滞回结构随机地震反应概率密度演化分析
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摘要
在工程实际中,要合理地评估复杂结构在地震作用下的整体性能,需要考虑结构参数的随机性。概率密度演化理论可以直接获取随机结构动力反应的概率密度函数及其演化过程。本文以广义F-偏差最小化作为代表点选取准则,采用扩展的Bouc-Wen滞回模型,对具有随机参数的滞回非线性多自由度结构进行了地震动反应概率密度演化分析。结果表明,随机结构的动力反应具有显著且复杂的演化特征,这些特征可以通过概率密度演化理论进行精细化分析。
In engineering practice,the randomness of structural parameters should be considered in order to assess reasonably the global performance of complicated structures under earthquake excitation. The probability density evolution method( PDEM) is capable of capturing the probability density functions and the corresponding evolution of the dynamical response of a stochastic structure. In this paper,the generalized F-discrepancy is adopted as the criterion of point selection. The extended Bouc-Wen hysteretic model is employed to characterize the nonlinear property of the restoring forces. The dynamical seismic response analysis of a nonlinear multi-degree-of-freedom structure with uncertain parameters is implemented by PDEM. The results demonstrate that the PDEM could be applied to capture the performance of hysteretic structures under strong earthquakes.
In engineering practice,the randomness of structural parameters should be considered in order to assess reasonably the global performance of complicated structures under earthquake excitation. The probability density evolution method( PDEM) is capable of capturing the probability density functions and the corresponding evolution of the dynamical response of a stochastic structure. In this paper,the generalized F-discrepancy is adopted as the criterion of point selection. The extended Bouc-Wen hysteretic model is employed to characterize the nonlinear property of the restoring forces. The dynamical seismic response analysis of a nonlinear multi-degree-of-freedom structure with uncertain parameters is implemented by PDEM. The results demonstrate that the PDEM could be applied to capture the performance of hysteretic structures under strong earthquakes.
引文
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[8]Wu CL,Ma XP,Fang T.A complementary note on Gegenbauer polynomial approximation for random response problem of stochastic structures[J].Probabilistic Engineering Mechanics,2006,21,410-419.
[9]Li J,Chen J,Sun W,Peng Y.Advances of the probability density evolution method for nonlinear stochastic systems[J].Probabilistic Engineering Mechanics,2012,28:132-142.
[10]Li J,Chen JB.Stochastic Dynamics of Structures[M].John Wiley&Sons,2009.
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[12]Chen JB,Zhang SH.Improving point selection in cubature by a new discrepancy[J].SIAM Journal on Scientific Computing,2013,35(5):A2121-A2149.
[2]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 J B,LI J.Probability density evolution method for stochastic seismic response and reliability of structures[J].Engineering Mechanics,2014,31(4):1-10.(in Chinese)
[3]Shinozuka M.Monte Carlo solution of structural dynamics[J].Computers&Structures,1972,2(5):855-874.
[4]Skorokhod AV,Hoppensteadt FC,Salehi HS.Random perturbation methods with applications in science and engineering.Springer,2002.
[5]李杰.随机结构系统——分析与建模[M].北京:科学出版社,1996.LI J.Stochastic structural system:Analysis and modeling[M].Beijing:Science Press,1996.(in Chinese)
[6]Au SK,Beck JL.Estimation of small failure probabilities in high dimensions by subset simulation[J].Probabilistic Engineering Mechanics,2001,16,263-277.
[7]Kleiber M,Hien TD.The Stochastic Finite Element Method:Basic Perturbation Technique and Computer Implementation[M].John Wiley&Sons,1992.
[8]Wu CL,Ma XP,Fang T.A complementary note on Gegenbauer polynomial approximation for random response problem of stochastic structures[J].Probabilistic Engineering Mechanics,2006,21,410-419.
[9]Li J,Chen J,Sun W,Peng Y.Advances of the probability density evolution method for nonlinear stochastic systems[J].Probabilistic Engineering Mechanics,2012,28:132-142.
[10]Li J,Chen JB.Stochastic Dynamics of Structures[M].John Wiley&Sons,2009.
[11]Ma F,Bockstedte A,Foliente G C,et al.Parameter analysis of the differential model of hysteresis[J].Journal of Applied Mechanics,2004,71(3):342-349.
[12]Chen JB,Zhang SH.Improving point selection in cubature by a new discrepancy[J].SIAM Journal on Scientific Computing,2013,35(5):A2121-A2149.
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