Stress-constrained concurrent topology optimization of two-scale hierarchical structures

This article develops a concurrent topology optimization approach for designing two-scale hierarchical structures under stress constraints without specifying the topology of the unit cell as a priori. Compared with traditional stress-constrained topology optimization, the number of stress constraints involved in concurrent topology optimization is much larger and the sensitivity analysis for stress constraints is computationally more expensive. To address these challenges, a novel hierarchical aggregation strategy is proposed to handle the large number of stress constraints and an adjoint method is developed for efficient sensitivity analysis. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. It is also found that the structures obtained by traditional topology optimization usually perform better than the two-scale structures obtained by concurrent topology optimization when only concentrated loads are considered, while the latter may exhibit better performance in the case that distributed loads are involved.