Harmonic Response - Problem Description
Tutorial 8: Checking Mesh Quality - Solid Mesh Checking
Carry out the Solid Automeshing procedure as shown in Tutorial 6 with the Target Type set to Tet4. After meshing, change the Brick Outlines to black and also turn on Light Shade; this will make the model appear more realistic.
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;
Determinant of Jacobian;
Mixed Product; and Dihedral Angles.
Aspect Ratio
Similar 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 8.10 below shows the solid meshed bike hub contoured by Aspect Ratio (Max/Min) with the histogram option turned on.
Figure 8.10 - Aspect Ratio (Max/Min) Contour of the Bike Hub
As seen from the histogram above, the majority of the elements have an aspect ratio of less than 3.5. However, there are some elements that have an aspect ratio as high as 10.4. It is important to know where such poor elements are
mesh near the region where the poor element was found or changing the internal element density in the Solid Automeshing dialog box.
It is possible to locate the element with the highest aspect ratio by using the Find tool. To activate this tool,
1. Choose Edit/Find (alternatively, press CTRL+F);
The Find Entity dialog box appears as shown in Figure 8.11 below.
Figure 8.11 - Find Entity dialog box
The brick with the highest aspect ratio is shown in the legend of Figure 8.10 above as being Brick Number 18605. Use the Find tool to locate this brick element. Figure 8.12 below shows this brick element located within the interior of the axle of the hub.
Figure 8.12 - Brick Element with the Highest Aspect Ratio
Strand7 also allows you to control the limits and display of the contours. It is possible to set user limits for the range of the scale and then select how elements that fall outside of this range are displayed. Elements outside the range can be represented with a colour or can not be contoured at all. Instead they can be shown in wireframe mode. This is very useful in locating distorted elements.
1. Open the Entity Display dialog box.
2. Click the Brick Display options button.
3. Under Colours change Outline to Light Grey (this is necessary because we have black outlines and a black background).
4. Under Contour Type click Settings.
5. Click the Style tab.
6. Under Colours clear the < Min check box.
7. Under Colours clear the > Max check box.
8. Click the Limits tab.
9. Under Contour Limits select User Range.
10. Under Limits enter 3 in the Min text box.
12. Click OK to close the Contour Configuration dialog box.
13. Click OK to close the Entity Display dialog box.
These settings will plot the legend between 3 and 7 and only display the brick elements that fall into this range. Hide the nodes on the screen by clicking Hide Nodes on the left toolbar. Your screen should look like Figure 8.13 below.
Figure 8.13 - Contouring with User-Defined Limits
Before proceeding we want to turn off these settings.
1. Open the Entity Display dialog box.
2. Click the Brick Display options button.
3. Under Colours change Outline to Black.
4. Under Contour Type click Settings.
5. Click the Style tab.
6. Under Colours select the < Min check box.
7. Under Colours select the > Max check box.
8. Click the Limits tab.
9. Under Contour Limits select Default.
10. Click OK to close the Contour Configuration dialog box.
11. Click OK to close the Entity Display dialog box.
12. Show the nodes on the screen by clicking Show Nodes on the left toolbar.
Internal Angle
The internal angle contour option for bricks is identical to the one 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 8.14 below shows the bike hub contoured by Internal Angle with the histogram option turned on.
Figure 8.14 - Internal Angle Contour of the Bike Hub
It can be seen from the histogram in Figure 8.13 above that the majority of elements have reasonable internal angles.
Unselected button. 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 adequate quality then the solid mesh is suitable for analysis.
Mixed Product
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 1; conversely, those that are not square are given a value less than 1. In the case of tetrahedral meshes, 'squareness' of corners is not expected for optimal elements. Instead, tetrahedral elements should have a mixed product that is close to 0.707. Figure 8.15 below shows the histogram for the Mixed Product contour type for the hub mesh.
Figure 8.15 - Mixed Product Contour of the Bike Hub
Dihedral Angle
The dihedral angle is a measure of the internal angle between two connected faces of a brick. For a tetrahedron, the optimum dihedral angle is near 70.5 deg , for a hexahedron it is 90 deg . The dihedral angle ratio is a normalised 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 much larger than the optimum is given a ratio close to 1. Conversely, those with an angle much smaller than the optimum is given a ratio close to -1. Figure 8.16 below shows the bike hub mesh
contoured by Dihedral Angle Ratio.
Figure 8.16 - Dihedral Angle Ratio Contour of the Bike Hub
Note the histogram for the dihedral angle ratio will show a distribution that is concentrated above and below the optimum. In this case, there are slightly more elements with acute angles than obtuse angles.
Det (Jacobian)
This contour gives the lowest Jacobian determinant at any Gauss point within the element. A negative value indicates an invalid brick, it may be collapsed - i.e. element nodes are too close together or even at the same location. In the case of quadratic brick elements, it may also mean that the mid-side node is too close to a corner node. Generally, mid-side nodes should be kept no closer than one third of the distance between the corner nodes. Any brick elements reporting negative values should be adjusted or removed from the mesh. Figure 8.17 below shows the bike hub mesh contoured by Det(Jacobian).
Figure 8.17 - Det(Jacobian) Contour of the Bike Hub