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

Abstract

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.

Multi-material and strength-oriented microstructural topology optimization applied to discrete phase and functionally graded materials

“…In that more complex framework, a variety of stress fields exist, spanning loads from bulk to shear type, which, as envisaged here, will impact differently in material combinations for stress mitigation. Since multiscale TO is nowadays quite a hot research topic (Wu et al 2021), it would be an interesting research avenue bringing stress control into such problem (see e.g., Zhao et al 2021aZhao et al , 2021b, which would also advance the authors' previous works (Coelho et al 2008;Rodrigues et al 2002). The connectivity issue of microstructures in the multiscale problem would be also an interesting aspect to consider (see e.g., Du et al 2018).…”

“…Since this work increases not only the number of variables, needed for material selection, but also the number of constraints, to control stresses locally, the MMA effectiveness can be questioned. In fact, recent attention has been given to handle stresses as they are, local, i.e., pursuing stress aggregation-free approaches, see e.g., Giraldo-Londoño et al (2021a, 2021b, Senhora et al (2020) and da Silva et al (2020Silva et al ( , 2021. As detailed thereafter, to handle TO problem formulations minimizing peak stresses in microstructural design, having as many stress constraints as the number of FE in the mesh, the authors here still propose using the common TO framework with design updates by MMA.…”

Stress‐constrained multiscale topology optimization with connectable graded microstructures using the worst‐case analysis

“…40 Zhao et al proposed a concurrent topology optimization approach for designing two-scale hierarchical structures under stress constraints without specifying the topology of the unit cell. 41 In this article, we will study stress-constrained multiscale topology optimization approach with connectable graded microstructures. In our method, the shape interpolation method is employed to generate a series of connectable microstructures based on the specified prototype microstructure.…”

“…Yu et al handled the shell‐lattice infill structural design under the von Mises stress‐based and Tsai‐Hill yield criteria‐based constraints by using the level set method 40 . Zhao et al proposed a concurrent topology optimization approach for designing two‐scale hierarchical structures under stress constraints without specifying the topology of the unit cell 41 …”