基于二阶摄动法求解区间参数结构动力响应

李琦; 邱志平; 张旭东

doi:10.6052/0459-1879-14-088

基于二阶摄动法求解区间参数结构动力响应

北京航空航天大学航空科学与工程学院, 北京 100191

基金项目: 高等学校学科创新引智计划(B07009), 国家自然科学基金(11372025,11002013),国防基础科研计划基金(A0820132001, JCKY2013601B)和航空科学基金(2012ZA51010)资助项目.

详细信息

作者简介:
李琦,在读博士,主要研究方向:不确定结构分析与优化. E-mail: lq12131010@163.com

中图分类号: O327
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出版历程
- 收稿日期: 2014-03-31
- 修回日期: 2014-09-18
- 刊出日期: 2015-01-17

SECOND-ORDER PARAMETER PERTURBATION METHOD FOR DYNAMIC STRUCTURES WITH INTERVAL PARAMETERS

School of Aeronautic Science and Technology, Beijing University of Aeronautics and Astronaut ics, Beijing 100191, China

Funds: The project was supported by the 111 Project (B07009), the National Natural Science Foundation of China (11372025, 11002013), the Defense Industrial Technology Development Program (A0820132001, JCKY2013601B) and Aeronautical Science Foundation of China (2012ZA51010).

摘要

摘要: 在处理区间参数结构动力响应问题时,现有的分析方法大多局限于一阶区间分析方法. 如果参数的不确定量稍大,采用一阶区间分析方法对结构动力响应范围进行估计可能会失效,所以需要考虑二阶区间分析方法.但是采用基于区间运算的二阶区间分析方法得到的结果将会对动力响应范围过分高估. 为了克服以上缺点,首先基于二阶摄动法得到结构动力响应广义函数. 然后通过求解此动力响应函数的最大和最小值,将结构动力响应区间的问题转化为序列低维箱型约束下的二次规划问题. 最后采用DC 算法(di erence of convex functionsalgorithm) 对这些箱型约束下的二次规划问题进行求解. 这样可以在不引入过多计算量的情况下,避免了对动力响应范围的过分估计. 通过数值算例,将该方法和其他区间分析方法进行比较,验证了该方法的有效性与精确性.
- 区间参数 /
- 二阶摄动 /
- 不确定结构动力响应 /
- 二次规划 /
- DC 算法
Abstract: When considering the problem of the dynamic responses of structures with interval parameters, previous interval analysis methods are mostly restricted to its first-order. But if the uncertainties of the parameters are fairly large, the response region obtained using the first-order interval analysis method would fail to contain the real region of the dynamic response of uncertain structures. Therefore, the second-order analysis method should be considered. However, the second-order analysis method relating to operations of interval may result in an exorbitantly overestimated dynamic response region, which makes the result useless for practical engineering problems. To circumvent this drawback, firstly the general function of the dynamic response of structures in terms of structural parameters is obtained based on the second-order parameter perturbation method. Then via solving the maximum and minimum of the function, the problem of determining the bounds of the dynamic response of uncertain structures is changed into a series of low dimensional box constrained quadratic problems, and these box constrained quadratic programming problems can be solved using the DC algorithm (difference of convex functions algorithm) effectively. The proposed method can avoid the exorbitant overestimate of the dynamic response region of uncertain structures, while does not introduce much more computational expense. A numerical example is used to illustrate the accuracy and the efficiency of the proposed method when comparing with other methods.
- interval parameters /
- second-order parameter perturbation method /
- dynamical response of uncertain structures /
- quadratic problems /
- DC algorithm

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