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SADÍLEK, V. VOŘECHOVSKÝ, M.
Original Title
Improved Gaussian Approximation of the Bundle Strength of Daniels' Model with Brittle Weibull Fibers
Type
conference paper
Language
English
Original Abstract
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. 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.
Keywords
Fiber bundle model; strength of the bundle; Daniels bundle model; equal load sharing; Weibull distribution; cumulative distribution function
Authors
SADÍLEK, V.; VOŘECHOVSKÝ, M.
RIV year
2015
Released
25. 9. 2015
Publisher
M. Papadrakakis, V. Papadopoulos, G. Stefanou
Location
Crete Island, Greece
ISBN
978-960-99994-9-6
Book
Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering, held in Crete, Greece
Pages from
986
Pages to
994
Pages count
8
BibTex
@inproceedings{BUT118939, author="Václav {Sadílek} and Miroslav {Vořechovský}", title="Improved Gaussian Approximation of the Bundle Strength of Daniels' Model with Brittle Weibull Fibers", booktitle="Proceedings of the 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering, held in Crete, Greece", year="2015", pages="986--994", publisher="M. Papadrakakis, V. Papadopoulos, G. Stefanou", address="Crete Island, Greece", isbn="978-960-99994-9-6" }