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 relatively straightforward and monotonic. This is especially true for the shape optimization procedure within ProTOp, where shape optimization is engaged only as a supplemental process, aimed to improve the surfaces obtained after stripping the topologically optimized model.
In ProTOp the shape optimizer assumes that the surface to be optimized is already rather well smoothed. Therefore, the mesh smoothing tool has to be run before running any shape optimization. This means that the whole optimization procedure should consist at least of the following successive stages:
All other specialized tools may be engaged as needed in more complex scenarios.
In ProTOp the shape optimizer improves the surface by relying on the sensitivity information, which is used to move the stripped-surface nodes into adequate (better) positions. This process usually (but not always) improves the objective of the optimization (either lower strain energy, or higher fundamental eigenfrequency).
Although the optimization objective improvements are typically rather minor, what is really valuable here is the collateral effect of reduced stress concentrations. Namely, during this process stress concentrations may often be reduced significantly which may increase the service life of a load-carrying part significantly.
Finally, it is worth noting that stress concentrations are related only to stress FEA load cases. This means that eigenfrequency FEA load cases are typically not very useful and can simply be excluded when running the shape optimization process.
It is important to note that shape optimization may come with significant benefits, even if the considered structure was topology optimized. This is especially true for shell/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 stripped 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, are not enforced in 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. Although the structural strain energy was reduced only slightly, 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; the structural strain energy was reduced only slightly, but the max stress levels dropped significantly to around 100 MPa.
NOTE. Supplemental shape optimization can bring significant benefits in terms of structural durability, even for topologically optimized structures. This is especially true for the shell/lattice configured structures.