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Mesh Quality

In a finite element mesh, it is generally desirable to avoid elements of high aspect ratio (i.e. long "thin" elements). The presence of such elements can have adverse effects on the analysis results.

  • In general, such elements can influence analysis results, and lead to misleading and inaccurate results, which are dependent on the mesh.
  • In extreme cases, such elements may even be responsible for non-convergence of the finite element solution, and the analysis will be aborted.

In order to help the user determine the "quality" of a finite element mesh, Slide2 can automatically locate and highlight elements in a mesh, which are deemed to be of "poor" quality, according to user-definable criteria.

This is done with the Show Mesh Quality and Define Mesh Quality options, in the Mesh Refinement sub-menu of the Mesh menu.

Show Mesh Quality

In order to locate and highlight poor quality elements in a mesh, select the Show Mesh Quality option in the Mesh Refinement sub-menu of the Mesh menu. If poor quality elements exist:

  • All poor quality elements will be filled with a red hatch pattern
  • Since these elements will often be difficult to see, without zooming in to view, the general area(s) where poor quality elements have been found, will be additionally highlighted, by rectangular boxes drawn around the regions of poor quality elements. The display of these boxes can be turned off if desired, by de-selecting the Highlight checkbox in the Define Mesh Quality dialog.

The elements which are highlighted, are those which conform to the criteria of a "poor quality" element, as defined in the Define Mesh Quality dialog. In most cases, you will need to zoom in to get a good view of the highlighted poor quality elements, and determine what may be the cause of the problem.

Define Mesh Quality

The Define Mesh Quality dialog allows the user to specify the criteria which define a "poor quality" element. There are three criteria which may be specified:

  • ratio of (maximum side length) / (minimum side length)
  • Minimum interior angle
  • Maximum interior angle

The defaults for the above criteria, are 10 , 20 and 120, respectively. However, the user may change any of these criteria. NOTE that an element will be determined as "poor quality", if ANY of these three criteria are met.

Highlight

By default, the Highlight checkbox is toggled ON in the Define Mesh Quality dialog. This option draws an additional rectangle around regions of poor quality elements, since in many cases the poor quality elements may be difficult to see, even with the red hatch fill, unless you are zoomed in to that region of the mesh. If you do not wish to see these rectangles displayed, then you can turn the Highlight option OFF by clearing the checkbox.

Reasons for poor quality mesh elements

There are various reasons why poor quality mesh elements may be generated. Typically the problems are due to:

  1. Poorly graded discretization of model boundaries (for example, a finely discretized boundary immediately adjacent to, or close to, a coarsely discretized boundary, will often result in a poor quality mesh).
  2. Vertices which are very close to each other. This can happen when a boundary has been intersected with another boundary, without using vertex snap, such that two vertices end up very near to each other, when the user may have intended both vertices to be at the same location. Due to the automatic boundary intersecting capability of Slide2, this may occur without the user being aware of it.
  3. The geometry of your model boundaries may also be responsible, for example, the relative distances between boundaries, or the way in which they intersect (e.g. nearly parallel boundaries which intersect at a very small angle).

Fixing a poor quality mesh

  1. If a poor discretization is responsible for the poor mesh, then you will need to reset the mesh, and modify the discretization of the appropriate boundaries. This may involve use of the Custom Discretize option, or simply changing the Approximate Number of Elements in the Mesh Setup dialog.
  2. If the problem is vertices which are very close to each other, then you may need to delete unnecessary vertices, or move vertices, so that they are further apart, or exactly coincident. If vertices were intentionally located very near to each other, and this is causing a problem, then you may want to consider modifying your geometry slightly, so that poor quality elements are not generated.
  3. If the actual model geometry is responsible, then various solutions might be appropriate, involving Custom Discretize, or modifying the boundaries slightly, so that the problem does not occur.
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