## Abstract

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 language | English (US) |
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Pages (from-to) | 450-464 |

Number of pages | 15 |

Journal | Engineering Analysis with Boundary Elements |

Volume | 30 |

Issue number | 6 |

DOIs | |

State | Published - Jun 1 2006 |

## Keywords

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