Comprehensive study on fail-safe topological design method for 3D structures

Fail-safe topology optimization is valuable for ensuring that optimized structures remain operable even under damaged conditions. By selectively removing material stiffness in patches with a fixed shape, the complex phenomenon of local failure is modeled in fail-safe topology optimization. In this work, we first conduct a comprehensive study to explore the impact of patch size, shape, and distribution on the robustness of fail-safe designs. The findings suggest that larger sizes and finer distribution of material patches can yield more robust fail-safe structures. However, a finer patch distribution can significantly increase computational costs, particularly for 3D structures. To keep computational efforts tractable, an efficient fail-safe topology optimization approach is established based on the framework of multi-resolution topology optimization (MTOP). Within the MTOP framework, the extended finite element method is introduced to establish a decoupling connection between the analysis mesh and the topology description model. Numerical examples demonstrate that the developed methodology is 2 times faster for 2D problems and over 25 times faster for 3D problems than traditional fail-safe topology optimization while maintaining similar levels of robustness.