Shape optimization process
Optimization objective

In ProTOp each shape optimization cycle consists of the following two successive steps:

• the geometry-based step and
• the stress-based step.

The shape optimization objective is defined indirectly by favoring one of these two steps. Effectively, this is achieved by increasing the size of the favored step while reducing at the same time the size of the disfavored step.

Geometry-based step

The geometry-based step exploits the geometrical properties of the surface in order to improve its smoothness. The surface nodes are moved so that the element and nodal normals are better aligned.

Figure. Geometry-based step: improved smoothness is achieved by aligning element and nodal normals.

Favoring of the geometry-based step effectively results in putting more weight on geometrical smoothness of the resulting surface.

Stress-based step

The stress-based step aims to reduce the highest stress levels on the surface in the sense of making the stress field more uniform. The high-stress surface nodes are moved in the outer normal direction, while the low-stress nodes are moved in the opposite direction.

Figure. Stress-based step: high-stress nodes are moved outwards; low-stress nodes are moved inwards.

Favoring of the stress-based step effectively results in putting more weight on stress levels uniformity of the resulting surface.

Setting the objective

For a number of reasons there are no firm mechanical or other guidelines on how to set the optimization objective in a particular shape optimization problem. Consequently, setting the objective is typically heavily influenced by engineering experience and feedback information from the running optimization process. This means that interactive optimization process guidance is here absolute necessity and should be done in a careful and gradual manner.

Although precise instructions can not be offered, there are some general recommendations that have often proved to be useful. These can be outlined as follows:

• Start by geometry-based steps. It is typically a good idea to start the shape optimization process by favoring strongly (or exclusively) the geometrical smoothness of the structure. This can even be done without much progress monitoring since the process will typically converge to the best result obtainable. Note that FEA computations can even be completely suppressed in this stage in order to make the process fast.
• Engage stress-based steps latter and with caution. As the structural smoothness is at least somewhat improved, one can start engaging also the stress-based steps in addition to geometry-based steps. This should be done with caution by monitoring the progress and using the optimization feedback to adjust the optimization parameters.

NOTE. Although these general recommendations are often useful, they may not be the best choice under any circumstances. So, careful interactive examination of the progress is always recommended in order to do eventual parameter adjustments in time and prevent the design to become distorted unacceptably.