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

M. P. Savruk, Sergey V Shkarayev

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)263-275
Number of pages13
JournalTheoretical and Applied Fracture Mechanics
Volume36
Issue number3
DOIs
StatePublished - Nov 2001

Fingerprint

Stress Singularity
Boundary Integral Equation Method
Boundary integral equations
Notch
notches
integral equations
Inclusion
inclusions
Three-dimensional
Integral equations
apexes
Logarithmic Kernel
singular integral equations
Integral Transformation
integral transformations
characteristic equations
Characteristic equation
Singular Integrals
Quadrature Formula
Singular Integral Equation

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.

In: Theoretical and Applied Fracture Mechanics, Vol. 36, No. 3, 11.2001, p. 263-275.

Research output: Contribution to journalArticle

@article{7b19ee2bbafd40988894219675ec8387,
title = "Stress singularities for three-dimensional corners using the boundary integral equation method",
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.",
author = "Savruk, {M. P.} and Shkarayev, {Sergey V}",
year = "2001",
month = "11",
doi = "10.1016/S0167-8442(01)00076-3",
language = "English (US)",
volume = "36",
pages = "263--275",
journal = "Theoretical and Applied Fracture Mechanics",
issn = "0167-8442",
publisher = "Elsevier",
number = "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 -