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.
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))
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))
- F. Erdogan, G. D. Gupta, and T. S. Cook, Numerical solution of singular integral equations, Mechanics of fracture, Vol. 1, Noordhoff, Leiden, 1973, pp. 368–425. MR 0471394
- F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 29 (1971/72), 525–534. MR 408277, DOI https://doi.org/10.1090/S0033-569X-1972-0408277-4
- M. M. Chawla and T. R. Ramakrishnan, Modified Gauss-Jacobi quadrature formulas for the numerical evaluation of Cauchy type singular integrals, Nordisk Tidskr. Informationsbehandling (BIT) 14 (1974), 14–21. MR 331729, DOI https://doi.org/10.1007/bf01933113
- Steen Krenk, On the use of the interpolation polynomial for solutions of singular integral equations, Quart. Appl. Math. 32 (1974/75), 479–484. MR 474919, DOI https://doi.org/10.1090/S0033-569X-1975-0474919-7
Z. Kopal, Numerical analysis, Chapman and Hall, London, 1961
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)
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))
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))
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
F. Erdogan and G. D. Gupta, On the numerical solution of singular integral equations, Quart. Appl. Math. 30, 525–534 (1972)
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)
S. Krenk, On the use of the interpolation polynomial for solutions of singular integral equations, Quart. Appl. Math. 32, 479–484 (1975)
Z. Kopal, Numerical analysis, Chapman and Hall, London, 1961
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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© Copyright 1977
American Mathematical Society