Strict bounds for computed stress intensity factors

Computers and Structures

Volumn 87, Issue 15-16, 2009, Pages 1015-1021

  Panetier, J ^a   Ladeveze P ^a   Louf, F ^a  

^a CNRS   (France)

Author keywords

Error estimation; Extended finite element method; Stress intensity factors; Strict bounds

Indexed keywords

CONSTITUTIVE RELATIONS; ERROR ESTIMATION; EXTENDED FINITE ELEMENT METHOD; LOCAL ERROR; MIXED-MODE STRESS; STANDARD FINITE ELEMENT; STRICT BOUNDS; THEORY OF ERRORS;

ASPHALT PAVEMENTS; ERROR ANALYSIS; ESTIMATION; FRACTURE MECHANICS; STRENGTH OF MATERIALS; STRESS INTENSITY FACTORS;

FINITE ELEMENT METHOD;

EID: 67349155575     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2008.11.014     Document Type: Article

References (26)

1. Ladevèze P., and Pelle J.P. Mastering calculations in linear and non linear mechanics. Mechanical engineering series (2005), Springer
2. Babuska I., and Strouboulis T. The finite element method and its reliability (2001), Oxford University Press, Oxford
3. Zienckiewicz O.C., and Zhu J.Z. A simple error estimator and adaptative procedure for practical engineering analysis. Int J Numer Meth Eng 24 (1987) 337-357
4. Rannacher R., and Stuttmeier F.T. A feedback approach to error control in finite element methods: application to linear elasticity. Comput Mech 19 (1997) 434-446
5. Rannacher R., and Stuttmeier F.T. A posteriori error control and mesh adaptation for f. e. models in elasticity and elastoplasticity. In: Ladevèze P., and Oden J.T. (Eds). Advances in computational methods in mechanics (1998), Elsevier, Amsterdam
6. Péraire J., and Patera A. Bounds for linear-functional outputs of coercive partial differential equations local error indicators and adaptive refinement. In: Ladevèze P., and Oden J.T. (Eds). Advances in adaptive computational methods (1998), Elsevier
7. Ladevèze P., Rougeot Ph., Blanchard P., and Moreau J.P. Local error estimators for finite element linear analysis. Comput Meth Appl Mech Eng 176 (1999) 231-246
8. Prudhomme S., and Oden J.T. On goal-oriented error estimation for elliptic problems: application to the control of pointwise error. Comput Meth Appl Mech Eng 176 (1999) 313-331
9. Strouboulis T., Babuska I., Datta D.K., Copps K., and Gangaraj S.K. A posteriori estimation and adaptive control of the error in the quantity of interest. Part I: A posteriori estimation of the error in the Von Mises stress and the stress intensity factors. Comput Meth Appl Mech Eng 181 (2000) 261-294
10. Heintz P., and Samuelson K. On adaptative strategies and error control in fracture mechanics. Comput Struct 82 (2004) 485-497
11. Rüter M., and Stein E. Goal oriented a posteriori error estimates in linear elastic fracture mechanics. Comput Meth Appl Mech Eng 195 (2006) 251-278
12. Xuan Z.C., Parès N., and Peraire J. Computing upper and lower bounds for the J-integral in two dimensional linear elasticity. Comput Meth Appl Mech Eng 195 (2006) 430-443
13. Gallimard L., and Panetier J. Error estimation of stress intensity factors for mixed-mode crack. Int J Numer Meth Eng 68 (2006) 299-316
14. Belytschko T., and Black T. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Eng 45 (1999) 601-620
15. Moës N., Dolbow J., and Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Meth 46 (1999) 131-150
16. Melenk J.M., and Babuska I. The partition of unity finite element method: basic theory and applications. Comput Meth Appl Mech Eng 139 (1996) 289-314
17. Ladevèze P., Pelle J.P., and Rougeot Ph. Error estimation and mesh optimization for classical finite elements. Eng Comput 8 (1991) 69-80
18. Ladevèze P., and Rougeot Ph. New advances on a posteriori error on constitutive relation in f.e. analysis. Comput Meth Appl Mech Eng 150 (1997) 239-249
19. Prager W., and Synge J.L. Approximation in elasticity based on the concept of functions space. Quart Appl Math 5 (1947) 261-269
20. Ladevèze P. Upper error bounds of calculated outputs of interest for linear and non linear structural problems. CR Méc (2006) 334
21. Stern M., Becker E.B., and Dunham R.S. A contour integral computation of mixed-mode stress intensity factors. Int J Fract 12 (1976) 359-368
22. Osher S., and Sethian S.A. Fronts propagating with curvature dependent speed: algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79 (1988) 12-49
23. Laborde P., Pommier J., Renard Y., and Salaün M. High-order extended finite element method for crack domains. Int J Numer Meth Eng 24 (2005) 354-381
24. Babuska I., and Miler A. The post-processing approach in the finite element method. Part 2. The calculation of stress intensity factors. Int J Numer Meth Eng 20 (1984) 1111-1129
25. Stone T.J., and Babuska I. A numerical method with a posteriori error estimation for determining the path taken bay a propagating crack. Comput Meth Appl Mech Eng 160 (1998) 245-271
26. Strouboulis T., Lin Z., Delin W., and Babuska I. A posteriori error estimation for generalized finite element methods. Comput Meth Appl Mech Eng 195 (2006) 852-879