弦支双曲扁网壳结构的鲁棒构型分析及试验研究

针对不良拓扑布置导致的结构鲁棒性不佳问题，以系统传递函数的H₂范数为基础，建立结构鲁棒性定量评价指标和鲁棒构型求解方法。以单元相对密度为设计变量，采用变密度模型描述材料的刚度，将结构的鲁棒设计转化为连续体拓扑优化，并对大爆炸算法进行二级搜索的改进，进而求解连续体拓扑优化模型。以四点支承的弦支双曲扁网壳结构为例，分析不同荷载作用下的鲁棒构型，探索不同参数的大爆炸算法优化效果，通过静力试验和冲击试验，对优化后模型和未优化模型进行对比分析。结果表明，二级搜索的大爆炸算法可以有效地应用于弦支结构的鲁棒设计中，改进的大爆炸算法加快了收敛速度，依据鲁棒构型进行杆件布置，可显著提高结构的力学性能和抗干扰能力。

Robust configuration analysis and experimental study of cablesupported hyperbolic flat latticed shell structure

Aiming at the problem that bad topological layout leads to poor structure robustness and based on the H₂ norm of system transfer function, quantitative evaluation index of structural robustness and robust configuration solving method were established firstly. Secondly, the relative densities of elements were chosen as design variables and the solid isotropic material with penalization (SIMP) model was used to describe the stiffness of the material, the robustness based structural design was transformed into continuum topology optimization. Then, the big bang-big crunch (BB-BC) method was improved by two-stage search and was used to solve the continuum topology optimization model. After that, taking cable supported hyperbolic flat latticed shell structure with four supports as an example, robust configurations under different load conditions were analyzed and the optimized effect of BB-BC method with different parameters was explored too. At last, comparative analysis between optimized model and conventionally designed model was conducted by static experiment and impact experiment. Results show that the two-stage BB-BC method can be well implemented for the robust design of cable supported structure, the improved BB-BC method can speed up the convergence, and arranging members based on the robust configuration can significantly increase the structure’s mechanical property and anti-interference capability.