A response surface method for stochastic dynamic analysis

A Response Surface (RS) strategy is presented for the evaluation of the response statistics of dynamic systems subjected to stochastic excitation. The proposed approach adopts a strategy based on the High Dimensional Model Representation (HDMR), which gives a Gaussian Model (GM) of the response. The GM requires only a reduced number of analyses which can be adopted for all the degrees of freedom of a MDOF dynamic system and it can be successfully adopted for weakly nonlinear dynamic systems. For more strongly nonlinear systems a Non-Gaussian approximation may be necessary for the highest response thresholds. In this paper this issue is accomplished through the FORM solution, and the design point is obtained by using a response surface method recently proposed by the author and Der Kiureghian to this aim. The latter response surface is based on a variant of the Model Correction Factor Method (MCFM), which is here applied by using as a starting model the GM itself. In many applications of engineering interest, both the input and the response processes are stationary, so that the stochastic excitation through the Fourier series can be modeled in terms of the underlying Power Spectral Density (PSD). In these cases, it is seen that the dynamic computations required by the proposed approach can decrease significantly. The application to SDOF and MDOF hysteretic systems shows the effectiveness of the presented method.