Stochastic finite-element-based seismic risk of nonlinear structures

An efficient and accurate algorithm is proposed to evaluate risk in the time domain for nonlinear structures subjected to short duration dynamic loadings, especially seismic loading. The algorithm is based on the stochastic finite-element concept. Uncertainties in the dynamic and seismic excitation and the resistance-related parameters are incorporated by modeling them as realistically as possible. The proposed algorithm integrates the concepts of the response surface method, the finite-element method, the first-order reliability method, and the iterative linear interpolation scheme. Two iterative response surface schemes consisting of second-order polynomials (with and without cross terms) are proposed. A mixture of saturated and central composite design is used to assure both efficiency and accuracy in the algorithm. Sensitivity analysis is used to improve the efficiency further. The risk corresponding to both the serviceability and strength limit states is estimated. The unique feature of the algorithm is that actual earthquake loading time histories can be used to excite structures, enabling a realistic representation of the loading conditions. The algorithm is further clarified with the help of two examples.