Publication detail

Improved Gaussian Approximation of the Bundle Strength of Daniels' Model with Brittle Weibull Fibers

SADÍLEK, V. VOŘECHOVSKÝ, M.

Original Title

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

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"
}