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Articles

Numerical solution of a singular integral equation arising in a cruciform crack problem

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Pages 1767-1783 | Received 07 Sep 2016, Accepted 26 Mar 2017, Published online: 08 Apr 2017

References

  • Polyanin AD, Manzhirov AV. Handbook of integral equations. New York (NY): CRC Press LLC; 1998.
  • Wazwaz A. Linear and nonlinear integral equations: methods and applications. Beijing: High Education Press; 2011.
  • Bardzokas DI, Filshtinsky ML, Filshtinsky LA. Mathematical methods in electro-magneto-elasticity. Berlin: Springer-Verlag; 2007.
  • Wang X. A mode III arc-shaped crack with surface elasticity. Z Angew Math Phys. 2015;66:1987–2000.
  • Golberg MA. Numerical solution of integral equations. New York (NY): Plenum Press; 1990.
  • Kythe PK, Puri P. Computational methods for linear integral equations. Boston: Birkhauser; 2002.
  • Erdogan F. Approximate solutions of systems of singular integral equations. SIAM J Appl Math. 1969;17(6):1041–1059.
  • Kaya AC, Erdogan F. On the solution of integral equations with strongly singular kernesl. Quart Appl Math. 1987;XLV:105–122.
  • Muskhelisvili NI. Singular integral equations. Groningen: Noordhoff; 1953.
  • Bardzokas DI, Mkhitaryan SM, Sfyris GI. The methods of complex potentials, singular integral equations and integral transformations in a series of problems for the reinforcement of cracked plates. Acta Mech. 2011;221:147–174.
  • Erdogan F, Gupta GD, Cook TS. Numerical solution of singular integral equations. In: Sih GC, editor. Mechanics of fracture I. Methods of analysis and solutions to crack problems. Leyden: Noordhoff International Publishing; 1973. p. 368–425.
  • Krenk S. On the use of the interpolation polynomial for solutions of singular integral equations. Quart Appl Math. 1975;32(4):479–484.
  • Li X, Zhou YT, Zhong Z. On the analytical solution for sliding contact of piezoelectric materials subjected to a flat or parabolic indenter. Z Angew Math Phys. 2015;66:473–495.
  • Theocaris PS, Ioakimidis NI. Numerical integration methods for the solution of Singular integral equations. Quart Appl Math. 1977;35:173–183.
  • Theocaris PS, Ioakimidis NI. On the numerical solution of Cauchy type singular integral equations and the determination of stress intensity factors in case of complex singularities. J Appl Math Phy (ZAMP). 1977;28:1085–1098.
  • Setia A. Numerical solution of various cases of Cauchy type singular integral equation. Appl Math Comput. 2014;230:200–207.
  • Rooke DP, Sneddon IN. The crack energy and the stress intensity factor for a cruciform crack deformed by internal pressure. Int J Eng Sci. 1969;7:1079–1089.
  • Stallybrass MP. A pressurized crack in the form of a cross. Quart J Mech Appl Math. 1970;23:35–48.
  • Theocaris PS, Ioakimidis NI. A method of solution of the problem of the unsymmetric cruciform crack in an infinite plane isotropic elastic medium. Acta Mech. 1978;29:127–133.
  • Elliott D. The cruciform crack problem and sigmoidal transformations. Math Meth Appl Sci. 1997;20:121–132.
  • Li XF. T-stress near the tips of a cruciform crack with unequal arms. Eng Fract Mech. 2006;73:671–683.
  • Tang BQ, Li XF. Approximate solution to an integral equation with fixed singularity for a cruciform crack. Appl Math Lett. 2008;21:1238–1244.
  • Zhong XC, Huang QA. Approximate solution of three-point boundary value problems for second order ordinary differential equations with variable coeffcients. Appl Math Comput. 2014;247:18–29.
  • Huang QA, Zhong XC, Guo BL. Approximate solution of Bagley-Torvik equations with variable coeffcients and three-point boundary-value conditions. Int J Appl Comput Math. 2016;2:327–347.
  • Wei HM, Zhong XC, Huang QA. Uniqueness and approximation of solution for fractional Bagley-Torvik equations with variable coefficients. Int J Comput Math. Forthcoming 2016. DOI:10.1080/00207160.2016.1212024
  • Lang S. Real and functional analysis. 3rd ed. New York (NY): Springer-Verlag; 1993.
  • Monegato G, Prössdorf S. On the numerical treatment of an integral equation arising from a cruciform crack problem. Math Meth Appl Sci. 1990;12(6):489–502.

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