### Abstract

The boundary integral equation method is developed to study three-dimensional asymptotic singular stress fields at vertices of a pyramidal notch or inclusion in an isotropic elastic space. Two-dimensional boundary integral equations are used for the infinite body with pyramidal notches and inclusions when either stresses or displacements are specified on its surface. Applying the Mellin integral transformation reduces the problem to one-dimensional singular integral equations over a closed, piece-wise smooth line. Using quadrature formulas for regular and singular integrals with Hilbert and logarithmic kernels, these integral equations are reduced to a homogeneous system of linear algebraic equations. Setting its determinant to zero provides a characteristic equation for the determination of the stress singularity power. Numerical results are obtained and compared against known eigenvalues from the literature for an infinite region with a conical notch or inclusion, for a Fichera vertex, and for a half-space with a wedge-shaped notch or inclusion.

Original language | English (US) |
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Pages (from-to) | 263-275 |

Number of pages | 13 |

Journal | Theoretical and Applied Fracture Mechanics |

Volume | 36 |

Issue number | 3 |

DOIs | |

State | Published - Nov 2001 |

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### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials

### Cite this

**Stress singularities for three-dimensional corners using the boundary integral equation method.** / Savruk, M. P.; Shkarayev, Sergey V.

Research output: Contribution to journal › Article

*Theoretical and Applied Fracture Mechanics*, vol. 36, no. 3, pp. 263-275. https://doi.org/10.1016/S0167-8442(01)00076-3

}

TY - JOUR

T1 - Stress singularities for three-dimensional corners using the boundary integral equation method

AU - Savruk, M. P.

AU - Shkarayev, Sergey V

PY - 2001/11

Y1 - 2001/11

N2 - The boundary integral equation method is developed to study three-dimensional asymptotic singular stress fields at vertices of a pyramidal notch or inclusion in an isotropic elastic space. Two-dimensional boundary integral equations are used for the infinite body with pyramidal notches and inclusions when either stresses or displacements are specified on its surface. Applying the Mellin integral transformation reduces the problem to one-dimensional singular integral equations over a closed, piece-wise smooth line. Using quadrature formulas for regular and singular integrals with Hilbert and logarithmic kernels, these integral equations are reduced to a homogeneous system of linear algebraic equations. Setting its determinant to zero provides a characteristic equation for the determination of the stress singularity power. Numerical results are obtained and compared against known eigenvalues from the literature for an infinite region with a conical notch or inclusion, for a Fichera vertex, and for a half-space with a wedge-shaped notch or inclusion.

AB - The boundary integral equation method is developed to study three-dimensional asymptotic singular stress fields at vertices of a pyramidal notch or inclusion in an isotropic elastic space. Two-dimensional boundary integral equations are used for the infinite body with pyramidal notches and inclusions when either stresses or displacements are specified on its surface. Applying the Mellin integral transformation reduces the problem to one-dimensional singular integral equations over a closed, piece-wise smooth line. Using quadrature formulas for regular and singular integrals with Hilbert and logarithmic kernels, these integral equations are reduced to a homogeneous system of linear algebraic equations. Setting its determinant to zero provides a characteristic equation for the determination of the stress singularity power. Numerical results are obtained and compared against known eigenvalues from the literature for an infinite region with a conical notch or inclusion, for a Fichera vertex, and for a half-space with a wedge-shaped notch or inclusion.

UR - http://www.scopus.com/inward/record.url?scp=0035519650&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035519650&partnerID=8YFLogxK

U2 - 10.1016/S0167-8442(01)00076-3

DO - 10.1016/S0167-8442(01)00076-3

M3 - Article

AN - SCOPUS:0035519650

VL - 36

SP - 263

EP - 275

JO - Theoretical and Applied Fracture Mechanics

JF - Theoretical and Applied Fracture Mechanics

SN - 0167-8442

IS - 3

ER -