不同分布随机参数结构非线性地震反应的概率密度演化

杨俊毅; 陈建兵; 李杰

doi:10.3969/j.issn.0258-2724.2015.06.010

不同分布随机参数结构非线性地震反应的概率密度演化

doi: 10.3969/j.issn.0258-2724.2015.06.010

基金项目:

国家自然科学基金资助项目(11172210,51261120374)

国家十二五科技支撑计划资助项目(2011BAJ09B03-02)

详细信息

作者简介:
杨俊毅(1989-),男,博士研究生,研究方向为结构随机动力学,E-mail:yangjunyistill@163.com

通讯作者:
陈建兵(1975-),男,教授,博士生导师,研究方向为结构随机动力学、地震工程与结构可靠度,E-mail:chenjb@tongji.edu.cn

计量
- 文章访问数: 878
- HTML全文浏览量: 255
- PDF下载量: 321
- 被引次数: 0
出版历程
- 收稿日期: 2014-07-30
- 刊出日期: 2015-12-25

Probability Density Evolution Analysis of Nonlinear Seismic Response of Structures with Random Parameters Following Different Distributions

摘要

摘要: 为了准确把握实际工程结构在地震作用下的整体性能,需要合理考虑结构参数的随机性.本文采用概率密度演化理论,结合以广义F-偏差最小化为准则的点集优选策略,实现了含有数十个随机参数的多自由度结构非线性随机反应分析.在此基础上,重点考察了基本随机参数的不同分布类型和不同变异系数对结构非线性反应特性的影响.研究表明,由于结构随机参数不同分布类型的影响,结构反应的二阶矩差异可达30%;当基本变量变异系数很小和很大时,不同分布类型对二阶矩的影响程度均较大但影响趋势相反,因而存在结构反应二阶矩对不同分布类型不敏感的变异系数值域.随机参数的分布类型对结构反应的概率密度函数影响显著,甚至可能导致定性性质的改变.
- 随机结构 /
- 地震反应 /
- 非线性 /
- 广义F-偏差 /
- 概率密度演化理论
Abstract: The randomness of structural parameters should be reasonably taken into account to assess the global performance of complex structures subjected to seismic actions. In the present paper, incorporating the generalized F-discrepancy (GF-discrepancy) based optimal point selection strategy and the probability density evolution method (PDEM), the effects of different distribution types and different coefficients of variation of the random parameters on the response of a multi-degree-of-freedom nonlinear structure with tens of random parameters are studied. The results show that the difference between the second-order moments of the structural responses with different types of distributions could be in the order of 30%. When the coefficients of variation of the basic parameters are either very small or fairly large, the effects of different types of distributions on the second-order moments of responses are relatively large, but in an opposite tendency. Therefore, there exists a range of the coefficients of variation in which the different types of distributions have little effects on the second-order moments of responses. However, the probability density functions (PDFs) of the responses are always affected considerably, even may change qualitatively by the types of distributions of the random parameters.
- stochastic structures /
- seismic response /
- nonlinearity /
- generalized F-discrepancy /
- probability density evolution method

HTML全文

参考文献(20)

李杰,李国强. 地震工程学导论 [M]. 北京:地震出版社,1992: 3.

CHEN Jianbing, LI Jie. Stochastic seismic response analysis of structures exhibiting high nonlinearity[J]. Computers and Structures, 2010, 88(7): 395-412.

李杰. 随机结构系统:分析与建模 [M]. 北京:科学出版社,1996: 4.

SHINOZUKA M. Monte Carlo solution of structural dynamics[J]. Computers and Structures, 1972, 2(5): 855-874.

LIU W K, BELYTSCHKO T, MANI A. Probabilistic finite element methods for nonlinear structural dynamics[J]. Comput. Methods Appl. Mech. Eng., 1986, 56: 61-81.

KLEIBER M, HIEN T D. The stochastic finite element method: basic perturbation technique and computer implementation[M]. New York: Wiley, 1992: 1-200.

WU Cunli, MA Xiaoping, FANG Tong. A complementary note on Gegenbauer polynomial approximation for random response problem of stochastic structure[J]. Probabilistic Engineering Mechanics, 2006, 21(4): 410-419.

GOLLER B, PRADLWARTER H J, SCHUELLER G I. Reliability assessment in structural dynamics[J]. Journal of Sound and Vibration, 2013, 332: 2488-2499.

ZHAO Yangang, IDOTA H. Response uncertainty and time-variant reliability analysis for hysteretic MDF structures[J]. Earthquake Engineering and Structural Dynamics, 1999, 28: 1187-1213.

CHEN Jianbing, LI Jie. Development-process of nonlinearity: based reliability evaluation of structures[J]. Probabilistic Engineering Mechanics, 2007, 22(3): 267-275.

朱位秋. 随机振动 [M]. 北京:科学出版社,1992: 223-227.

LI Jie, CHEN Jianbing. Stochastic dynamics of structures[M]. : John Wiley and Sons, 2009: 191-284.

陈建兵,李杰. 结构随机地震反应与可靠度的概率密度演化分析研究进展[J]. 工程力学,2014,31(4): 1-10. CHEN Jianbing, LI Jie. Probability density evolution method for stochastic seismic response and reliability of structures[J]. Engineering Mechanics, 2014, 31(4): 1-10.

王华琪. 混凝土工程质量抽样检验技术研究 [D]. 上海:同济大学,2006.

CHEN Jianbing, LI Jie. A note on the principle of preservation of probability and probability density evolution equation[J]. Probabilistic Engineering Mechanics, 2009, 24(1): 51-59.

LI Jie, CHEN Jianbing, SUN Weiling, et al. Advances of the probability density evolution method for nonlinear stochastic systems[J]. Probabilistic Engineering Mechanics, 2012, 28: 132-142.

XU Jun, CHEN Jianbing, LI Jie. Probability density evolution analysis of engineering structures via cubature points[J]. Computational Mechanics, 2012, 50(1):135-156.

陈建兵,张圣涵. 非均布随机参数结构非线性响应的概率密度演化[J]. 力学学报,2014,46(1): 136-144. CHEN Jianbing, ZHANG Shenghan. Probability density evolution analysis of nonlinear response structures with non-uniform random parameters[J]. Chinese Journal of Theoretical and Applied Mechanics, 2014, 46(1): 136-144.

CHEN Jianbing, ZHANG Shenghan. Improving point selection in cubature by a new discrepancy[J]. SIAM Journal on Scientific Computing, 2013, 35(5): A2121-A2149.

MA F, ZHANG H, BOCKSTEDTE A, et al. Parameter analysis of the differential model of hysteresis[J]. Journal of Applied Mechanics, 2004, 71(3): 342-349.

施引文献

附加材料(0)

访问统计