Although stress-constrained topology optimization has been extensively studied in structural design, the development of optimization frameworks to enable the creation of metamaterials with optimal mechanical performance is still an open problem. This study incorporates local stress constraints into the topology optimization framework for metamaterial microstructure design, aiming to avoid the stress concentration in the optimized microstructure. For the efficient solution of multi-constraint topology optimization problems, the Augmented Lagrangian formulation is extended to address local minimization problems subjected to the combined action of local and global constraints. Additionally, as an extension of static load conditions, this study further investigates the design of metamaterial microstructures under cyclic loading. Finally, the effectiveness of the proposed approach is demonstrated through a series of two-dimensional and three-dimensional benchmark problems.

翻译：尽管应力约束拓扑优化在结构设计中已得到广泛研究，但开发能够创建具有最优力学性能超材料的优化框架仍是一个开放性问题。本研究将局部应力约束纳入超材料微结构设计的拓扑优化框架，旨在避免优化微结构中的应力集中。为高效求解多约束拓扑优化问题，本研究扩展了增广拉格朗日公式以处理同时受局部与全局约束作用的局部最小化问题。此外，作为静态载荷条件的延伸，本研究进一步探究了循环载荷下超材料微结构的设计。最后，通过一系列二维与三维基准问题验证了所提方法的有效性。