Structural System Reliability Quantification Using Multipoint Function Approximations

Abstract

In structural problems, when dealing with uncertainties, the failure probability of the structure is estimated subject to a particular performance criterion. However, when the failure of a structural system is governed by multiple failure criteria, all of the measures have to be considered in the failure probability estimation. These failure criteria are usually correlated, and the accuracy of the estimated structural failure probability highly depends on the ability to model the joint failure surface. For example, in an aircraft structure, the stresses in each of the members of a wing can be posed as limit-state functions, along with the displacements and the natural frequencies of the wing. There are no criteria to disregard one limit state over the other, or to convert the system reliability problem into component reliability (dealing with displacement, stress, and frequency individually). Each failure criterion is modeled as a limit-state function for the reliability analysis, which is an implicit function of the random variables. The evaluation of this limit state often requires an expensive finite element simulation or a computational fluid dynamics simulation. Therefore, to predict the failure probability of a structural system efficiently, function approximations for the limit states are considered. An accurate way of defining highly nonlinear functions is presented using a new class of approximations. These approximations are used in conjunction with the Monte Carlo simulation to estimate the structural failure probability. Numerical examples are presented to show the applicability of the proposed method.