Stochastic seismic response analysis of structures exhibiting high nonlinearity

A physical stochastic ground motion model and the extended Bouc-Wen model are incorporated into the probability density evolution method for stochastic seismic response analysis of structures exhibiting high nonlinearity. Fundamentals and numerical algorithms for the synthesized method are described. Case studies demonstrate that coupling of nonlinearity and randomness will greatly change the response characteristics of the structure. The popular viewpoint that randomness of structural parameters is trivial compared to that of excitations is overthrown. Besides, whether localization or dispersion of nonlinearity will occur in the structure depends mainly on the configuration of the structural parameters.

[1]  Jianbing Chen,et al.  The Number Theoretical Method in Response Analysis of Nonlinear Stochastic Structures , 2007 .

[2]  Jianbing Chen,et al.  Probability density evolution method for dynamic response analysis of structures with uncertain parameters , 2004 .

[3]  Jianbing Chen,et al.  The principle of preservation of probability and the generalized density evolution equation , 2008 .

[4]  Jianbing Chen,et al.  Dynamic response and reliability analysis of non-linear stochastic structures , 2005 .

[5]  Weiqiu Zhu,et al.  Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation , 2006 .

[6]  P. Spanos,et al.  Random vibration and statistical linearization , 1990 .

[7]  Muneo Hori,et al.  Three‐dimensional stochastic finite element method for elasto‐plastic bodies , 2001 .

[8]  Vitelmo V. Bertero,et al.  Earthquake Engineering: From Engineering Seismology To Performance-Based Engineering , 2020 .

[9]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[10]  Masanobu Shinozuka,et al.  Monte Carlo solution of structural dynamics , 1972 .

[11]  Wing Kam Liu,et al.  Probabilistic finite elements for nonlinear structural dynamics , 1986 .

[12]  William Hung Kan Lee,et al.  International handbook of earthquake and engineering seismology , 2002 .

[13]  Jianbing Chen,et al.  The equivalent extreme-value event and evaluation of the structural system reliability , 2007 .

[14]  Wilfred D. Iwan,et al.  On the dynamic response of non-linear systems with parameter uncertainties , 1996 .

[15]  Christian A. Schenk,et al.  Uncertainty assessment of large finite element systems , 2005 .

[16]  Thomas T. Baber,et al.  Random Vibration Hysteretic, Degrading Systems , 1981 .

[17]  Li Jie,et al.  Joint Probability Density Function of the Stochastic Responses of Nonlinear Structures , 2007 .

[18]  Roger Ghanem,et al.  Partition of the probability-assigned space in probability density evolution analysis of nonlinear stochastic structures , 2009 .

[19]  Christian Soize,et al.  Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies , 2008 .

[20]  Yu-Kweng Michael Lin.  Probabilistic Theory of Structural Dynamics , 1976 .

[21]  N. Impollonia,et al.  Explicit solutions in the stochastic dynamics of structural systems , 2006 .

[22]  Piero Colajanni,et al.  Stochastic linearization critically re-examined , 1997 .

[23]  Humberto Contreras,et al.  The stochastic finite-element method , 1980 .

[24]  Yi-Lung Mo,et al.  Seismic simulation of RC wall-type structures , 2008 .

[25]  Jianbing Chen,et al.  A note on the principle of preservation of probability and probability density evolution equation , 2009 .

[26]  Kiyoshi Kanai,et al.  Semi-empirical Formula for the Seismic Characteristics of the Ground , 1957 .

[27]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[28]  Frederic Ward Williams,et al.  RANDOM SEISMIC RESPONSES OF MULTI-SUPPORT STRUCTURES IN EVOLUTIONARY INHOMOGENEOUS RANDOM FIELDS , 1997 .

[29]  Jintai Chung,et al.  A new family of explicit time integration methods for linear and non‐linear structural dynamics , 1994 .

[30]  H. Keng,et al.  Applications of number theory to numerical analysis , 1981 .

[31]  I. Elishakoff,et al.  Finite Element Methods for Structures with Large Stochastic Variations , 2003 .

[32]  Ted Belytschko,et al.  Transient probabilistic systems , 1988 .

[33]  H. Zhang,et al.  Parameter Analysis of the Differential Model of Hysteresis , 2004 .

[34]  Y. Wen.  Method for Random Vibration of Hysteretic Systems , 1976 .

[35]  Marcin Kamiński,et al.  Generalized perturbation-based stochastic finite element method in elastostatics , 2007 .

[36]  Mohammad Noori,et al.  Random Vibration of Degrading, Pinching Systems , 1985 .

[37]  Christian Soize,et al.  Transient responses of dynamical systems with random uncertainties , 2001 .

[38]  Xilin Lu,et al.  Study on a new shear wall system with shaking table test and finite element analysis , 2000 .

[39]  Stephen H. Crandall.  A half-century of stochastic equivalent linearization , 2006 .

[40]  Jianbing Chen,et al.  Stochastic Dynamics of Structures , 2009 .

[41]  M. Shinozuka,et al.  Simulation of Stochastic Processes by Spectral Representation , 1991 .

[42]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[43]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[44]  Jianbing Chen,et al.  The probability density evolution method for dynamic response analysis of non‐linear stochastic structures , 2006 .