A boundary integral method for multiple circular holes in an elastic half-plane

Alexandre Dejoie, Sofia Mogilevskaya, Steven L Crouch

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25 Scopus citations


This paper presents a semi-analytical method for solving the problem of an isotropic elastic half-plane containing a large number of randomly distributed, non-overlapping, circular holes of arbitrary sizes. The boundary of the half-plane is assumed to be traction-free and a uniform far-field stress acts parallel to that boundary. The boundaries of the holes are assumed to be either traction-free or subjected to constant normal pressure. The analysis is based on solution of complex hypersingular integral equation with the unknown displacements at each circular boundary approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using a Taylor series expansion. The resulting semi-analytical method allows one to calculate the elastic fields everywhere in the half-plane. Several examples available in the literature are re-examined and corrected, and new benchmark examples with multiple holes are included to demonstrate the effectiveness of the approach.

Original languageEnglish (US)
Pages (from-to)450-464
Number of pages15
JournalEngineering Analysis with Boundary Elements
Issue number6
StatePublished - Jun 1 2006


  • Complex hypersingular integral equation
  • Elasticity
  • Half-plane
  • Multiple circular holes


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