Browse > Article
http://dx.doi.org/10.12989/sem.2006.22.5.613

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)
Publication Information
Structural Engineering and Mechanics / v.22, no.5, 2006 , pp. 613-629 More about this Journal
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.
Keywords
stress concentration; scaled boundary finite element method; stress intensity factor; T-stress; higher order terms;
Citations & Related Records

Times Cited By Web Of Science : 1  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 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
2 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   DOI   ScienceOn
3 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   DOI   ScienceOn
4 Dyskin, A.V. (1997), 'Crack growth criteria incorporating non-singular stresses: Size effects in apparent fracture toughness', Int. J. Fracture, 83, 191-206   DOI
5 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   DOI   ScienceOn
6 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   DOI   ScienceOn
7 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   DOI   ScienceOn
8 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   DOI
9 Song, C. (2004), 'A super-element for crack analysis in the time domain', Int. J. Numer. Meth. Eng., 61, 1332-1357   DOI   ScienceOn
10 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   DOI   ScienceOn
11 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   DOI   ScienceOn
12 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   DOI   ScienceOn
13 Williams, M.L. (1957), 'On the stress distribution at the base of a stationary crack', J. Appl. Mech., ASME, 24, 109-114
14 Wolf, J.P. (2003), The Scaled Boundary Finite Element Method, John Wiley & Sons Ltd, England
15 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   DOI   ScienceOn
16 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   DOI
17 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   DOI   ScienceOn
18 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   DOI   ScienceOn
19 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   DOI   ScienceOn
20 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   DOI   ScienceOn
21 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   DOI
22 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   DOI   ScienceOn