Multi-scale robust design and optimization considering load uncertainties

Uncertainty is ubiquitous in practical engineering design applications. Recent years have witnessed a growing research interest in the study of structural topology optimization problems considering uncertainties. Most of these works, however, are focused on the optimization of macro-scale structures. 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. It is found 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. The conclusions drawn from the present work are helpful for manufacturing hierarchical structures with Additive Manufacturing technologies.