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… 

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References

SHOWING 1-7 OF 7 REFERENCES
On the numerical solution of singular integral equations
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
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
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,
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