On the stochastic response of nonlinear FE models

Abstract

This paper focuses on the stochastic dynamic response of structures modeled by finite elements with a relatively large number of degrees of freedom. FE models with nonlinearities and uncertain (stochastic) system properties are discussed. It is shown that component mode synthesis can be used most advantageously to solve the issue of computational efficiency and feasibility. The stochastic response due to stochastic loading of large FE models with nonlinear elements is determined by statistical equivalent linearization (EQL). The developed component-mode synthesis allows to determine the complex modal properties of arbitrary large linearized finite element models. Nonsymmetric structural matrices, as a result of the EQL, and filters for modeling of filtered white noise can be treated by the suggested approach. Since the efficiency of the procedure is nearly independent of the number of degrees-of-freedom (DOF) involved, statistical equivalent linearization becomes applicable for arbitrary detailed FE models. Furthermore, the dynamic response of FE models with uncertain or stochastic system properties is discussed. In this case, Monte Carlo simulation is suggested as the most appropriate approach for FE models. The paper focuses on the random eigenvalue problem for large FE systems as the computationally most demanding part of the dynamic analysis. Component-mode synthesis is used to provide in an efficient manner all the eigenvalue solutions of the FE system needed by the Monte Carlo simulation.