DOI QR코드

DOI QR Code

Numerical solution of singular integral equation for multiple curved branch-cracks

  • Chen, Y.Z. (Division of Engineering Mechanics, Jiangsu University) ;
  • Lin, X.Y. (Division of Engineering Mechanics, Jiangsu University)
  • 투고 : 2007.04.16
  • 심사 : 2009.10.19
  • 발행 : 2010.01.10

초록

In this paper, numerical solution of the singular integral equation for the multiple curved branch-cracks is investigated. If some quadrature rule is used, one difficult point in the problem is to balance the number of unknowns and equations in the solution. This difficult point was overcome by taking the following steps: (a) to place a point dislocation at the intersecting point of branches, (b) to use the curve length method to covert the integral on the curve to an integral on the real axis, (c) to use the semi-open quadrature rule in the integration. After taking these steps, the number of the unknowns is equal to the number of the resulting algebraic equations. This is a particular advantage of the suggested method. In addition, accurate results for the stress intensity factors (SIFs) at crack tips have been found in a numerical example. Finally, several numerical examples are given to illustrate the efficiency of the method presented.

키워드

참고문헌

  1. Ballarini, R. and Vallaggio, P. (2006), "Frobenius' method for curved cracks", Int. J. Fracture, 139, 59-69. https://doi.org/10.1007/s10704-006-6730-0
  2. Boiko, A.V. and Karpenko, L.N. (1981), "On some numerical methods for the solution of the plane elasticity problem for bodies with cracks by means of singular integral equation", Int. J. Fracture, 17, 381-388. https://doi.org/10.1007/BF00036190
  3. Burton Jr., J. K. and Phoenix, S.L. (2000), "Superposition method for calculating singular stress fields at kinks, branches, and tips in multiple crack arrays", Int. J. Fracture, 102, 99-139. https://doi.org/10.1023/A:1007558018808
  4. Chau, K.T. and Wang, Y.B. (1999), "A new boundary integral formulation for plane elastic bodies containing cracks and holes", Int. J. Solids Struct., 36, 2041-2074. https://doi.org/10.1016/S0020-7683(98)00078-X
  5. Cheeseman, B.A. and Santare, M.H. (2000), "The interaction of a curved crack with a circular elastic inclusion", Int. J. Fracture, 103, 259-277. https://doi.org/10.1023/A:1007663913279
  6. Chen, Y.Z. (1995), "A survey of new integral equation in plane elasticity crack problem", Eng. Fracture Mech., 51, 97-134. https://doi.org/10.1016/0013-7944(94)00229-B
  7. Chen, Y.Z. (2003), "A numerical solution technique of hypersingular integral equation for curved cracks", Commun. Numer. Meth. Eng., 19, 645-655. https://doi.org/10.1002/cnm.623
  8. Chen, Y.Z. and Lin, X.Y. (2008), "T-stress evaluation for curved crack problems", Acta Mech., 198, 35-50. https://doi.org/10.1007/s00707-007-0519-8
  9. Chen, Y.Z., Lin, X.Y. and Wang, Z.X. (2008), "T-stress evaluation for slightly curved crack using perturbation method", Int. J. Solids Struct., 45, 211-224. https://doi.org/10.1016/j.ijsolstr.2007.07.020
  10. Chen, Y.Z. and Hasebe, N. (1995), "New integration scheme for the branch crack problem", Eng. Fracture Mech., 52, 791-801. https://doi.org/10.1016/0013-7944(95)00052-W
  11. Cheung, Y.K. and Chen, Y.Z. (1987), "New integral equation for plane elasticity crack problem", Theor. Appl. Fracture Mech., 7, 177-184. https://doi.org/10.1016/0167-8442(87)90033-4
  12. Daux, C., Moes, N., Dolbow, J., Sukumar, N. and Belytschko, T. (2000), "Arbitrary branched and intersecting cracks with the extended finite element method", Int. J. Numer. Meth. Eng., 48, 1741-1760. https://doi.org/10.1002/1097-0207(20000830)48:12<1741::AID-NME956>3.0.CO;2-L
  13. Dreilich, L. and Gross, D. (1985), "The curved crack", Z. Angew. Math. Mech., 65, 132-134.
  14. Englund, J. (2006), "Stable algorithm for the stress field around a multiply branched crack", Int. J. Numer. Meth. Eng., 63, 926-946.
  15. Jin, X. and Keer, L.M. (2006), "Solution of multiple edge cracks in an elastic half plane", Int. J. Fracture, 137, 121-137. https://doi.org/10.1007/s10704-005-3063-3
  16. Linkov, A.M. (2002), Boundary Integral Equations in Elasticity Theory. Kluwer: Dordrecht.
  17. Linkov, A.M. and Mogilevskaya, S.G. (1994), "Complex hypersingular integrals and integral equations in plane elasticity", Acta Mech., 105,189-205. https://doi.org/10.1007/BF01183951
  18. Martin, P.A. (2000), "Perturbed cracks in two dimensions: an integral-equation approach", Int. J. Fracture, 104, 317-327.
  19. Mayrhofer, K. and Fischer, F.D. (1992), "Derivation of a new analytical solution for a general two-dimensional finite-part integral applicable in fracture mechanics", Int. J. Numer. Meth. Eng., 33, 1027-1047. https://doi.org/10.1002/nme.1620330509
  20. Mogilevskaya, S.G. (2000), "Complex hypersingular integral equation for the piece-wise homogeneous half-plane with cracks", Int. J. Fracture, 102, 177-204. https://doi.org/10.1023/A:1007633814813
  21. Muskhelishvili, N.I. (1953), Some Basic Problems of the Mathematical Theory of Elasticity. Noordhoff, Groningen.
  22. Murakami, Y. (ed) (1987), Stress Intensity Factors Handbook Vol. I and II. Pergamon, Oxford.
  23. Nik Long, N.M.A. and Eshkuvatov, Z.K. (2009), "Hypersingular integral equation for multiple curved cracks problem in plane elasticity", Int. J. Solids Struct., 46, 2611-2617. https://doi.org/10.1016/j.ijsolstr.2009.02.008
  24. Savruk, M.P. (1981), Two-dimensional Problems of Elasticity for Body with Crack. Naukoya Dumka, Kiev. (in Russian)
  25. Theocaris, P.S. (1977), "A synmmetric branching of cracks", J. Appl. Mech., ASME, 44, 611-618. https://doi.org/10.1115/1.3424145
  26. Xu, Y.L. (1995), "A concentric arc crack in a circular disk", Int. J. Eng. Sci., 32, 2023-2040.

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