Stochastic Dynamic Analysis of Inelastic Structures Using Force Analogy Method

The force analogy method which has been proven to be very efficient in dynamic analysis of inelastic structures is here introduced for the first time into the field of stochastic dynamic analysis for inelastic structures. This stochastic force analogy method (SFAM) maintains the advantage of the high efficiency in the numerical computation of the force analogy method in dynamic analysis. According to the SFAM, the variance covariance functions of inelastic dynamic responses, such as displacement, velocity, inelastic displacement of the entire moment-resisting framed structures, and plastic rotation at individual plastic hinge location, can be produced for structures subject to random excitation. Detailed theoretical development of the SFAM is derived, and a simple numerical example using a single degree of freedom system is presented. The reasonability of the proposed method is validated by the good agreement between the results from the proposed SFAM and those obtained from Monte Carlo simulation.

[1]  Masanobu Shinozuka,et al.  EQUIVALENT LINEARIZATION METHOD IN NONLINEAR FEM , 1989 .

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

[3]  W. Zhu,et al.  On exact stationary solutions of stochastically perturbed Hamiltonian systems , 1990 .

[4]  T. Soong,et al.  Linearization in Analysis of Nonlinear Stochastic Systems , 1991 .

[5]  Y. K. Wen,et al.  Methods of Random Vibration for Inelastic Structures , 1989 .

[6]  T. K. Caughey,et al.  On the response of non-linear oscillators to stochastic excitation , 1986 .

[7]  Masanobu Shinozuka,et al.  Simulation of Nonstationary Random Process , 1967 .

[8]  H. Tajimi,et al.  Statistical Method of Determining the Maximum Response of Building Structure During an Earthquake , 1960 .

[9]  Zhe. Wang,et al.  Deterministic and stochastic dynamic study on inelastic structures with force analogy method , 2005 .

[10]  S. H. Crandall.  Non-Gaussianclosure techniques for stationary random vibration , 1985 .

[11]  Micromechanically based stochastic finite elements: length scales and anisotropy , 1996 .

[12]  Earl H. Dowell,et al.  Parametric Random Vibration , 1985 .

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

[14]  J.-S. Yu,et al.  The equivalent non-linear system method , 1989 .

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

[16]  I. Elishakoff,et al.  A new approximate solution technique for randomly excited non-linear oscillators—II , 1992 .

[17]  T. Caughey,et al.  The exact steady-state solution of a class of non-linear stochastic systems , 1982 .

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

[19]  Kevin K. F. Wong,et al.  Inelastic Dynamic Response of Structures Using Force Analogy Method , 1999 .

[20]  S. Soni,et al.  Transient Response of Nonlinear Systems to Stationary Random Excitation , 1975 .