System reliability assessment with nonlinear finite element analysis

System reliability concepts are applicable when the failure of the entire structure is of interest. For such general structural problems, the overall performance can often be predicted only by a nonlinear finite element technique. The development of a practical method to couple nonlinear finite element analysis with probability concepts to estimate the system reliability is the objective of this work;A method named Response Failure Surface Method is developed and illustrated for the case of plane trusses. The limit state of the structure is expressed in terms of the nodal displacements to accommodate either ultimate or serviceability conditions. The response failure surface is an approximation to the actual failure surface with several hyper-planes. The limit state value and its gradients with respect to the random variables are determined by a nonlinear finite element analysis. The gradient analysis is done in conjunction with the structural analysis by differentiating the equilibrium equations. The hyper-plane approximation to the actual failure surface replaces the nonlinear finite element analysis in a Monte Carlo procedure to evaluate the system reliability. In addition, the gradient analysis is incorporated into the Advanced First Order Second Moment method algorithm. An improvement in the probabilities of failure from the response failure surface method over the Advanced First Order Second Moment method is shown by comparing each with the exact limit state method in several examples. An inherent advantage of the response failure surface method is the capacity to account for the nonlinearity of the failure surface, the actual probability density function of the random variables, and the presence of several failure modes.