Reliability of Uncertain Nonlinear Trusses under Random Excitation. II

This is the second part of an investigation of the reliability of nonlinear‐truss structures with uncertain system parameters under random excitations. It develops a method for efficient reliability evaluation of such structures. A modified version of the fast integration method reported by Wen and Chen in 1987 in conjunction with a second‐order asymptotic method reported by Breitung in 1989 is developed to solve for the overall failure probability. The proposed method is applicable to problems for which the conditional failure probabilities given system parameters are available, for example, by random vibration or other empirical methods. It does not require the transformation of original random variables into standard normal variables; as a result, numerical efforts and mathematical complications associated with this transformation are eliminated. The sensitivity of the failure probability to changes in probability‐distribution parameters can be easily computed. The numerical study indicates that the proposed method yields accurate results with less computer time compared with the Monte Carlo simulation method. The system uncertainties contribute significantly to the overall failure probability.