| 张成,吴慧,高博青,董石麟.非概率不确定性结构的鲁棒性分析[J].计算力学学报,2013,30(1):51~56 |
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| 非概率不确定性结构的鲁棒性分析 |
| Analysis of structural robustness with non-probabilistic uncertainties |
| 投稿时间：2011-11-22 修订日期：2012-03-24 |
| DOI：10.7511/jslx201301009 |
| 中文关键词: 鲁棒性 鲁棒H∞控制 凸集模型 弹塑性 |
| 英文关键词:robustness robust H∞ control convex model elastic-plastic |
| 基金项目:国家自然科学基金(51178414);浙江省自然科学基金(Y1110438)资助项目. |
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| 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 robustness. 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 subjected 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 load-carrying capacity reserves of key components can enhance structural robustness, while fluctuations of external load and properties of structures will reduce structural robustness. |
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