Seismic response analysis of nonlinear structures with uncertain parameters under stochastic ground motions

An orthogonal expansion of stochastic ground motion model is incorporated into the probability density evolution method (PDEM). In this regard, a new methodology for seismic response analysis of nonlinear structures with uncertain parameters under stochastic ground motions can be formulated. The fundamentals and numerical algorithms of the methodology are introduced. Then, a rotational quasi-symmetrical point strategy (RQ-SPS) is developed for selecting the representative points in the random-variate space, which is of paramount importance to the tradeoff of accuracy and efficiency for the proposed methodology. An eight storey shear frame structure under seismic excitations, which exhibits strong nonlinear mechanical behaviors, is investigated. The effectiveness of the RQ-SPS is first verified, where the results by Monte Carlo simulations are also provided for comparisons. Then, case studies are implemented, in which the randomness involved in both stochastic ground motions and structural parameters are taken into account. The computational results demonstrate that the effect of randomness in structural parameters cannot be ignored compared to that in stochastic ground motions. Some features of the PDF evolutionary process of response are also discussed.