Statistical random response analysis and reliability design of structure system with non-linearity

In this paper, a method to analyse a complex non-linear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process for the statistical analysis. When modelling the overall non-linear system, the overall system is divided into substructures and these are approximately transformed into modal coordinates with the random excitation. The modal equations of the overall system are expanded sequentially according to the non-linear order. Then, the perturbed equations are synthesised into the overall system and solved in a probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with the non-linear stochastic problem. The obtained statistical properties of the non-linear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.