Boundary element analysis of non-planar three-dimensional cracks using complex variables

Dmitry V. Nikolskiy, Sofia Mogilevskaya, Joseph F Labuz

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This paper reports new developments on the complex variables boundary element approach for solving three-dimensional problems of cracks in elastic media. These developments include implementation of higher order polynomial approximations for the boundary displacement discontinuities and more efficient analytical techniques for evaluation of integrals. The approach employs planar triangular boundary elements and is based on the integral representations written in a local coordinate system of an element. In-plane components of the fields involved in the representations are separated and arranged in certain complex combinations. The Cauchy-Pompeiu formula is used to reduce the integrals over the element to those over its contour and evaluate the latter integrals analytically. The system of linear algebraic equations to find the unknown boundary displacement discontinuities is set up via collocation. Several illustrative numerical examples involving a single (penny-shaped) crack and multiple (semi-cylindrical) cracks are presented.

Original languageEnglish (US)
Pages (from-to)44-54
Number of pages11
JournalInternational Journal of Rock Mechanics and Mining Sciences
StatePublished - Jun 1 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Ltd.


  • Boundary element method
  • Computer simulations
  • Three-dimensional fractures


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