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Vol. 26 No. 17 (2014): Vol 26 Issue 17

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Analytical Solutions of Dynamic Extension Problem of Mode III Semi-Infinite Crack Subjected to Moving Increasing Loads

https://doi.org/10.14233/ajchem.2014.18141
Nian-Chun Lu
School of Material Engineering, Shenyang Ligong University, Shenyang 110168, P.R. China
Qian Xiang
School of Material Engineering, Shenyang Ligong University, Shenyang 110168, P.R. China
Guo-Dong Hao
Department of Chemistry, Mudanjiang Normal College, Mudanjiang 157001, P.R. China

Corresponding Author(s) : Nian-Chun Lu

lnc_65@163.com

Asian Journal of Chemistry, Vol. 26 No. 17 (2014): Vol 26 Issue 17

Abstract

Dynamic extension problem of mode III semi-infinite crack was investigated by means of the theory of complex variable functions, which can be facilely transformed into Riemann-Hilbert problems. Analytical solutions of stress, displacement and stress intensity factor under the conditions of moving increasing loads Px2/t2 and Pt3/x2, respectively, are very easily obtained using the ways of self-similar functions.

Keywords

Complex functions Dynamic propagation problems Mode III semi-infinite crack Self-similar functions Analytical solutions
Lu, N.-C., Xiang, Q., & Hao, G.-D. (2014). Analytical Solutions of Dynamic Extension Problem of Mode III Semi-Infinite Crack Subjected to Moving Increasing Loads. Asian Journal of Chemistry, 26(17), 5495–5501. https://doi.org/10.14233/ajchem.2014.18141
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References
  1. A.C. Erigen and E.S. Suhubi, Elastodynamics, Linear Theory, Academic Press, New York, San Francisco, London, Vol. 2 (1975).
  2. G.C. Sih, Mechanics of Fracture 1: Methods of Analysis and Solutions of Crack Problems, Noordhoff, Leyden (1977).
  3. F. Erdogan, Crack Propagation Theories: Fracture II, Academic Press, New York, pp. 497-509 (1968).
  4. G.P. Cherepanov, Mechanics of Brittle Fracture, McGraw Hill International Book Company, New York, pp. 732-792 (1979).
  5. G.C. Sih, Int. J. Fract. Mechan., 4, 51 (1968); doi:10.1007/BF00189147.
  6. B.V. Kostrov, J. Appl. Math. Mech., 28, 1077 (1964); doi:10.1016/0021-8928(64)90010-3.
  7. L.B. Freund, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge, UK (1990).
  8. G.C. Sih and B. MacDonald, Eng. Fract. Mech., 6, 361 (1974); doi:10.1016/0013-7944(74)90033-2.
  9. G.C. Sih, Handbook of Stress Intensity Factors, Inst. Frac. Solid. Mech. Lehigh University, Bethlehem, PA (1973).
  10. G.C. Sih, Mechanics of Fracture Initiation and Propagation, Kluwer Academic Publisher, Boston (1991).
  11. Y.H. Wang, Y.K. Cheung and C.W. Woo, Eng. Fract. Mech., 42, 971 (1992); doi:10.1016/0013-7944(92)90136-3.
  12. G. Ravichandran and W. G. Knauss, Int. J. Fract., 39, 235 (1989); doi:10.1007/BF00047452.
  13. Y.H. Wang, Eng. Fract. Mech., 42, 45 (1992); doi:10.1016/0013-7944(92)90275-J.
  14. L. Nian-chun, C. Jin and C. Yun-hong, Inst. Tech., 37, 1093 (2005) (in Chinese).
  15. L. Nian-chun, C. Yun-hong and C. Jin, J. Appl. Mech., 21, 156 (2004) (in Chinese).
  16. L. Nian-chun, C. Yun-hong, T. Xiu-bo and C. Jin, Inst. Tech., 38, 1310 (2006) (in Chinese).
  17. N.I. Muskhelishvili, Singular Integral Equations, Nauka, Moscow (1968).
  18. N.I. Muskhelishvili, Some Fundamental Problems in the Mathematical Theory of Elasticity, Nauka, Moscow (1966).
  19. C. Atkinson, Int. J. Eng. Sci., 13, 489 (1975); doi:10.1016/0020-7225(75)90018-X.
  20. C. Atkinson, Int. J. Eng. Sci., 3, 77 (1965); doi:10.1016/0020-7225(65)90021-2.
  21. R.F. Hoskins, Generalized functions, Ellis Horwood, pp. 19-125 (1979).
  22. X.-S. Wang, Singular Functions and Their Applications in Mechanics, Scientific Press, Beijing, pp. 3-45 (1993) (in Chinese).
  23. F.D. Gahov, Boundary-value problems, Fizmatgiz, Moscow, pp. 10-136 (1963).
  24. G.C. Sih, Mechanics of Fracture 4. Elastodynamics Crack Problems, Noordhoff, Leyden, pp. 213-247 (1977).
  25. R.P. Kanwal and D.L. Sharma, J. Elast., 6, 405 (1976); doi:10.1007/BF00040900.
  26. Editorial Group of Mathematics Handbook, Mathematics Handbook, Advanced Education Press, Beijing, pp. 244-300 (2002) (in Chinese).
  27. Teaching Office of Mathematics of Tongji University, Advanced Mathematics, Advanced Education Press, Beijing, Vol. 1, pp. 167-172 (1994) (in Chinese).
  28. K.-C. Wu, Int. J. Fract., 106, 1 (2000); doi:10.1023/A:1007621500585.
  29. N. Lü, Y. Cheng, X. Li and J. Cheng, Appl. Math. Mech., 29, 1279 (2008); doi:10.1007/s10483-008-1003-z.
  30. J.F. Kalthoff, J. Beinert and S. Winkler, ASTM Spec. Tech. Publ., 627, 161 (1977).
  31. A.S. Kobayashi, Dynamic Fracture Analysis by Dynamic Finite Element Method: Generation and Prediction Analyses, In: Nonlinear and Dynamic Fracture Mechanics, ASME, New York, NY: Amd., 35, pp. 19-36 (1979).
  32. K. Ravi-Chandar and W.G. Knauss, Int. J. Fract., 25, 247 (1984); doi:10.1007/BF00963460.
  33. K. Ravi-Chandar and W.G. Knauss, Int. J. Fract., 26, 65 (1984); doi:10.1007/BF01152313.
  34. K. Ravi-Chandar and W.G. Knauss, Int. J. Fract., 26, 141 (1984); doi:10.1007/BF01157550.
  35. K. Ravi-Chandar and W.G. Knauss, Int. J. Fract., 26, 189 (1984); doi:10.1007/BF01140627.
  36. N.C. Lü, Y.H. Cheng, X.G. Li and J. Cheng, Fati. Frac. Eng. Mater. Stru., 33, 141 (2010); doi:10.1111/j.1460-2695.2009.01418.x.
  37. N.C. Lü, Y.H. Cheng, X.G. Li and J. Cheng, Compos. Interfaces, 17, 37 (2010); doi:10.1163/092764409X12580201111548.
  38. N.I. Sneddon, Fourier Transform, McGraw-Hill, New York (1951).
  39. N.I. Muskhelishvili, Some Basic Problems from the Mathematical Theory of Elasticity, P. Noordoff, Groningen-Holland (1953).
  40. L.A. Galin, Contact Problems in Elasticity Theory, GITTL, Moscow (1953).
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