Stochastic finite element analyses of uncertain nonlinear plane trusses under random excitations

Abstract

A method of stochastic finite element analysis is developed in this study to solve for the response statistics and reliability of nonlinear truss structures with uncertain system parameters under random excitations. Emphasis is on structural nonlinear behavior due to both large deflection and inelastic deformation. The constitutive law is based on an explicit differential equation model, and the model parameters are determined in terms of material property constants according to plasticity theory. Random excitations are modeled as Gaussian filtered white noises, whereas uncertain system parameters are modeled as either random fields or random variables. Based on a total Lagrangian finite element formulation, a set of stochastic nonlinear equations of motion is obtained. A stochastic equivalent linearization method, in conjunction with a perturbation method, is then developed to solve for the total response statistics. A second order asymptotic method is proposed to evaluate the overall structural reliability.

Numerical studies indicate that the proposed method yields accurate results with much less computer time compared with the Monte-Carlo simulation method. It is found that the system uncertainties make a significant contribution to the total response statistics as well as to the overall probability of failure. Dominant system parameters are also identified by non-dimensional response sensitivity analyses.