Finite-element-based system reliability analysis of fatigue-induced sequential failures

When a structural system is subjected to repeated loadings, local fatigue-induced failures may initiate sequential failures and disproportionally large damage in the system. In order to quantify the likelihood of fatigue-induced sequential failures and identify critical failure sequences, a branch-and-bound method employing system reliability bounds (termed the B3 method) was recently developed and successfully demonstrated by a three-dimensional truss example. The B3 method identifies critical sequences of fatigue-induced failures in the decreasing order of their likelihood. Since the identified sequences are disjoint to each other, both lower and upper bounds on system failure probability are easily updated without performing additional system reliability analysis. The updated bounds provide reasonable criteria for terminating the branch-and-bound search without missing critical sequences or estimating the system-level risk inaccurately. Since the B3 method was originally developed for reliability analysis of discrete structures such as truss, however, the method is not applicable to continuum structures, which are often represented by finite element (FE) models. In particular, the method has limitations in describing general stress distributions in limit-state formulations, evaluating stress intensity range based on crack length, and in dealing with slow convergence of the upper and lower bounds for structures with high redundancy. In this paper, the B3 method is further developed for FE-based system reliability analysis of continuum structures by modifying the limit-state formulations, incorporating crack-growth analysis by external software, and introducing an additional search termination criterion. The proposed method is demonstrated by numerical examples including a continuum multi-layer Daniels system and an aircraft longeron structure.