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Reliability Calculus on Crack Propagation Problem with a Markov Renewal Process

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Computational Methods for Solids and Fluids

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 41))

Abstract

This chapter concerns a stochastic differential system that describes the evolution of a degradation mechanism, the fatigue crack propagation. A Markov process will be considered as the perturbing process of the system that models the crack evolution. With the help of Markov renewal theory, we study the reliability of a structure and propose for it a new analytical solution. The method we propose reduces the complexity of the reliability calculus compared with the previous resolution method. As numerical applications, we tested our method on a numerical example and on an experimental data set, which gave results in good agreement with a Monte Carlo estimation.

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Authors and Affiliations

  1. Sorbonne Universités, Université de Technologie de Compiègne, rue du Dr Schweitzer, CS 60319, 60203, Compiegne Cedex, France

    Chrysanthi A. Papamichail, Salim Bouzebda & Nikolaos Limnios

Authors
  1. Chrysanthi A. Papamichail
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  2. Salim Bouzebda
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  3. Nikolaos Limnios
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Correspondence to Nikolaos Limnios .

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Editors and Affiliations

  1. Laboratoire Mécanique Roberval, Université Technologie Compiègne, Compiegne, France

    Adnan Ibrahimbegovic

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Papamichail, C.A., Bouzebda, S., Limnios, N. (2016). Reliability Calculus on Crack Propagation Problem with a Markov Renewal Process. In: Ibrahimbegovic, A. (eds) Computational Methods for Solids and Fluids. Computational Methods in Applied Sciences, vol 41. Springer, Cham. https://doi.org/10.1007/978-3-319-27996-1_13

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  • DOI: https://doi.org/10.1007/978-3-319-27996-1_13

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