Statistical Characteristics of the Distraction Parameters in the Unbounded Anisotropic Plane Weakened by Multiple Random Cracks

  • L. A. Filshtinskii
  • D. M. NosovEmail author
  • Yu. V. Shramko
Conference paper
Part of the Trends in Mathematics book series (TM)


The boundary value problem of the theory of elasticity for a finite anisotropic plate with random cracks has been solved. Stress intensity factors and energy flows near the tips of cracks are determined as a linear functional on solutions to a system of singular integral equations. It is shown, that in case of the normal distribution of the cracks, the statistical characteristics (mathematical expectations and dispersions) of the distraction (stress intensity factors and energy flows) have also the normal law distribution.


Anisotropy Multiple cracks Singular integral equations Stress intensity factors 

Mathematics Subject Classification (2010)

Primary 74R74; Secondary 74B74 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • L. A. Filshtinskii
    • 1
  • D. M. Nosov
    • 2
    Email author
  • Yu. V. Shramko
    • 1
  1. 1.Sumy State UniversitySumyUkraine
  2. 2.Pedagogical University of CracowCracowPoland

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