Figure. Sensitivity-based shape improvement step: high-sensitivity nodes are moved outwards.
In ProTOp each shape optimization cycle consists of the following three successive steps:
Note that although mesh improvement and smoothing steps are optional, they typically should not be skipped in order to preserve the FE mesh quality and surface smoothness during optimization.
The sensitivity-based step aims to improve the topology optimization objective as defined during the topology optimization process. For this purpose, the sensitivity information computed at the FE nodes is utilized. More specifically, the high-sensitivity surface nodes are moved in the outer normal direction, depending on their corresponding sensitivity value.
Figure. Sensitivity-based shape improvement step: high-sensitivity nodes are moved outwards.
The shape optimizer aims to improve the optimization objective, which is related to either structural strain energy or fundamental eigenfrequency. Note, however, that the most valuable collateral effect of this process is the reduction of stress concentrations. This is especially true for shell/lattice-configured designs, where stress concentrations may emerge very quickly as a result of a limited design space.
These two steps are intended to prevent mesh quality and smoothness degradation caused by nodal movements during the sensitivity-based step. The quality improvement aims to raise the SI quality of the affected FE elements, while the smoothing step exploits the geometrical properties of the stripped surface to improve its smoothness. The smoothing effect is achieved by moving the FE nodes so that the element and nodal normals are better aligned.
Figure. Mesh smoothing step: improved smoothness is achieved by aligning element and nodal normals.