Figure. Topologically optimized and stripped lattice structure; max stress levels are around 150 MPa.
In contrast to topology optimization, shape optimization problems are usually less sophisticated from the procedural point of view. Namely, although these problems are still
they are typically rather non-flat problems. Therefore, the optimization process is usually rather straightforward and monotonic. This is especially true for the shape optimization procedure within ProTOp, where shape optimization is engaged primarily as a supplemental process, aimed to improve the surfaces obtained after stripping the topologically optimized model.
NOTE. In ProTOp shape optimization is engaged primarily as a supplemental process, aimed to improve the surfaces obtained after stripping the topologically optimized model.
In ProTOp the shape optimizer performs two steps within each cycle. These two steps are:
The geometry-based steps exploits the geometrical properties of the surface in order to improve its smoothness. On the other hand, the stress-based step aims to reduce the stress levels on the surface in the sense of making them more uniform. In both steps the improvements are achieved by moving the surface nodes into adequate (better) positions.
NOTE. Shape improvements are achieved by moving the surface nodes into adequate (better) positions.
It is important to note that supplemental shape optimization may come with significant benefits, even if the considered structure was topology optimized; this is especially true for lattice structures. Consider the following example.
The first figure below shows a structure that was configured by one lattice configurator, topology optimized, and stripped. Note that configurators can limit the design space significantly, which can be reflected in notable stress level variations, even on cut surfaces. This is a natural consequence of hindered material redistribution possibilities due to the limited design space.
In our case the optimized and stripped design exhibits max stress levels of about 150 MPa. This is the best possible result that could be obtained by the topology optimizer; further improvements are not possible due to the limited design space.
Figure. Topologically optimized and stripped lattice structure; max stress levels are around 150 MPa.
Design space limitations of the topology optimizer, however, do not apply to the shape optimizer because the later one is allowed to do only rather minor geometrical corrections. Note, however, that these minor geometrical corrections may result in significantly reduced and more uniform stress levels.
In the considered example the shape optimizer was run for a few cycles and the max stress levels dropped from 150 MPa to around 100 MPa. For the optimized structure this can mean a huge difference in its expected service life. In other words, supplemental shape optimization can bring significant benefits in terms of structural durability.
Figure. Topologically optimized, stripped, and shape optimized lattice structure; max stress levels are around 100 MPa.
NOTE. Supplemental shape optimization can bring significant benefits in terms of structural durability, even for topologically optimized structures.