This is a repository copy of A novel stochastic linearization framework for seismic demand estimation of hysteretic MDOF systems subject to linear response spectra.

440 INTRODUCTIONExcitations acting upon dynamical systems such as wind, wave, and seismic loads commonly exhibit evolutionary features. In this setting, not only the intensity of the excitation but also its frequency content exhibit strong variability. This fact necessitates the representation of this class of structural loads by non-stationary stochastic processes. Further, structural systems under severe excitations can exhibit significant nonlinear behavior of the hysteretic kind. Thus, of particular interest to the structural dynamics community is the development of techniques for determining the response and assessing the reliability of nonlinear/hysteretic systems subject to evolutionary stochastic excitations (e.g.,Further, in engineering dynamics, the evaluation of the probability that the system response stays within prescribed limits for a specified time interval is advantageous for reliability based system design applications. In this regard, the first-passage problem, that is, the determination of the above time-variant probability known as survival probability, has been a persistent challenge in the field of stochastic dynamics for many decades.Monte Carlo simulation techniques are among the most potent tools for assessing the reliability of a system (e.g. [4]). Nevertheless, there are cases where the computational cost of these techniques can be prohibitive, especially when large-scale complex systems are considered; thus, rendering the development of alternative efficient approximate analytical/numerical techniques for addressing the first-passage problem necessary. Indicatively, one of the early approaches, restricted to linear systems, relies on the knowledge of the mean up-crossing rates and on Poisson distribution based approximations (e.g., [5] to [7]). Further attempts to address the firstpassage problem range from analytical ones (e.g., [8]) to numerical ones (e.g., [9]

A novel approach for structural system optimal design considering life cycle cost is developed.Specifically, a performance-based multi-objective design optimization framework for nonlinear/hysteretic multi-degree-of-freedom (MDOF) structural systems subject to evolutionary stochastic excitation is formulated. In the core of the stochastic structural analysis component of the proposed framework lies an efficient approximate dimension reduction technique based on the concepts of statistical linearization and of stochastic averaging for determining the non-stationary system response amplitude probability density functions (PDFs); thus, computationally intensive Monte Carlo simulations are circumvented. Note that the approach can readily handle stochastic excitations of arbitrary non-separable evolutionary power spectral density (EPSD) forms that exhibit strong variability in both the intensity and the frequency content. Further, approximate closed-form expressions are derived for the non-stationary inter-story drift ratio amplitude PDFs corresponding to each and every DOF. In this regard, considering appropriately defined damage measures structural system related fragility curves are determined at a low computational cost as well. Finally, the structural system design optimization problem is formulated as a multi-objective one to be solved by a genetic algorithm based approach. A building structure comprising the versatile Bouc-Wen (hysteretic) model serves as a numerical example for demonstrating the efficiency of the proposed methodology.

This is a repository copy of Modal decomposition method for response spectrum based analysis of nonlinear and non-classically damped systems.