# NUMERICAL-INTEGRATION METHODS FOR SOLUTION OF SINGULAR INTEGRAL-EQUATIONS

@inproceedings{Theocaris1977NUMERICALINTEGRATIONMF, title={NUMERICAL-INTEGRATION METHODS FOR SOLUTION OF SINGULAR INTEGRAL-EQUATIONS}, author={Pericles S. Theocaris and Nikolaos I. Ioakimidis}, year={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 Lobatto-Chebyshev method of numerical solution of the corresponding system of singular integral equations is used instead of the method of Gauss-Chebyshev commonly applied to such problems. Comparison of results obtained by the two numerical methods when applied to the problem of a cruciform crack in an infinite…

## Figures from this paper

## 270 Citations

A combination of the finite element and singular‐integral equation methods for the solution of the generally cracked body

- Mathematics
- 1984

A superconvergence result for the natural extrapolation formula for the numerical determination of stress intensity factors

- Mathematics
- 1985

The best approach for the numerical determination of stress intensity factors at crack tips in plane and antiplane elasticity problems is frequently the numerical solution of the corresponding…

A combined integral-equation and finite-element method for the evaluation of stress intensity factors

- Mathematics
- 1982

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

- Mathematics
- 1982

Simple bounds for the stress intensity factors by the method of singular integral equations

- Mathematics
- 1983

Computational Analysis of Singular Integral Equations for Crack Problems

- Mathematics
- 1993

Computational method of singular Integral equations for crack problems is presented. This method is based on the concept of the boundary collocation and reduces the singular Integral equation Into a…

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 remark on the numerical evaluation of stress intensity factors by the method of singular integral equations

- Mathematics
- 1979

A modification of the numerical techniques of solution of Cauchy-type singular integral equations and determination of stress intensity factors at crack tips in plane elastic media is proposed. This…

## References

SHOWING 1-7 OF 7 REFERENCES

The crack energy and the stress intensity factor for a cruciform crack deformed by internal pressure

- Physics
- 1969

On the numerical solution of singular integral equations

- Mathematics
- 1972

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…

On the use of the interpolation polynomial for solutions of singular integral equations

- Mathematics
- 1975

On the basis of integration of singular integral equations by means of Gaussian quadrature, it is demonstrated how to obtain the corresponding approximate polynomial solution. For some special cases…

Modified gauss-jacobi quadrature formulas for the numerical evaluation of cauchy type singular integrals

- Mathematics
- 1974

We obtain modified Gauss-Jacobi quadrature formulas for the numerical evaluation of Cauchy principal values of integralsα,β>−1, wheref(x) possesses one or more simple poles in (−1, 1). Forα=β=±1/2,…

A system of arbitrarily oriented cracks in elastic solids: PMM vol. 37, n≗2, 1973, pp. 326–332

- Political Science
- 1973

Savruk, A system of arbitrarily oriented cracks in elastic solids

- J. Appl. Math. Mech. (PMM)
- 1973

Determination of crack opening and stress intensity coefficients for a smooth curvilinear crack in an elastic plane

- Mech. Solids
- 1972