Reliability of Uncertain Nonlinear Trusses Under Random Excitation. I

This is the first part of a two‐part investigation of reliability of nonlinear‐truss structures with uncertain system parameters under random excitations. The objective is to develop a method of stochastic finite‐element analysis for obtaining response statistics. The related reliability problem is considered in the companion paper. In this study, random excitations are modeled as filtered Gaussian white noises and uncertain system parameters are modeled as either random fields or random variables. Structural nonlinear behavior due to both large deflection and inelastic deformation is considered. The structure is discretized via a total Lagrangian finite‐element formulation that yields a set of stochastic nonlinear equations of motion. An equivalent linearization method in conjunction with a perturbation method is then developed to solve for the total response statistics. No separate mesh for each random field is necessary in this formulation. Numerical examples 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 contribute significantly to the total response statistics.