FE mesh quality is quite an important factor in assuring a successful and effective optimization process. Therefore, mesh quality monitoring and improvement should be an obligatory part of both, topology and shape optimization procedures.
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:
A FEA process may fail or deliver poor results if singular or low-quality regular elements are present. Therefore, a good mesh should contain only regular elements with their qualities being as close as possible to Q = +1.0. ProTOp's mesh improvement procedure is capable of raising the quality of processed elements, which includes turning singular elements into regular ones.
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.
SI quality threshold for element activation
Range: [0.0, 1.0]
This parameter sets the threshold quality for an element to qualify for a potential improvement operation. More precisely, an element is activated and may be processed for improvement only if its SI quality is below the specified threshold.
Process intensity factor
Range: [0.05, 1.0]
This parameter defines the extent of adjustments made to the model. Low intensity means that only small adjustments are performed and the required processing time is also relatively low.
Surface edge threshold angle
Range: [0.1, 5.0]
This parameter is the threshold angle in degrees for a line between two element faces to be classified as a geometrical edge on the surface of the model. If the angle between the normal vectors of the two faces is below this threshold, the faces are considered to belong to a smooth surface.
The computational efficiency of the process can be improved by limiting the active region. This might be useful once the whole mesh was already previously improved and the subsequent mesh improvement operations are needed only in the vicinity of stripped surfaces.
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 declare various surface node sets such as, for example, the loaded surface nodes as unmovable.