A FASTER SIMULATION METHOD FOR THE STOCHASTIC RESPONSE OF HYSTERETIC STRUCTURES SUBJECT TO EARTHQUAKES

A semi-analytical forward-difference Monte Carlo simulation procedure is proposed for the determination of the lower order statistical momen ts and the joint probability density function of the stochastic respon se of hysteretic non-linear multi-degree-of-freedom structural systems subject to nonstationary gaussian white noise excitation, as an alter native to conventional direct simulation methods. The method generaliz es the so-called Ermak-Allen algorithm developed for simulation applic ations in molecular dynamics to structural hysteretic systems. The pro posed simulation procedure rely on an assumption of local gaussianity during each time step. This assumption is tantamount to various linear izations of the equations of motion. The procedure then applies an ana lytical convolution of the excitation process, hereby reducing the gen eration of stochastic processes and numerical integration to the gener ation of random vectors only. Such a treatment offers higher rates of convergence, faster speed and higher accuracy. The procedure has been compared to the direct Monte Carlo simulation procedure, which uses a fourth-order Runge-Kutta scheme with the white noise process approxima ted by a broad band Ruiz-Penzien broken line process. The considered s ystem was a multi-dimenensional hysteretic shear frame, where the cons titutive equation of the hysteretic shear forces are described by a bi linear hysteretic model. The comparisons show that significant savings in computer time and accuracy can be achieved. Copyright (C) 1996 Els evier Science Limited.