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

三维结构失效-安全拓扑设计方法的综合研究

作　　者：Hongxin Wang Yujun Liao Guilin Wen Liangliang Chen Jie Liu 王洪鑫;廖宇君;文桂林;陈亮亮;刘杰

机构地区：[1]Center for Research on Leading Technology of Special Equipment,School of Mechanical and Electric Engineering,Guangzhou University,Guangzhou,510006,China [2]Department of Rehabilitation Medicine,The Fifth Affiliated Hospital of Guangzhou Medical University,Guangzhou,510735,China [3]Hebei Innovation Center for Equipment Lightweight Design and Manufacturing,School of Mechanical Engineering,Yanshan University,Qinhuangdao,066004,China

出　　处：《Acta Mechanica Sinica》2024年第6期87-99,共13页力学学报（英文版）

基　　金：financially supported by the National Natural Science Foundation of China(Grant Nos.12172095,11832009,and 12302008);the Natural Science Foundation of Guangdong Province(Grant No.2023A1515011770);Guangzhou Science and Technology Planning Project(Grant Nos.202201010570,202201020239,202201020193,and 202201010399)。

摘　　要：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.失效-安全拓扑优化对于确保优化结构在发生局部失效后仍能继续工作具有重要价值.失效-安全拓扑优化方法选择性地降低局部失效区域内材料刚度,以模拟结构发生局部失效的复杂行为.在该研究工作中,我们首先探讨了局部失效区域大小、形状和分布方案对失效-安全设计鲁棒性的影响.研究结果表明,较大的局部失效区域以及更细的局部失效分布方案可以产生更具鲁棒性的失效-安全结构.然而,更细的局部失效分布方案会显著增加优化成本,特别是对于三维结构而言.为了提高优化效率,我们基于多分辨率拓扑优化(MTOP)框架建立了一种高效的失效-安全拓扑优化方法.在MTOP框架中,引入了扩展有限元方法(XFEM),以在分析网格和拓扑优化模型之间建立解耦关系.数值算例表明,所提出的方法在确保优化结构具有较高失效-安全鲁棒性的同时,对二维平面结构的优化效率比传统失效-安全优化方法提高近2倍左右,而对三维结构的优化效率比传统方法提高25倍以上.

关 键 词：Robust design Fail-safe structures Multi-resolution topology optimization Computational efficiency XFEM 

分 类 号：O189[理学—数学]