Topology optimization process
Targeting options

ProTOp allows for several targeting options, related to volume, stresses and displacements. However, it should be noted that these options have to be divided into primary and secondary targeting options as follows:

• Primary target
  • Volume part
• Secondary targets
  • Misses stress
  • Maximal displacement

When running a new optimization task, the first approximate optimal design should always be obtained by using the primary targeting - volume part. However, after the approximate design is found, one can optionally switch to secondary targeting in order to fine tune the final result. Note that ProTOp allows for target switching at any time, even during a running optimization process.

NOTE. Primary targeting should always be used when starting a new optimization task. Secondary targeting is only for fine tuning of the approximate optimal design.

Primary targeting - volume part

An optimization task should always be started by targeting the volume part. It should be noted that the volume part is always computed as the current material volume within the free domain, divided by the total volume of the free domain. This means that fixed regions are not taken into account. For example, in the figure below the current material volume is shown in blue and the free domain volume in transparent blue. The fixed region (grey) is not taken into account for the volume part computation.

Figure. Volume part computation refers only to the free region: material volume (blue) and domain volume (transparent blue)

Secondary targeting

Once an approximate optimal design has been obtained by using primary targeting, the final optimal design can be obtained by engaging other targeting options. For example, let us assume we already have an approximate optimal design as shown on the Figure below. We are now in position to switch to secondary targeting related to stresses or displacements.

Figure. Approximate optimal design obtained by volume part targeting

IMPORTANT. It is important to note that secondary targeting is done by referring to stress and displacement fields, obtained by applying the MAX operator across all load cases. In other words, stress and displacement fields are first used to find maximal values across all load cases. The resulting field is then used to evaluate targeting quantities.

Targeting von Misses stress

In ProTOp the targeting of von Misses stresses is based on the so called reference boundary stress measure. This is a scalar quantity defined as some measure of von Misses stresses on cut surfaces. Note that in computing the reference boundary stress, the following stresses are neglected:

• stresses in fixed regions,
• interior stresses in free regions, and
• stresses on surfaces that are not cut.

The way how the reference boundary stress is computed can be influenced by an optimization parameter. By varying this parameter, the boundary stress is influenced as follows

• as this parameter approaches 0.0, the reference boundary stress approaches the average von Misses stress on cut surfaces
• as this parameter approaches 1.0, the reference boundary stress approaches the maximum von Misses stress on cut surfaces

Figure. The reference boundary stress measure is related only to the stresses on cut surfaces

Targeting maximal displacement

Alternatively to stresses, displacements can also be addressed by secondary targeting. In ProTOp displacements targeting is based on the maximal displacement quantity, which is the defined as the maximal absolute nodal displacement within the structure.

Figure. The maximal displacement measure is the maximal magnitude of all nodal displacements.