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Mathematical Problems in Engineering
Volume 2014, Article ID 539738, 16 pages
Research Article

Non-Gaussian Stochastic Equivalent Linearization Method for Inelastic Nonlinear Systems with Softening Behaviour, under Seismic Ground Motions

1Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas 152, San Bartolo Atepehuacán, 07730 Del. Gustavo A. Madero, DF, Mexico
2Coordinación de Mecánica Aplicada, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510 Del. Coyoacán, DF, Mexico

Received 20 July 2014; Revised 6 October 2014; Accepted 20 October 2014; Published 25 November 2014

Academic Editor: Salvatore Caddemi

Copyright © 2014 Francisco L. Silva-González et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A non-Gaussian stochastic equivalent linearization (NSEL) method for estimating the non-Gaussian response of inelastic non-linear structural systems subjected to seismic ground motions represented as nonstationary random processes is presented. Based on a model that represents the time evolution of the joint probability density function (PDF) of the structural response, mathematical expressions of equivalent linearization coefficients are derived. The displacement and velocity are assumed jointly Gaussian and the marginal PDF of the hysteretic component of the displacement is modeled by a mixed PDF which is Gaussian when the structural behavior is linear and turns into a bimodal PDF when the structural behavior is hysteretic. The proposed NSEL method is applied to calculate the response of hysteretic single-degree-of-freedom systems with different vibration periods and different design displacement ductility values. The results corresponding to the proposed method are compared with those calculated by means of Monte Carlo simulation, as well as by a Gaussian equivalent linearization method. It is verified that the NSEL approach proposed herein leads to maximum structural response standard deviations similar to those obtained with Monte Carlo technique. In addition, a brief discussion about the extension of the method to muti-degree-of-freedom systems is presented.