Mesh Quality Book Snippet

The Mesh Quality section from Chapter 3: Modeling/ Pre-Processing is reproduced on this page for clarity of the included figures.

Viewing Mesh Quality

It is always a good idea to keep tabs on mesh quality while meshing. To actively show a contour of mesh quality that updates in real time, use View > Advanced Post > Model Data Contour. Make sure the checkbox for Show Model Data Contour is checked and select Jacobian from the Element Quality tree. The Jacobian is a measure element quality and once enabled, a legend with colors ranging from pink (highest quality) to red (lowest quality) can be seen. Other measures of quality are provided; all gauge the quality of an element with respect to an ideal condition. All other options at their default settings to see a contour.


The ideal CQUAD and CTRIA element is a flat square and equilateral triangle, respectively, but small imperfections are ok. What is more important is that any one element not be too misshapen. This can lead to unrealistic stresses around a poorly meshed area. Here is a surface meshed with CQUAD elements, and the corresponding Jacobian contour:

no hole

On the left is the mesh as displayed in the graphics window. On the right is a contour of mesh quality. There’s only one color, but it’s rare to have such a perfectly square surface to mesh! Real world geometry includes complicating features such as holes and uneven edges. Here is an example of how the presence of a hole affects mesh quality:

small hole

Depending on the relative size of the hole, it may be permissible to ignore. If that is the case, it may be excised from the underlying surface with the Feature Removal tools in the Meshing Toolbox. With Loops selected, clicking either of the two curves that describe the hole on the surface will prompt the removal of the entire hole.


If the hole is a structurally important feature, the next best thing is to improve the quality of the mesh around it. A technique for improving the local element quality is to break up the surfaces around the hole. The Pad operation under Geometry Editing from the Meshing Toolbox uses curves to create four symmetric surfaces around the original hole.


This creates a local area to install a transitional mesh. The new surfaces aid the transition from a circular loop to the straight edges of the outer surface. These surfaces have effectively isolated the area of poor mesh quality. After remeshing, the resulting mesh looks like the figure on the left.

pad meshpad mesh 3

This demonstrates how the Pad operation isolates the transition, although the interior elements are still of poor quality. The second figure above is the mesh after increasing the mesh seeding on the curves of the new pad surfaces near the hole. As the element quality inside the pad improves, the quality outside suffers. If it is possible to change the mesh seeding on the edges of the outer surface, then two further steps may be taken. The first step is to make Point to Edge cuts under Geometry Editing.


Point to Edge cuts further break up the outer surface. These are made by selecting one of the outer corners of the pad surfaces and then the outer surface curves. By making one Point to Edge operation per dashed line in the above figure and setting equal mesh seeding, a final mesh of improved quality is obtained:



Mesh Fix Example

Fixing a flawed mesh can be accomplished in a number of ways. Here is an example of how one such plate-based mesh with a few obscured problems is investigated. These problems could have originated during any session from accidental mistakes related to the mesh generation or underlying geometry used to produce the mesh. For the first step, the Jacobian Model Data Contour is enabled.

  1. The element quality contour is enabled. One particular element shaped close to an ideal equilateral triangle has a Jacobian of 2, which indicates something is awry, since a triangle (CTRIA3) element with that shape should have a Jacobian closer to the ideal value of 0.
    1. 5
  2. The element is edited with Modify > Edit > Element, and it becomes apparent that the definition doesn’t match the intent. Somehow a quadrilateral (CQUAD4) element exists at this location.


Two of the four edge nodes must be overlapping. This element could simply be redefined as a triangular element, but it is just deleted for the sake of this example. Now the contour looks like below:


  1. With one offending element eliminated, the peak Jacobian for this group of elements is still 2 (the legend automatically scales to the maximum). Element shrink is another tool employed to locate more offending elements. A shortcut to enabled shrink can be found under the View Style button.
    1. 6
  2. Three sliver elements have been exposed. They look like line elements but have planar definitions. If the location has been narrowed down, element shrink is a useful tool for identifying sliver elements. Shrink is best used with a light-colored background so that the thin elements become discernible.
    1. sliver6
  3. The three slivers are deleted by manual selection methods (Delete > Model > Mesh). The legend updates the peak Jacobian, which is now 0.551, considerably less than before and now in the range of reason.

This example established with the element quality contour and shrink commands that the source of the poor element quality were badly misshapen elements. One quadrilateral that appeared to be triangular and three sliver elements were present and drove up the maximum Jacobian. This demonstrated real world meshing quality problems that were difficult to detect upon first inspection, but that were overcome with the use of Femap tools.