Stochastic Finite Element Analysis of Uncertain Nonlinear Trusses under Random Loadings

Abstract

A method of analysis is developed of the responses of nonlinear trusses with uncertain system parameters under random loadings. The structural nonlinear behaviors may arise from large deflection and/or inelastic deformation. Based on a total Lagrangian finite element formulation, a stochastic equivalent linearization method in conjunction with a perturbation method is developed to solve for the response statistics. Responses of a structure under Gaussian filtered white noise ground excitation are obtained and compared with Monte-Carlo simulation results. The stochastic equivalent linearization method was found to yield reasonably accurate results with much less computational time. Depending on the amount of system uncertainties, their contribution to the total response statistics can be quite significant, i.e., more than that due to the randomness of the loading time history. A non-dimensional response sensitivity coefficient is also defined to identify the most dominant system parameters in terms of the contribution to the response variability.