基于概率密度演化理论的结构抗震可靠性分析
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摘要
运用随机过程的正交展开方法,将地震动加速度过程表示为由10个左右的独立随机变量所调制的确定性函数的线性组合形式。结合概率密度演化方法和等价极值事件的基本思想,研究了非线性结构的抗震可靠度分析问题。以具有滞回特性的非线性结构为例,对某一多自由度的剪切型框架结构进行了抗震可靠性分析。结果表明:按照复杂失效准则计算的结构抗震可靠度较之结构各层抗震可靠度均低。这一研究为基于概率密度函数的、精细化的抗震可靠度计算提供了新的途径。
Employing an orthogonal expansion method,an earthquake acceleration random process was represented as a linear combination of deterministic functions modulated by 10 independent random variables. So,it was natural to combine the probability density evolution method (PDEM) and the orthogonal expansion of a seismic ground motion to study a nonlinear stochastic earthquake response. Furthermore,the aseismatic reliability of structures was assessed using the idea of equivalent extreme-value which can be used accurately to evaluate structural systems under a compound failure criterion. A hysteretic nonlinear structure was taken as an example. The failure probability and reliability of the nonlinear shear frame structure with 10 degrees of freedom subjected to stochastic ground motions were investigated. The result indicated the system reliability of the structure was lower than the reliability of each story. The investigation showed that the proposed approach has fair accuracy and acceptable efficiency for seismic reliability.
Employing an orthogonal expansion method,an earthquake acceleration random process was represented as a linear combination of deterministic functions modulated by 10 independent random variables. So,it was natural to combine the probability density evolution method (PDEM) and the orthogonal expansion of a seismic ground motion to study a nonlinear stochastic earthquake response. Furthermore,the aseismatic reliability of structures was assessed using the idea of equivalent extreme-value which can be used accurately to evaluate structural systems under a compound failure criterion. A hysteretic nonlinear structure was taken as an example. The failure probability and reliability of the nonlinear shear frame structure with 10 degrees of freedom subjected to stochastic ground motions were investigated. The result indicated the system reliability of the structure was lower than the reliability of each story. The investigation showed that the proposed approach has fair accuracy and acceptable efficiency for seismic reliability.
引文
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[6]Chen J B,Li J.Dynamic response and reliability analysis of non-linear stochastic structures[J].Probabilistic Engineering Mechanics,2005,20(1):33-44.
[7]Chen J B,Li J.The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain pa-rameters[J].Structural Safety,2007,29(2):77-93.
[8]Li J,Chen J B,Fan W L.The equivalent extreme-value e-vent and evaluation of the structural system reliability[J].Structural Safety,2007,29(2):112-131.
[9]李杰,刘章军.基于标准正交基的随机过程展开法[J].同济大学学报(自然科学版),2006,34(10):1279-1283.
[10]刘章军,李杰.地震动随机过程的正交展开[J].同济大学学报(自然科学版),2008,36(9):1153-1159.
[11]Deodatis G.Non-stationary stochastic vector processes:seis-mic ground motion applications[J].Probabilistic Engineer-ing Mechanics,1996,11:149-168.
[12]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学,2007.
[13]Ma F,Zhang H,Bockstedte A,et al.Parameter analysis of the differential model of hysteresis[J].Journal of Applied Mechanics,2004,71:342-349.
[14]Li J,Chen J B.The number theoretical method in response a-nalysis of nonlinear stochastic structures[J].Computational Mechanics,2007,39(6):693-708.
[2]Ditlevsen O.Narrow reliability bounds for structural systems[J].Journal of Structural Mechanics,1979,7(4):453-472.
[3]Murotsu Y,Okada H,Taguchi K,et al.Automatic genera-tion of stochastically dominant failure modes of frame struc-tures[J].Structural Safety,1984,2(1):17-25.
[4]Li J,Chen J B.Probability density evolution method for dy-namic response analysis of structures with uncertain parame-ters[J].Computational Mechanics,2004,34(5):400-409.
[5]Li J,Chen J B.The principle of preservation of probability and the generalized density evolution equation[J].Structural Safety,2008,30(1):65-77.
[6]Chen J B,Li J.Dynamic response and reliability analysis of non-linear stochastic structures[J].Probabilistic Engineering Mechanics,2005,20(1):33-44.
[7]Chen J B,Li J.The extreme value distribution and dynamic reliability analysis of nonlinear structures with uncertain pa-rameters[J].Structural Safety,2007,29(2):77-93.
[8]Li J,Chen J B,Fan W L.The equivalent extreme-value e-vent and evaluation of the structural system reliability[J].Structural Safety,2007,29(2):112-131.
[9]李杰,刘章军.基于标准正交基的随机过程展开法[J].同济大学学报(自然科学版),2006,34(10):1279-1283.
[10]刘章军,李杰.地震动随机过程的正交展开[J].同济大学学报(自然科学版),2008,36(9):1153-1159.
[11]Deodatis G.Non-stationary stochastic vector processes:seis-mic ground motion applications[J].Probabilistic Engineer-ing Mechanics,1996,11:149-168.
[12]刘章军.工程随机动力作用的正交展开理论及其应用研究[D].上海:同济大学,2007.
[13]Ma F,Zhang H,Bockstedte A,et al.Parameter analysis of the differential model of hysteresis[J].Journal of Applied Mechanics,2004,71:342-349.
[14]Li J,Chen J B.The number theoretical method in response a-nalysis of nonlinear stochastic structures[J].Computational Mechanics,2007,39(6):693-708.
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