Fail-safe optimization of beam structures

In the current work, a fail-safe optimization of beam structures is carried out. This approach may provide an insight into the robustness of lattice structures. The use of beam elements allows a commonly used engineering approach for obtaining a fail-safe design to be applied. This consists of removing one beam element at a time and optimizing the remaining structure. At the end of the process, the maximum beam radii are used for the final design. This approach is computationally extremely expensive for lattice structures, as it requires one optimization per removed beam. In our contribution, we show that the design obtained from this approach does not actually achieve the desired fail-safe behaviour. We therefore apply a multi-model approach in which the fail-safe requirement is an optimization constraint. This is still computationally demanding and therefore, methods for reducing the number of failure cases to be considered within the optimization are discussed. Furthermore, the p -norm is applied to the stress constraints to reduce the computational effort for the gradient calculation. Reduction of failure cases and use of the p -norm have opposite effects on the conservatism of the result and therefore compensate each other to some extent.