Abstract
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.
Highlights
The method of stochastic equivalent linearization (SEL) is one of the most common methods within the approximate approaches for stochastic dynamic analysis of nonlinear systems
The authors [7] have found that when the hypothesis related to the response of single-degree-of-freedom (SDOF) systems with hysteretic behavior has Gaussian distribution, the standard deviation of the displacement response can be underestimated in the order of 45%; the probability of failure widely deviates from the Monte Carlo simulation results, especially for systems with high displacement ductility demands
This is mainly due to the fact that a Gaussian probability distribution is assumed for all variables; the restoring force should lie on a finite region, implying that its probability density function (PDF) is non-Gaussian
Summary
The method of stochastic equivalent linearization (SEL) is one of the most common methods within the approximate approaches for stochastic dynamic analysis of nonlinear systems. The authors [7] have found that when the hypothesis related to the response of single-degree-of-freedom (SDOF) systems with hysteretic behavior has Gaussian distribution, the standard deviation of the displacement response can be underestimated in the order of 45%; the probability of failure widely deviates from the Monte Carlo simulation results, especially for systems with high displacement ductility demands This is mainly due to the fact that a Gaussian probability distribution is assumed for all variables; the restoring force should lie on a finite region, implying that its probability density function (PDF) is non-Gaussian. In order to derive the non-Gaussian equivalent linearization coefficients, a model appropriately representing the time evolution of the joint probability density function of the structural response of softening systems subjected to seismic ground motions is used. An extension of the proposed method to multi-degree-offreedom (MDOF) systems is outlined at the end of the paper
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