Stochastic finite-element-based seismic risk of nonlinear structures

An efficient and accurate algorithm is proposed to evaluate risk in the tim e domain for nonlinear structures subjected to short duration dynamic loadi ngs, especially seismic loading. The algorithm is based on the stochastic f inite-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 o f the response surface method, the finite-element method, the first-order r eliability method, and the iterative linear interpolation scheme. Two itera tive response surface schemes consisting of second-order polynomials (with and without cross terms) are proposed. A mixture of saturated and central c omposite design is used to assure both efficiency and accuracy in the algor ithm. Sensitivity analysis is used to improve the efficiency further. The r isk corresponding to both the serviceability and strength limit states is e stimated. The unique feature of the algorithm is that actual earthquake loa ding time histories can be used to excite structures, enabling a realistic representation of the loading conditions. The algorithm is further clarifie d with the help of two examples.