First-excursion probability of uncertain structures

Abstract

The first-order reliability method (FORM) is used to estimate the first-excursion probability of uncertain structures subjected to deterministic dynamic loading. The limit-state function for the first-excursion event is formulated. A general purpose finite element code is used to compute the limit-state function and its gradient with respect to random structural properties. An algorithm is developed that successively finds the locally minimum distance points on the limit-state surface in the order of increasing distance from the origin in the standard normal space. A standard series system reliability analysis is then performed to compute the first-excursion probability. Two example inelastic structures are used to demonstrate the application and validity of the proposed method.