Two methods for the numerical solution of Bueckner's singular integral equation for plane elasticity crack problems

1982 ◽  
Vol 31 (2) ◽  
pp. 169-177 ◽  
Author(s):  
N.I. Ioakimidis
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Numerical Solution ◽  
Singular Integral ◽  
Plane Elasticity ◽  
Crack Problems

The Solution of Crack Problems by Using Distributed Strain Nuclei

1996 ◽  
Vol 210 (1) ◽  
pp. 23-31 ◽  
Author(s):  
A M Korsunsky ◽  
D A Hills
Keyword(s):  
Integral Equation ◽  
Stress Field ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Crack Problems ◽  
The Relationship ◽  
Distributed Strain

Crack problems may be solved by first establishing the stress field in the crack's absence and distributing strain nuclei along the line of the crack in order to render its faces traction-free. The relationship between the different possible forms of nucleus and the kinds of singular integral equation to which they lead are explored. The merits of each are then highlighted.

scholarly journals Numerical solution of a weakly singular integral equation by the method of orthogonal polynomials

2021 ◽  
pp. 98-103
Author(s):  
Sergei M. Sheshko
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Orthogonal Polynomials ◽  
Numerical Solution ◽  
Singular Integral ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Expansion Coefficients ◽  
Analytical Expressions

A scheme is constructed for the numerical solution of a singular integral equation with a logarithmic kernel by the method of orthogonal polynomials. The proposed schemes for an approximate solution of the problem are based on the representation of the solution function in the form of a linear combination of the Chebyshev orthogonal polynomials and spectral relations that allows to obtain simple analytical expressions for the singular component of the equation. The expansion coefficients of the solution in terms of the Chebyshev polynomial basis are calculated by solving a system of linear algebraic equations. The results of numerical experiments show that on a grid of 20 –30 points, the error of the approximate solution reaches the minimum limit due to the error in representing real floating-point numbers.

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