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

@article{Ioakimidis1982TwoMF, title={Two methods for the numerical solution of Bueckner's singular integral equation for plane elasticity crack problems}, author={Nikolaos I. Ioakimidis}, journal={Computer Methods in Applied Mechanics and Engineering}, year={1982}, volume={31}, pages={169-177} }

## 25 Citations

Numerical Solution for an Epicycloid Crack

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Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained and gives an excellent agreement to the existing asymptotic solutions.

A one-dimensional hypersingular integral equation for axisymmetric planar cracks in three-dimensional isotropic elasticity

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The problem of an axisymmetric planar crack (or a system of such cracks) under an arbitrary axisymmetric normal loading distribution inside an infinite three-dimensional isotropic elastic medium is…

A new singular integral equation for the classical crack problem in plane and antiplane elasticity

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- 1983

A new singular integral equation (with a kernel with a logarithmic singularity) is proposed for the crack problem inside an elastic medium under plane or antiplane conditions. In this equation the…

Numerical Solutions for a Nearly Circular Crack with Developing Cusps under Shear Loading

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A modification of the generalized airfoil equation and the corresponding numerical methods

- Mathematics, Engineering
- 1982

The two-dimensional problem of steady, inviscid, irrotational, subsonic flow around a straight or curvilinear thin airfoil or an array of such airfoils inside a wind tunnel is generally reduced to a…

Introduction to the Numerical Solution of Cauchy Singular Integral Equations

- Mathematics
- 1990

In this chapter we present a survey of many of the polynomial-based projection and quadrature methods that have been developed in the past 15 years for the numerical solution of Cauchy singular…

Mangler-type principal value integrals in hypersingular integral equations for crack problems in plane elasticity

- Mathematics
- 1988

Numerical Solution of Singular Integro-differential Equations with Cauchy Kernel

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- 2011

The main purpose of this article is to present an approximation method of for singular integro- differential equations with Cauchy kernel in the most general form under the mixed conditions in terms…

Approximate Methods for Solving Linear and Nonlinear Hypersingular Integral Equations

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- 2020

An iterative projection method for solving linear and nonlinear hypersingular integral equations with non-Riemann integrable functions on the right-hand sides based on the Lyapunov stability theory of solutions of ordinary differential equation systems is proposed.

## References

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Application of finite-part integrals to the singular integral equations of crack problems in plane and three-dimensional elasticity

- Mathematics
- 1982

SummaryA modification of the form of the singular integral equation for the problem of a plane crack of arbitrary shape in a three-dimensional isotropic elastic medium is proposed. This modification…

NUMERICAL-INTEGRATION METHODS FOR SOLUTION OF SINGULAR INTEGRAL-EQUATIONS

- Mathematics
- 1977

The evaluation of the stress intensity factors at the tips of a crack in a homogeneous isotropic and elastic medium may be achieved with higher accuracy and much less computation if the…

A remark on the numerical solution of singular integral equations and the determination of stress-intensity factors

- Mathematics
- 1979

SummaryAs is well-known, an efficient numerical technique for the solution of Cauchy-type singular integral equations along an open interval consists in approximating the integrals by using…

A new singular integral equation for the classical crack problem in plane and antiplane elasticity

- Mathematics
- 1983

A new singular integral equation (with a kernel with a logarithmic singularity) is proposed for the crack problem inside an elastic medium under plane or antiplane conditions. In this equation the…

Field singularities and related integral representations

- Mathematics
- 1973

This chapter is concerned with certain stress fields in isotropic elastic bodies. Assumed will be the laws of linear elasticity where the stresses and strains are related to one another by Hooke’s…

On the numerical solution of singular integral equations

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In this Chapter the numerical methods for the solution of two groups of singular integral equations will be described. These equations arise from the formulation of the mixed boundary value problems…

Approximate Solutions of Systems of Singular Integral Equations

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Using the properties of the related orthogonal polynomials, approximate solutions of systems of simultaneous singular integral equations are obtained, in which the essential features of the…