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An approximate stochastic dynamics approach for efficient performance-based earthquake engineering

A novel approach for structural system optimal design considering seismic 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 earthquake excitation is formulated.
The core of the developed framework is an efficient approximate analytical dimension reduction approach for determining the system response evolutionary power spectrum (EPS) matrix based on the concepts of statistical linearization and stochastic averaging; thus, computationally intensive Monte Carlo simulations are circumvented. Note that the approach can handle readily stochastic excitations of arbitrary EPS forms, even of the non-separable kind. Further, approximate closed-form expressions are derived for the non-stationary response amplitude PDFs of the inter-story drift ratios (IDRs) corresponding to each and every DOF. In this regard, considering appropriately defined damage measures (DMs) structural system related fragility curves are determined at a low computational cost as well.
Furthermore, conceptually consistent with the performance-based earthquake engineering (PBEE) methodology, the structural system design optimization problem is formulated as a multi-objective optimization problem to be solved by a Genetic Algorithm based approach, specifically tailored to meet the characteristics of the problem under consideration. In this regard, different compromise solutions are obtained; thus, providing the designer with enhanced flexibility regarding decision-making analysis. A building structure comprising the versatile Bouc-Wen (hysteretic) model serves as a numerical example for demonstrating the efficiency and reliability of the proposed methodology.

Author(s):

Ioannis P. Mitseas    
University of Liverpool
United Kingdom

Ioannis A. Kougioumtzoglou    
Columbia University
United States

Michael Beer    
University of Liverpool
United Kingdom