中文摘要：

针对目前评价结构的鲁棒性还没有统一标准的问题,基于H∞鲁棒控制理论,建立了不确定性结构鲁棒性定量的评价方法。将外部荷载和结构自身的非概率不确定性用凸集模型表达,采用结构系统传递函数的H∞范数作为结构鲁棒性的定量评价指标。引入L2范数作为评价信号的度量,给出了考虑弹塑性的结构鲁棒性计算公式。分析单自由度并联结构体系,表明不考虑塑性将会高估结构的鲁棒性。分析桁架结构在静力与动力条件下结构的鲁棒性,验证了H∞鲁棒性评价指标可以合理有效地反映结构的鲁棒性。结果表明,增大结构的冗余度、提高关键构件的承载力储备可以增强结构的鲁棒性,而外部荷载和结构本身的属性的波动将降低结构的鲁棒性。

英文摘要：

Currently there is no generally accepted criterion for a quantitative measure of structural ro- bustness. Taking basis in robust H∞ control theory, a framework for quantitative assessing structural robustness considering uncertainties is proposed. Non-probabilistic uncertainties of external loads and structure itself are expressed by convex model, and structural robustness can be assessed by H∞ norm of the transfer function. Specific formula for elastic-plastic structural robustness is given, using L2 norm as an evaluation of signal. Analysis results of a single degree of freedom parallel system indicate that structural robustness will be overestimated without considering plasticity. Analysis of a truss structure subected to static and dynamic load indicates that H∞ structural robustness index can effectively and reasonably reflect structural robustness. The results show that increasing redundancy of structures or loadcarrying capacity reserves of key components can enhance structural robustness, while fluctuations of external load and properties of structures will reduce structural robustness.