Figure. Cut surfaces are generated by the optimizer when material is removed.
ProTOp is capable of addressing the two most common topology optimization problem types. These two types are:
Understanding the basic properties of these two optimization procedures is of vital importance for the process of formulating and solving a topology optimization problem in a satisfactory manner.
After a satisfactory design topology has been found, ProTOp can be engaged to improve the design by using its shape optimizer. This procedure can often further improve the durability of the structural part, especially its fatigue crack resistance.
From the engineering point of view, strain energy minimization is actually an extremely useful procedure because it comes with some very convenient collateral effects. Namely, the optimized structure automatically exhibits:
Note that a good topology optimizer will make the stress concentrations vanish, but, of course, only on cut surfaces.
Figure. Cut surfaces are generated by the optimizer when material is removed.
It is important to recognize that the optimizer can not do anything useful on surfaces where the domain of the part would need to be expanded in order to get a better design. Since domain expansion is not possible, the design domain has to be prepared very carefully. Otherwise, the final design might end up with stress concentrations in some regions where material could not be added. Such regions are typically encountered at non-cut surfaces of a poorly designed domain.
Figure. Stress concentrations may remain on non-cut surfaces if the domain of the part is not carefully designed.
IMPORTANT. The domain of a part must be designed very carefully to avoid remaining stress concentrations on non-cut surfaces.
Maximization of the lowest eigenfrequency is a relatively stable process, but only until the lowest and the second lowest frequencies meet. Namely, as the optimization proceeds, the lowest eigenfrequency increases while the second lowest eigenfrequency typically decreases.
Figure. At some optimization stage the lowest and second lowest eigenfrequencies will usually meet.
Once the lowest and second lowest eigenfrequencies meet, the stability of the process becomes problematic because of the switching of the eigenmodes.
Figure. Two close lowest eigenfrequencies may cause eigenmode switching in sequential optimization cycles.
An eigenmode-switching situation can be usually relatively satisfactory solved by taking numerical measures such as dumping. It should be noted, however, that stopping the optimization process is usually also a reasonable solution because it typically does not make much sense to run the optimization further.
NOTE. Once the lowest and second lowest eigenfrequencies meet, it might be quite reasonable to finish the optimization process. Further possible improvements of the design are likely to be negligible.
Note that the design obtained by solving either of the above listed topology optimization problems can be improved by ProTOp by engaging its specialized shape optimization procedure.
The specialized shape optimizer is intended to work preferably on surfaces obtained by stripping the mesh after topology optimization. The stripped surfaces are typically quite rough but can be improved significantly by adequate shape optimization.
Figure. Stripped surface obtained after topology optimization - typically quite rough.
Figure. Stripped surface after shape optimization
Note that under some circumstances, for example when optimizing lattice structures, shape optimization can significantly reduce the stress levels and make the stresses more uniform. This can have a substantial positive effect on structural service life and resistance against fatigue crack initiation.