基于鲁棒性的索穹顶结构截面优化设计

针对索穹顶结构缺乏有效的基于鲁棒性能的截面优化设计理论现状，基于H∞范数极小控制方法，利用非线性系统运动方程构建输入变量到输出响应的系统传递函数，通过引入L2性能准则并结合随机理论建立索穹顶结构非线性鲁棒性定量评价指标IR，在此基础上，利用MATLAB和ANSYS软件交互算法给出基于遗传算法的截面优化设计的具体步骤，并以内蒙古伊旗一实际肋环型索穹顶工程结构为分析对象，采用遗传算法开展基于结构鲁棒性的截面优化设计。研究表明，杆件截面变化对结构鲁棒性具有不同的敏感性，在保持质量不增加的前提下，通过增加对结构鲁棒性影响敏感构件的截面面积及减少对结构鲁棒性影响不敏感构件的截面面积,可有效提高结构鲁棒性，经优化后鲁棒性提高了39.2%，有效提升了结构抵抗产生不相称破坏的能力。

Section optimization design of a cable dome structure based on robustness

As the current literature lacks an effective section optimization design theory for the robustness of flexible cable dome structures, further studies were conducted and presented in this paper. Based on the H∞ theory, the system transfer function was set up with the motion equations of the nonlinear structural system. The nonlinear quantitative evaluation index IR of structural robustness can be achieved through the induction of L2 performance criterion and the random theory. Following this, the genetic algorithm was applied through the MATLAB and ANSYS software to achieve section optimization of robustness. A real Geiger Cable Dome structure in Inner Mongolia was studied as research object to carry out the section optimization design based on the structural robustness by genetic algorithm. The result reveals that the changes in the section of various elements show different sensitivities to the influence of structural robustness. Meantime, without affecting quality, the structural robustness can be effectively improved by increasing the cross-section area of elements with a significant effect on the structural robustness and reducing the cross-section area of elements with a minor effect on the structural robustness. The optimization reveals that the robustness can be improved by 39.2% and its structure capacity can be effectively enhanced to resist disproportionate damage and avoid eventual collapse.