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Fast multipole DBEM analysis of fatigue crack growth

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Abstract

A fast multipole method (FMM) based on complex Taylor series expansions is applied to the dual boundary element method (DBEM) for large-scale crack analysis in linear elastic fracture mechanics. Combining multipole expansions with local expansions, both the computational complexity and memory requirement are reduced to O(N), where N is the number of DOF. An incremental crack-extension analysis based on the maximum principal stress criterion and the Paris law is used to simulate the fatigue growth of numerous cracks in a 2D solid. Some examples are presented to validate the numerical scheme.

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References

  1. Cruse TA (1996) BIE fracture mechanics analysis 25 years of developments. Comput Mech 18(1):1–11

    Article  MATH  MathSciNet  Google Scholar 

  2. Cruse TA (1988) Boundary Element Analysis in Computational Fracture Mechanics. Kluwer, Dordrecht

  3. Lachat JC, Watson JO (1976) Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastoplastic. Int J Numer Meth Eng 10:991–1005

    Article  MATH  Google Scholar 

  4. Blandford GE, Ingraffea AR, Liggett JA (1981), Two-dimensional stress intensity factor computations using the boundary element method. Int J Numer Meth Eng 17:387–404

    Article  MATH  Google Scholar 

  5. Portela A, Aliabadi MH (1992) The dual boundary element method: effective implementation for crack problems. Int J Numer Meth Eng 33:1269–1287

    Article  MATH  Google Scholar 

  6. Portela A, Aliabadi MH, Rooke DP (1993), Dual boundary element incremental analysis of crack propagation. Comput Struct 46(2):237–247

    Article  MATH  Google Scholar 

  7. Mi Y, Aliabadi MH (1992) Dual boundary element method for three-dimensional fracture mechanics analysis. Eng Anal Bound Elem 1:161–171

    Article  Google Scholar 

  8. Cisilino AP, Aliabadi MH (1997) Three-dimensional BEM analysis for fatigue crack growth in welded components. Int J Pressure Vessels and Piping 70:135–144

    Article  Google Scholar 

  9. Wilde AJ, Aliabadi MH (1999) A 3-D Dual BEM formulation for the analysis of crack growth. Comput Mech 23:250–257

    Article  MATH  Google Scholar 

  10. Leitão VM, Aliabadi MH, Rooke DP (1995) The dual boundary element formulation for elastoplastic fracture mechanics. Int J Numer Meth Eng 38:315–333

    Article  Google Scholar 

  11. Cisilino AP, Aliabadi MH (1998) A three-dimensional dual boundary element formulation for the elastoplastic analysis of cracked bodies. Int J Numer Meth Eng 42:237–256

    Article  MATH  Google Scholar 

  12. Cisilino AP, Aliabadi MH (1999) Three-dimensional boundary element analysis of fatigue crack growth in linear and non-linear fracture problems. Eng Frac Mech 63:713–733

    Article  Google Scholar 

  13. Peirce AP, Napier JAL (1995) A spectral multipole method for efficient solutions of large scale boundary element models in elastostatics. Int J Numer Meth Eng 38:4009–4034

    Article  MATH  MathSciNet  Google Scholar 

  14. Fu YH, Klimkowski KJ, Rodin GJ (1998) A fast solution method for three-dimensional many-particle problems of linear elasticity. Int J Numer Meth Eng 42:1215–1229

    Article  MATH  Google Scholar 

  15. Popov V, Power H (2001) An O(N) Taylor series multipole boundary element method for three-dimensional elasticity problems. Eng Anal Bound Elem 25:7–18

    Article  MATH  Google Scholar 

  16. Yoshida K, Nishimura N, Kobayashi S (2001) Application of new fast multipole boundary integral equation method to crack problems in 3D. Eng Anal Bound Elem 25:239–247

    Article  MATH  Google Scholar 

  17. Yoshida K, Nishimura N, Kobayashi S (2001) Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems in 3D. Int J Numer Meth Eng 50(3):525–547

    Article  MATH  Google Scholar 

  18. Wang HT, Yao ZH (2005) A new fast multipole boundary element method for large scale analysis of mechanical properties in 3D Particle-reinforced composites. Comput Model Eng Sci 7(1):85–95

    Article  MathSciNet  MATH  Google Scholar 

  19. Wang HT, Yao ZH (2004) Application of a new fast multipole BEM for simulation of 2D elastic solid with large number of inclusions. Acta Mech Sin 20(6):613–622

    Article  Google Scholar 

  20. Nishimura N (2002) Fast multipole accelerated boundary integral equation methods. Appl Mech Rev 55(4):299–324

    Article  Google Scholar 

  21. Barnes J, Hut PA (1986) Hierarchical O(NlogN) force calculation algorithm. Nature 324:446–449

    Article  Google Scholar 

  22. Greengard L, Rokhlin V (1997) A fast algorithm for particle simulation. J Comput Phys 135:280–292

    Article  MATH  MathSciNet  Google Scholar 

  23. Wang PB, Yao ZH, Wang HT (2005) Fast multipole BEM for simulation of 2-D solids containing large numbers of cracks. Tsing Scien Technol 10(1):76–81

    Article  MATH  Google Scholar 

  24. Guiggiani M (1992) A general algorithm for the numerical solution of hypersingular boudary integral equations. J Appl Mech 59:604–614

    Article  MATH  MathSciNet  Google Scholar 

  25. Vavasis SA (1992) Preconditioning for boundary integral equations. SIAM J Matrix Anal Appl 13(3):905–925

    Article  MATH  MathSciNet  Google Scholar 

  26. Mukhopadhyay NK, Maiti SK, Kakodkar A (2000) A review of SIF evaluation and modelling of singularities in BEM. Comput Mech 25:358–375

    Article  MATH  Google Scholar 

  27. Aliabadi MH, Rooke DP (1992) Numerical Fracture Mechanics. Computational Mechanics Publications, Dordrecht

  28. Tanaka K (1974) Fatigue crack propagation from a crack inclined to the cyclic tensile axis. Eng Frac Mech 6:493–507

    Article  Google Scholar 

  29. Isida M (1971) Effects of width and length on stress intensity factor for the tension of internal cracked plates under various boundary conditions. Int J Fract Mech 7:301–306

    Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, Beijing, 100084, China

    P. B. Wang & Z. H. Yao

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  1. P. B. Wang
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  2. Z. H. Yao
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Correspondence to Z. H. Yao.

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Wang, P., Yao, Z. Fast multipole DBEM analysis of fatigue crack growth. Comput Mech 38, 223–233 (2006). https://doi.org/10.1007/s00466-005-0743-9

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  • DOI: https://doi.org/10.1007/s00466-005-0743-9

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