Shape optimization process
Mesh quality considerations

During the shape optimization process FE nodes are being moved in order to improve the surface in terms of smoothness and stress field uniformity. 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 distortion. This happens automatically in the background, but the user should be aware of this fact to understand the possibility of nodes being moved less than expected.

Element distortion

During shape optimization element distortion is practically unavoidable. In ProTOp the appearance of distorted elements can be attributed to the following two reasons:

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

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

Preventing mesh degradation

ProTOp will do automatically its best to reduce the mesh degradation and related negative effects. Note, however, that the user can also help substantially to mitigate this problem by considering the following recommendations:

• Start optimization by favoring geometrical smoothness. Although this may not be always true, experience shows that favoring geometrical smoothness at the start of optimization will usually positively influences mesh quality later during optimization.
• Drive the optimization process cautiously. Shorter steps with carefully balanced objective (geometry-stress) are usually preferable. This may help in both reducing element distortion and preventing local near-surface mesh regions to become nearly-defective.
• Monitor the progress and clean and refine the mesh occasionally. Try cleaning the mesh on appearance of highly distorted elements or nearly-defect regions. Mesh cleaning may result in somewhat larger elements; engage mesh refinement to correct this. Note, however, that these tools also have to be engaged cautiously with carefully chosen parameters.

The figure below illustrates an example of a lattice structure, where the mesh cleaning and refining procedures could resolve all problems so that the shape optimizer could do a good job in fine tuning of the final design.

Figure. Successfully cleaned, refined, and shape optimized mesh of a lattice structure.

NOTE. Drive the optimization process cautiously and monitor the mesh. Engage mesh cleaning and refining tools in time to prevent excessive and irreparable mesh degradation.