Figure. Top-down mode: initial full-material design and the design after running a few optimization cycles.
The term optimization direction is here used to specify whether during the optimization process material is mainly removed or restored (from void). ProTOp is well equipped to engage both optimization directions, termed as the
In ProTOp both modes are not symmetric in the sense that they would differ only in the sign of material addition. Consequently, the results obtained by engaging either one or another mode may well be quite different. Additionally, the asymmetry of both modes may be used to achieve certain special effects in finding the optimal solution. Therefore, good understanding of how both modes operate, might be quite useful.
Topology optimization conventionally runs in the top-down mode. A good example of this mode is starting and running optimization from a full-material initial design (the free region of the part does not contain any voids). Consequently, during the optimization process material is mainly removed and redistributed.
Figure. Top-down mode: initial full-material design and the design after running a few optimization cycles.
Note that material removal can happen at any material point of the free domain. In other words, there are no free material points that would be temporarily prevented against becoming void.
Besides of the conventional top-down mode, ProTOp enables also to run optimization in the opposite bottom-up mode. A good example of this mode is starting and running optimization from a full-void initial design (the free region of the part does not contain any material). Consequently, during the optimization process material is mainly restored and redistributed.
Figure. Bottom-up mode: initial full-void design and the design after running a few optimization cycles.
In contrast to top-down, in bottom-up mode material restore can not happen at any point of the free domain. Namely, the semi-active finite element technology of ProTOp takes care of considering as active only the material finite elements and the elements contained within a relatively narrow transition layer surrounding the material part of the free region. Since inactive finite elements are not processed, void points only within the transition layer can be restored to a material state. In other words, in a bottom-up mode material can be restored only within a transition layer surrounding the material part of the free region.
Figure. Void elements can be restored to a material state only within a transition layer surrounding the material part of the free region
The semi-active finite elements technology in connection with the top-down and bottom-up mode switching can be utilized to achieve certain special effects. Perhaps the most useful effect is the fragmentation reduction by target volume manipulation. In this process the target volume is first intentionally reduced to a level well below the actual target. In this process the optimizer typically removes fine material region connections; in other words, material domain fragmentation is reduced. After that, the target volume is raised back to the actually desired level. This increases the volume part, but now material is added by the optimizer only within the transition layer surrounding the material region. In this way, the previously obtained low fragmentation is preserved.
Consider the example structure - a cantilever loaded with a concentrated force - shown in the figures below. The first figure shows the optimized structure obtained by the conventional top-down optimization at the actual target volume part of 50%.
Figure. The structure obtained by the conventional top-down procedure at the desired volume part of 50%.
Suppose, that the design is estimated to be too much fragmented. To reduce the fragmentation, the target volume is reduced to 30% and optimization is continued. After reaching the target volume of 30%, the structure looks as follows.
Figure. The structure obtained by continuing optimization down to the reduced volume part of 30%.
Optimization to a reduced target volume removed fine material connections. Now the target volume can be restored back to the desired target volume part of 50% and optimization can be continued until the final design is reached.
Figure. The structure obtained by continuing optimization up to the desired volume part of 50%.
While increasing the volume part from 30% to 50%, material state of void points is restored only within the transition layer. In this way low fragmentation of the design, obtained previously by volume reduction, is preserved.