Finite-part integral and boundary element method to solve flat crack problems

In this paper, we study the behavior of the solution at the crack edges for a nearly circular crack with developing cusps subject to shear loading. The problem of finding the resulting force can be written in the form of a hypersingular integral equation. The equation is then transformed into a similar equation over a circular region using conformal mapping. The equation is solved numerically for the unknown coefficients, which will later be used in finding the stress intensity factors. The sliding and tearing mode stress intensity factors are evaluated for cracks and displayed graphically. Our results seem to agree with the existing asymptotic solution.

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Numerical solutions for a nearly circular crack with developing cusps under shear loading

Long

Koo

Eshkuvatov

2011

Acta Mechanica Solida Sinica

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Numerical Solution for an Epicycloid Crack

Long

Feng

Eshkuvatov

2014

Journal of Applied Mathematics

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A flat crack,Ω, is lying in a three-dimensional homogenous isotropic elastic solid subjected to shear loading. A mathematical formulation is developed based on the mixed boundary values forΩsuch that the problem of finding the resulting force can be written in the form of hypersingular integral equation. Employing conformal mapping, the integral equation is transformed to a similar equation over a circular region,D. By making a suitable representation of hypersingular integral equation, the problem is reduced to solve a system of linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions.

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Finite-part integral and boundary element method to solve flat crack problems

Cited by 2 publications

References 7 publications

Numerical solutions for a nearly circular crack with developing cusps under shear loading

Numerical solutions for a nearly circular crack with developing cusps under shear loading

Numerical Solution for an Epicycloid Crack

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