title: An efficient stochastic dynamics framework for response determination, reliability assessment, and performance based design of nonlinear structural systems
Creators: name: Mitseas, Ioannis
Publisher: name: University of Liverpool Repository
Year: 2015

description: An approximate analytical technique for determining the survival probability and first-passage probability density function (PDF) of nonlinear multi-degree-of-freedom (MDOF) structural systems subject to an evolutionary stochastic excitation vector is developed. The proposed technique can be construed as a two-stage approach. First, relying on statistical linearization and utilizing a dimension reduction approach the nonlinear n-degree-of-freedom system is decoupled and cast into (n) effective single-degree-of-freedom (SDOF) linear time-varying (LTV) oscillators corresponding to each and every DOF of the original MDOF system. Second, utilizing the effective SDOF LTV oscillator time-varying stiffness and damping elements in conjunction with a stochastic averaging treatment of the problem, the MDOF system survival probability and first-passage PDF are efficiently determined. Applications regarding MDOF structural systems exhibiting highly nonlinear behavior subject to stochastic excitations possessing separable as well as non-separable evolutionary power spectra (EPS) are included. Furthermore, a computationally efficient methodology for conducting fragility analysis of nonlinear/hysteretic MDOF structural systems is developed. Specifically, fragility surfaces are estimated for nonlinear/hysteretic MDOF structural systems subject to evolutionary stochastic earthquake excitations. An approximate nonlinear stochastic dynamics formulation which consist the core of the developed methodology, allows for the efficient computation of structural system fragilities in a straightforward manner while it keeps the computational cost for the corresponding analyses at a minimum level. Nonlinear MDOF structural systems exhibiting a hysteretic restoring force-displacement Bouc-Wen feature, serve as numerical examples for demonstrating the efficiency of the proposed methodology. Comparisons with pertinent Monte Carlo simulations are included as well demonstrating the satisfactory level of the exhibited accuracy. Appended to the above, a novel integrated approach for structural system optimal design considering life cycle cost (LCC) is developed. Specifically, a performance-based multi-objective design optimization framework for nonlinear/hysteretic MDOF structural systems subject to non-stationary stochastic excitations is formulated. The developed approach encompasses an efficient analytical nonlinear stochastic dynamics approach for the determination of the response EPS as well as the non-stationary inter-story drift ratio (IDR) amplitude PDFs, circumventing computationally intensive numerical integrations of the nonlinear equations of motion. It is notable that the proposed framework complies with the most contemporary performance-based earthquake engineering (PBEE) provisions proposed by the Pacific Earthquake Engineering Research (PEER) center. Although the herein developed framework is tailored specifically for earthquake engineering related applications, it can be readily modified to account for other hazard kinds as well. Nonlinear building structures comprising the versatile Bouc-Wen (hysteretic) model serve as numerical applications for demonstrating the efficiency of the developed methodology.