An approximate stochastic dynamics approach for nonlinear structural system performance-based multi-objective optimum design

• Approximate nonlinear stochastic dynamic analysis.
• Life-cycle cost stochastic design problem.
• Random vibration based techniques.
• Dealing efficiently with moving resonance phenomena.
• Structural system fragility curves are determined at a low computational cost.

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.