Structural Engineering and Mechanics

Techno-Press (테크노프레스)
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An efficient computational method for stress concentration problems

  • Shrestha, Santosh (Department of Civil and Environmental Engineering, Ehime University) ;
  • Ohga, Mitao (Department of Civil and Environmental Engineering, Ehime University)
  • Received : 2005.07.05
  • Accepted : 2005.12.09
  • Published : 2006.03.30
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Abstract

In this paper a recently developed scaled boundary finite element method (SBFEM) is applied to simulate stress concentration for two-dimensional structures. In addition, a simple and independent formulation for evaluating the coefficients, not only of the singular term but also higher order non-singular terms, of the stress fields near crack-tip is presented. The formulation is formed by comparing the displacement along the radial points ahead of the crack-tip with that of standard Williams' eigenfunction solution for the crack-tip. The validity of the formulation is examined by numerical examples with different geometries for a range of crack sizes. The results show good agreement with available solutions in literatures. Based on the results of the study, it is conformed that the proposed numerical method can be applied to simulate stress concentrations in both cracked and uncracked structure components more easily with relatively coarse and simple model than other computational methods.

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References

  1. Chidgzey, S.R. and Deeks, A.J. (2005), 'Determination of coefficients of crack-tip asymptotic fields using scaled boundary finite element method', Eng. Fract. Mech., 72, 2019-2036 https://doi.org/10.1016/j.engfracmech.2004.07.010
  2. Deeks, A.J. (2002), 'Calculation of stress-intensity factors using the scaled boundary finite-element method', Proc. Int. Conf. Struct. Integrity and Fracture, Perth, 3-8
  3. Deeks, A.J. and Wolf, J.P. (2002a), 'An h-hierarchical adaptive procedure for the scaled boundary finite-element method', Int. J. Numer. Meth. Eng., 54, 585-605 https://doi.org/10.1002/nme.440
  4. Deeks, A.J. and Wolf, J.P. (2002b), 'Stress recovery and error estimation for the scaled boundary finite-element method.' Int. J. Numer. Meth. Eng., 54(4), 557-583 https://doi.org/10.1002/nme.439
  5. Deeks, A.J. and Wolf, J.P. (2002c), 'A virtual work derivation of the scaled boundary finite element method for elastostatics', Comput. Mech., 28, 489-509 https://doi.org/10.1007/s00466-002-0314-2
  6. Du, Z.Z. and Hancock, J.W. (1991), 'The effect of non-singular stresses on crack-tip constraint', J. Mechanics and Physics of Solids, 39, 555-567 https://doi.org/10.1016/0022-5096(91)90041-L
  7. Dyskin, A.V. (1997), 'Crack growth criteria incorporating non-singular stresses: Size effects in apparent fracture toughness', Int. J. Fracture, 83, 191-206 https://doi.org/10.1023/A:1007304015524
  8. Jeon, I. and Im, S. (2001), 'The role of higher order eigenfields in elastic-plastic cracks', J. Mechanics and Physics of Solids, 49, 2789-2818 https://doi.org/10.1016/S0022-5096(01)00097-7
  9. Karihaloo, B.L. and Xiao, Q.Z. (2001), 'Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack elements with p-adaptivity', Eng. Fract. Mech., 68, 1609-1630 https://doi.org/10.1016/S0013-7944(01)00063-7
  10. Larsson, S.G. and Carlsson, A.J. (1973), 'Influence of non-singular stress terms and specimen geometry on the small-scale yielding at crack-tip in elasto-plastic material', J. Mechanics and Physics of Solids, 21, 263-277 https://doi.org/10.1016/0022-5096(73)90024-0
  11. Oh, H.S., and Babuska, I. (1992), 'The p-version of the finite element method for the elliptic boundary value problems with interfaces', Comput. Meth. Appl. Mech. Eng., 97, 211-231 https://doi.org/10.1016/0045-7825(92)90164-F
  12. Rahaulkumar, P., Saigal, S., and Yunus, S. (1997), 'Singular p-version finite elements for stress intensity factor computations', Int. J. Numer. Meth. Eng., 40, 1091-1114 https://doi.org/10.1002/(SICI)1097-0207(19970330)40:6<1091::AID-NME102>3.0.CO;2-X
  13. Song, C. (2004), 'A super-element for crack analysis in the time domain', Int. J. Numer. Meth. Eng., 61, 1332-1357 https://doi.org/10.1002/nme.1117
  14. Song, C. (2005), 'Evaluation of power-logarithmic singularities, T-stresses and higher order terms of in-plane singular stress fields at cracks and multi-material comers', Eng. Fract. Mech., 72, 1498-1530 https://doi.org/10.1016/j.engfracmech.2004.11.002
  15. Song, C. and Wolf, J.P. (2002), 'Semi-analytical representation of stress singularity as occurring in cracks in anisotropic multi-materials with the scaled boundary finite-element method', Comput. Struct., 80, 183-197 https://doi.org/10.1016/S0045-7949(01)00167-5
  16. Tan, C.L. and Wang, X. (2003), 'The use of quarter-point crack-tip elements for T-stress determination in boundary element method analysis', Eng. Fract. Mech., 70, 2247-2252 https://doi.org/10.1016/S0013-7944(02)00251-5
  17. Wang, X. (2002), 'Determination of weight function for elastic T-stress from reference T-stress solution', Fatigue & Fracture of Engineering Materials and Structures, 25, 965-973 https://doi.org/10.1046/j.1460-2695.2002.00557.x
  18. Williams, M.L. (1957), 'On the stress distribution at the base of a stationary crack', J. Appl. Mech., ASME, 24, 109-114
  19. Wolf, J.P. (2003), The Scaled Boundary Finite Element Method, John Wiley & Sons Ltd, England
  20. Xiao, Q.Z., Karihaloo, B.L. and Liu, X.Y. (2004), 'Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element', Int. J. of Fracture, 125, 207-225 https://doi.org/10.1023/B:FRAC.0000022229.54422.13
  21. Yan, X. (2004), 'A numerical analysis of cracks emanating from a square hole in a rectangular plate under biaxial loads', Eng. Fract. Mech., 71, 1615-1623 https://doi.org/10.1016/j.engfracmech.2003.08.005
  22. Yang, S., Chao, Y.J. and Sutton M.A. (1993), 'Higher order asymptotic crack-tip fields in a power-law hardening materials', Eng. Fract. Mech., 45, 1-20 https://doi.org/10.1016/0013-7944(93)90002-A