Non-stationary response of large, non-linear finite element systems under stochastic loading

A very efficient and straightforward numerical procedure for the computation of statistical second moment characteristics of large, non-linear finite element systems under stochastic loading is presented. For the modeling of both the loading and the response of the system an orthogonal series expansion of the corresponding covariance matrix, the so-called Karhunen–Loève expansion is applied, allowing to incorporate potentially available statistical data of an excitation process directly into the analysis. The non-linear equation of motion is linearized by the method of equivalent statistical linearization. According to the present capabilities of this linearization technique, one-dimensional hysteretic elements are used for modeling the non-linear system behavior. The mode acceleration method is applied in order to reduce significantly the size of the system equation and thus increasing the computational efficiency of the proposed procedure. Contrary to methodologies based on state space formulations, this procedure relies on deterministic step by step integration, implying that the dimension of the system equation is the same as in a purely deterministic analysis.