can be defined for the Mirror tool by any 3 nodes on these planes. Because the model is a 1/8 symmetric mesh, the mirror function has to be performed 3 times to restore the full model, which is shown in Figure 17. The following steps show how this function can be performed:
1
Select all bricks using the Select All button;2
Click TOOLS, Mirror;3
Select 3 Nodes as the plane - this changes the pointer into a hot pointer (as shown in Figure 16);4
Click on 3 nodes that lie on a plane of symmetry the model is to be mirrored about;5
Click Apply.Figure 15. Contouring by Dihedral Angle Ratio
Figure 16. Mirror tool dialog
Figure 17. Mirrored mesh