On the analysis of nonlinear systems under stochastic excitations

The work presented here addresses the evaluation of the stochastic response of nonlinear FE-systems with a relatively large number of degrees of freedom (DOF’s) under random excitation. In order to perform a realistic analysis for such systems, FE-models with nonlinearities are generally considered. Most of the available analytical and numerical methods to calculate the stochastic response are quite limited in many aspects such as the size of the structural system, types of nonlinearity and the excitation modeling, respectively. However, there are mainly two approaches which are capable of dealing with general nonlinear systems with a large number of DOF’s, namely, Monte Carlo simulation (MCS) and statistical equivalent linearization (EQL). For the latter method, a computational procedure is shown where the nonlinear part is discretized into nonlinear elements. It is proposed to linearize each element independently of the other elements using any criterion of linearization. Useful simple FE-element transformation are applied to perform the linearization in suitable minimal local coordinates and to determine the linearization coefficient in the global coordinate system. The approach has been applied to estimate the stochastic response of a 12-story office building using EQL and MCS. The sampling density at the tails of the response distributions has been increased using the weight controlled MCS technique Double&Clump (8; 15).