Investigation on response aggregation for structural optimization of a wing structure

Kurzfassung

Solving large scale optimization problems may become demanding in terms of user waiting time and computational resources. Hence reducing the num- ber of constraints simplifies the optimization problem and could improve the computational performance. One possibility is to split the constraints into aggregation domains. Then, an aggregation function is used to merge all values per domain into a single value, which can then be used as a constraint instead. This approach is applied to many structural optimization problems, as the number of constraints is usualy large and scales directly with the number of load cases. Reducing the number of constraints per loadcase could allow to include more load cases in aeroelastic wing design. To investigate the benefits of an aggregation approach, the Kreisselmeier-Steinhauser function is integrated in the model for MSC-Nastran, which provides a common framework for aeroelastic design. The test case is the wing structure of the common research model. Weight is minimized, while the structure has to withstand strength and stability constraints for four pull-up load cases. The Modified Method of Feasible Direction (MMFD) and the Interior Point Method (IPOPT) are used as optimization algorithms. The MMFD includes only active constraints while IPOPT applies barrier functions on all constraints. Constraints are grouped per type (strength, stabiltiy) and per load case. Different aggregation stratgies for those groups are applied. The first simply aggregates all values of each group. The second splits each group into domains, dependent on their spanwise position of the wing (each bay). The third splits each group into domains per design field. All optimization results of each aggregation scheme are compared to an optimization without aggregation. While the first and the second approach turn out to be even more time consuming and do not provide good designs, the aggregation per design field shows to be promising. The MMFD algorithm combined with this aggregation scheme could determine better designs than without aggregation. The IPOPT algorithm which has a longer computational run time compared to MMFD, could be speed up by using the design fields as aggregation domains. The resulting design is almost as good as the results from the optimization without aggregation.