Shape optimization process
Mesh quality considerations

During the shape optimization process, the surface FE nodes are being moved in order to improve the optimization objective. This can also result in some negative effects related to the quality of the mesh. The two most common situations are:

• element distortion, caused by the near-surface element becoming very thin and disproportional, and
• geometrical mesh defects, caused by folding or twisting of near-surface regions of the mesh.

The figure below illustrates a classic situation of element distortion, caused by node movement in an otherwise regular and non-problematic mesh.

Figure. Element distortion due to shape optimization: before optimization (left) and after (right); some elements became quite thin.

At this point it should be noted that ProTOp will automatically reduce and limit the step-size of the shape optimizer in order to prevent excessive element distortions. Additionally, the shape optimization cycle is by default enriched by (optional) inclusion of mesh improvement and mesh smoothness procedures. At this point it is important to note that the included mesh procedures run with some default values of their operating parameters, which should deliver somewhat beneficial results on average. However, in order to achieve the best possible results, these two procedures should be run from within the corresponding specialized tools. To maximize the efficiency of these tools, it may be worth making a brief review of the sources of element distortions and geometrical mesh defects within ProTOp.

Element distortions

In ProTOp, the appearance of distorted elements can be attributed to the following two reasons:

• mesh stripping, which is typically done after topology optimization, and
• changing surface node positions, done by mesh smoothing and shape optimization.

The figure below illustrates a clipped view of such a mesh; the distorted elements were generated by the mesh stripping procedure.

Figure. Clipped view of a stripped lattice structure with several distorted elements.

Geometrical mesh defects

In ProTOp, a typical source of geometrical mesh defects are defective or nearly-defective mesh regions, generated by mesh stripping done after topology optimization. Although, this process is not well controlled and problematic regions may occur anywhere, there are some situations especially prone to mesh defects of this kind. Frequent examples of such situations are:

• material regions being relatively thin when compared to the size of involved finite elements;
• narrow void regions with some elements bridging the void gap; and
• lattice-shell-solid crossings and interfaces.

The figure below illustrates a clipped view of a stripped lattice structure with a possible mesh defect.

Figure. Clipped view of a stripped lattice structure with a possible mesh defect.