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Mode III fracture analysis by Trefftz boundary element method

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Abstract

This paper presents a hybrid Trefftz (HT) boundary element method (BEM) by using two indirect techniques for mode III fracture problems. Two Trefftz complete functions of Laplace equation for normal elements and a special purpose Trefftz function for crack elements are proposed in deriving the Galerkin and the collocation techniques of HT BEM. Then two auxiliary functions are introduced to improve the accuracy of the displacement field near the crack tips, and stress intensity factor (SIF) is evaluated by local crack elements as well. Furthermore, numerical examples are given, including comparisons of the present results with the analytical solution and the other numerical methods, to demonstrate the efficiency for different boundary conditions and to illustrate the convergence influenced by several parameters. It shows that HT BEM by using the Galerkin and the collocation techniques is effective for mode III fracture problems.

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References

  1. Trefftz, T.E.: Ein Gegenstück zum Ritzschen Verfahren. In: Proceedings 2nd International Congress of Applied mechanics, Zurich, pp. 131–137 (1926)

  2. Huang S.C. and Shaw R.P. (1995). The Trefftz method as an internal equation. Adv. Eng. Softw. 24: 57–63

    Article  MATH  Google Scholar 

  3. Mikhlin S.G. (1964). Variational Methods in Mathematical Physics. Pergamon Press, Oxford

    MATH  Google Scholar 

  4. Kupradze, V.D.: Three Dimensional Problems of the Mathematical Theory of Elasticity and Thermoelasticity. North Holland, Amsterdam (1979)

  5. Piltner R. (1995). Rencent developments in the Trefftz method for finite element and boundary element applications. Adv. Eng. Softw. 24: 107–115

    Article  MATH  Google Scholar 

  6. Zienkiewicz, O.C.: Trefftz type of approximation and the finite element method—history and development. In: First International Workshop on Trefftz Method—Recent Development and Perspectives. Cracow University of Technology, Poland, pp. 103 (1996)

  7. Jirousek, J., Zielinski, A.P.: Survey of Trefftz-type element formulations. In: First International Workshop on Trefftz Method—Recent Development and Perspectives. Cracow University of Technology, Poland, pp. 103 (1996)

  8. Qin Q.H. (2000) The Trefftz Finite and Boundary Element Method. WIT Press, Southampton

    MATH  Google Scholar 

  9. Jirousek, J., Venkatesh, A.: Hybrid-Trefftz plane elasticity elements with p-method capabilities. Int. J. Numer. Meth. Eng. 35, 1443–1472 (1992)

    Article  MATH  Google Scholar 

  10. Piltner R. (1985). Special finite elements with holes and internal cracks. Int. J. Numer. Meth. Eng. 21: 1471–1485

    Article  MATH  MathSciNet  Google Scholar 

  11. Venkatesh A. and Jirousek J. (1995). Accurate representation of local effect due to concentrated and discontinuous loads in hybrid-Trefftz plate bending elements. Comput. Struct. 57: 863–870

    Article  MATH  Google Scholar 

  12. Jirousek J. and Teodorescu P. (1982). Large finite elements method for the solution of problems in the theory of elasticity. Comput. Struct. 15: 575–587

    Article  MATH  MathSciNet  Google Scholar 

  13. Portela A., Aliabadi M.H. and Rooke D.P. (1992). The dual boundary element method: effective implementation for crack problems. Int. J. Numer. Methods Eng. 33: 1269–1287

    Article  MATH  Google Scholar 

  14. Freitas J.A.T. and Ji Z.Y. (1996). Hybrid-Trefftz equilibrium model for crack problems. Int. J. Numer. Meth. Eng. 39: 569–584

    Article  MATH  Google Scholar 

  15. Sabino J., Portela A. and Castro P.M.S.T. (1999). Trefftz boundary element method applied to fracture mechanics. Eng. Frac. Mech. 64: 67–86

    Article  Google Scholar 

  16. Gray L.J. (1987). Boundary Element Method for Regions with Thin Interal Cavities. IBM Bergen, Norway

    Google Scholar 

  17. Cui Y.H. and Qin Q.H. (2006). Discussion on anti-plane crack problems by hybrid Trefftz finite element approach. Acta Mech. Solida Sinica, 27: 167–174

    Google Scholar 

  18. Cui Y.H., Qin Q.H. and Wang J.S. (2006). Application of HT finite element approach on mode I, II and III complex problems. Eng. Mech. 23: 104–110

    Google Scholar 

  19. Portela A. and Charafi A. (1997). Porgramming Trefftz boundary elements. Adv. Eng. Softw. 28: 509–523

    Article  Google Scholar 

  20. Leitão V.M.A. (1998). Applications of multi-region Trefftz-collocation to fracture mechanics. Eng. Anal. Bound. Elem. 22: 251–256

    Article  MATH  Google Scholar 

  21. Domingues J.S., Portela A. and Castro P.M.S.T. (1999). Trefftz boundary element method applied to fracture mechanics. Eng. Fract. Mech. 64: 67–86

    Article  Google Scholar 

  22. Zielinski A.P. and Zienkiewicz O.C. (1985). Generalized finite element analysis with T-complete boundary solution functions. Int. J. Numer. Meth. Eng. 21: 509–528

    Article  MATH  Google Scholar 

  23. Rooke D.P. and Cartwright D.S. (1976). Compendium of Stress Intensity Factors. HerMajestys Stationery Office, London

    Google Scholar 

  24. Isida M. (1970). Analysis of stress intensity factors for plates containing a random array of cracks. Bull JSME 13: 635–642

    Google Scholar 

  25. Sih C.G. (1973). Handbook of Stress Intensity Factors. HerMajestys Stationery Office, London

    Google Scholar 

  26. Silling, S.A.: Singularities and phase transitions in elastic solids: numerical studies and stability analysis. (Ph. D. thesis), California Institute of Technology (1986)

  27. Horgan C.O. and Silling S.A. (1987). Stress concentration factors in finite anti-plane shear numerical calculations and analytical estimates. J. Elast. 18: 83–91

    Article  MATH  MathSciNet  Google Scholar 

  28. Zhang X.S. (1988). Thegeneral solution of an edge crack off the center line of a rectangular sheet for Mode III. Eng. Fract. Mech. 31: 847–855

    Article  Google Scholar 

  29. Sun Y.Z., Yang S.S. and Wang Y.B. (2003). A new formulation of boundary element method for cracked anisotropic bodies under anti-plane shear. Comput. Methods Appl. Mech. Eng. 192: 2633–2648

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mechanics, Tianjin University, Tianjin, 300072, China

    Yuhong Cui, Juan Wang & Qinghua Qin

  2. Centre for Railway Engineering, Central Queensland University, North Rockhampton, QLD 4702, Australia

    Manicka Dhanasekar

  3. Department of Engineering, Australian National University, Canberra, ACT 0200, Australia

    Qinghua Qin

Authors
  1. Yuhong Cui
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  2. Juan Wang
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  3. Manicka Dhanasekar
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  4. Qinghua Qin
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Corresponding author

Correspondence to Yuhong Cui.

Additional information

The project supported by the National Natural Science Foundation of China(10472082). The English text was polished by Keren Wang.

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Cui, Y., Wang, J., Dhanasekar, M. et al. Mode III fracture analysis by Trefftz boundary element method. Acta Mech Sin 23, 173–181 (2007). https://doi.org/10.1007/s10409-007-0056-7

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  • DOI: https://doi.org/10.1007/s10409-007-0056-7

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