FE mesh quality is quite an important factor in assuring an effective and successful optimization process. Therefore, mesh quality monitoring and improvement should be an obligatory part of topology optimization.
In ProTOp mesh quality is evaluated by using the SI element quality measure. This measure, here denoted by Q, is defined as
where C is a scaling constant, V is the signed element volume, and A is the element root-mean-square face area. The constant C depends on the finite element type and is used to scale the quality Q within the interval [-1.0, +1.0]. Based on Q, the finite elements can be classified as:
Theoretically, a FEA process should fail due to bad mesh quality only if at least one finite elements is singular. In practice, however, a nearly singular element with Q being positive, but close to zero may also cause the FEA to fail. A good mesh should therefore contain elements with their qualities being as close as possible to Q = +1.0.
The mesh quality improvement process is an extremely non-linear process, typically requiring many cycles. Due to its highly non-linear nature, the stopping criteria are not easily definable, especially with regard to tradeoff between achievable improvements and computation time. In practice this means that it might be worth running the process more than once, especially, if the user estimates that the required CPU time allows to do that. In such a case, a few recommendations can be given to get the maximal mesh improvement, as follows.
NOTE. If the consumed CPU time is acceptable, run the improvement procedure several times until no further progress can be obtained..
Favor either minimal or average quality
Range: [Minimal, Average]
This parameter sets a corresponding weight in order to favor more either improvement of minimal-quality elements or average-quality elements.
Processing precision
Range: [Lower, Higher]
This parameter influences the stopping criteria by setting them more tight or loose.
Edge definition limit angle
Range: [0.0 ~]
This parameter is the limit angle for a line between two element faces to be classified as a geometrical edge of the model. If the angle between the normals of the two faces is below this limit, the faces are considered to belong to a smooth surface.
Mesh improvement means moving FE nodes. Such operations may influence slightly the model geometry and boundary conditions, especially the applied loading. To prevent this, the user may fix various surface node sets such as, for example, the loaded surface nodes.