5. Concluding remarks
In the present paper, robust concurrent optimization of material and structure under unknown-but-bounded load uncertainties is investigated in a multi-scale framework. Problem formulation that can allow for the effect of worst-case scenario in a confidence way and the corresponding numerical solution procedure are proposed. Numerical examples demonstrate that when load uncertainties are considered, optimal material distributions in microstructures tend to be isotropic and Kagome structure seems to be superior to other forms of microstructures. In the present work, only load uncertainty is considered. Considering material uncertainty, which is ubiquitous in practical engineering design applications and may be possibly induced by material degradation, accidental damage or manufacture error, in a multiscale framework, however, is difficult since structural responses are usually implicit functions of material properties. This will pose great challenges to constructing the corresponding confidence robust formulation and developing the computationally tractable solution algorithms. We will pursue this issue in the future work.
