Although stresses are of higher practical relevance, most research dealing with uncertainties are compliance based optimizations, supposedly due to the easier to handle global quantity i.e. the compliance. Stresses on the other hand are very localized. Furthermore, it is the maximum stress which is crucial for the failure of a structural component. Thus, a common strategy is to apply so called aggregation function to approximate the maximum stress. Aggregation functions are differentiable with respect to the design variable and can hence be used in conjunction with gradient based optimization algorithms.

Uncertainties can be taken into account by a broad variety of methods such as Monte-Carlo, which is usually used as benchmark, or Polynomial-Chaos-Expansion. The most promising one is the Method of Moments (MoM), since it is superior in terms of computational efficiency.

It is expected that local stresses are very sensitive to variations of load, geometry and material properties, which may arise due to uncertain operational conditions or variations in process parameters. The correlation of aggregation strategies and probabilistic analyses within optimization under uncertainty are an open topic that will be investigated here.

This topic contributes to the objectives “Improving efficiency of optimization algorithms” and “Consideration of technical constraints”.

Contact: Micah Kranz