Nonlinear stochastic dynamic analysis for performance based multi-objective optimum design considering life cycle seismic loss estimation Mitseas, Ioannis P.; Kougioumtzoglou, Ioannis A.; Beer, Michael
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. The core of the developed framework is 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 handle readily stochastic excitations of arbitrary non-separable evolutionary power spectrum (EPS) 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 an example for demonstrating the efficiency of the methodology.
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