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The paper deals with the classical fiber bundle model with equal load sharing, sometimes referred to as the the Daniels bundle model or the democratic bundle. This model is significant for the strength of quasi-brittle structures and the reliability of many parallel systems. In the present paper, the authors exploit their own implementation of the recursive formula for the evaluation of the distribution function for fiber bundle strength. The implementation was carried out in the Python high-level programming language using the NumPy (scientific computing with arrays) and mpmath (library for real and complex floating-point arithmetic with arbitrary precision) packages. This implementation enables the calculation of cumulative distribution function values for large numbers (thousands) of fibers in a bundle, including values deep in the left tail of the distribution (probabilities 10−600). This computer program has been used to accurately calculate the distribution functions for bundles with Weibull fibers with the unit scale parameter, the varying number of filaments and the varying shape parameter. A database of these distribution functions has been used to calculate the mean values and standard deviations of the peak force to propose an improved Gaussian approximation of bundle strength.

IMPROVED GAUSSIAN APPROXIMATION OF THE BUNDLE STRENGTH OF DANIELS’ MODEL WITH BRITTLE WEIBULL FIBERS