Reliability Analysis of Dynamic Daniels Systems with Local Load‐Sharing Rule

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Abstract
A method is developed for estimating and bounding the probability of failure of Daniels systems with brittle fibers of random resistances that are subject to quasistatic or dynamic nonstationary Gaussian load processes. A simple local load‐sharing rule is considered in the analysis to model stress concentrations occurring in the vicinity of failed fibers. The system can have numerous failure paths, depending on the number of fibers, probabilistic characteristics of fiber resistances, and the local load‐sharing rule. Concepts of system reliability are employed to develop bounds of various degrees of accuracy on the reliability of Daniels systems. Random vibration techniques, results of the extreme theory of stochastic processes, and a generalized Slepian model are also used in the developments of the paper. Theoretical findings are illustrated by reliability analysis of Daniels systems with three and four fibers subjected to quasi‐static nonstationary Gaussian loads. Results sugggest that even the simplest bounds can provide a conservative estimate for the reliability of Daniels systems.