Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Numerical integration methods for the solution of singular integral equations


Authors: P. S. Theocaris and N. I. Ioakimidis
Journal: Quart. Appl. Math. 35 (1977), 173-183
MSC: Primary 65R05
DOI: https://doi.org/10.1090/qam/445873
MathSciNet review: 445873
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Abstract: 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 medium proves the potentialities of the new approach.


References [Enhancements On Off] (What's this?)

  • [1] R. V. Gol'dshtein and L. N. Savova, Determination of crack opening and stress intensity coefficients for a smooth curvilinear crack in an elastic plane, Mech. Solids 7, 64-71 (1972) (translation of: Izv. AN SSSR, Mekh. Tverdogo Tela 7, 69-78 (1972))
  • [2] A. P. Datsyshin and M. P. Savruk, A system of arbitrarily oriented, cracks in elastic solids, J. Appl. Math. Mech. (PMM) 37, 306-313 (1973) (translation of: Prik. Mat. Mekh. 37, 326-332 (1973))
  • [3] F. Erdogan, G. D. Gupta and T. S. Cook, Numerical solution of singular integral equations, in Methods of analysis and solutions of crack problems (Vol. 1 in the series Mechanics of fracture, edited by G. C. Sih), Noordhoff Int. Publ., Leyden, 1973, pp. 368-425 MR 0471394
  • [4] F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 30, 525-534 (1972) MR 0408277
  • [5] M. M. Chawla and T. R. Ramakrishnan, Modified Gauss-Jacobi quadrature formulas for the numerical evaluation of Cauchy-type singular integrals, BIT 14, 14-21 (1974) MR 0331729
  • [6] S. Krenk, On the use of the interpolation polynomial for solutions of singular integral equations, Quart. Appl. Math. 32, 479-484 (1975) MR 0474919
  • [7] Z. Kopal, Numerical analysis, Chapman and Hall, London, 1961
  • [8] D. P. Rooke and I. N. Sneddon, The crack energy and the stress intensity factor for a cruciform crack deformed by internal pressure, Int. J. Engng. Science 7, 1079-1089 (1969)

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DOI: https://doi.org/10.1090/qam/445873
Article copyright: © Copyright 1977 American Mathematical Society

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