Topology optimization of two-scale hierarchical structures with high-cycle fatigue resistance

Hierarchical structures with complicated two-scale configurations show great potential for applications with the advancement of additive manufacturing technology, while fatigue performance is one of the key challenges in structural design. In this study, a two-scale topology optimization method is proposed for designing lightweight hierarchical structures that simultaneously possess high structural stiffness while satisfying microscopic fatigue strength requirements. In the microstructural fatigue analysis, the modified Goodman criterion is adopted for evaluating fatigue failure by considering the high-cycle fatigue problem under proportional loading with constant amplitude. To analyze the fatigue performance of hierarchical structures rapidly and accurately, a microscopic fatigue failure criterion characterization for the two-scale structure is established. In the optimization model, the structural compliance is chosen as the objective function and the local fatigue failure criteria for the microstructures over the whole structures are taken as the optimization constraints. To mitigate the challenges posed by an excessive number of constraints in optimization problems, the enhanced aggregation strategy of the two-scale fatigue constraints is proposed for accurate controlling of fatigue failure criteria in two-scale structures with fewer numbers of constraints. The sensitivity of the aggregated local fatigue constraints is derived, and the optimization problems are solved with the method of moving asymptotes algorithm. Numerical examples demonstrate that two-scale optimized structures that have high stiffness and meet microstructural fatigue constraints can be obtained through the proposed optimization approach. Furthermore, the effect of different fatigue criteria used as constraints on the optimization results and the comparison with concurrent topology optimization are thoroughly discussed.