Calculation of the stress intensity factor and estimation of its error by a shape sensitivity analysis

Fatigue and Fracture of Engineering Materials and Structures

Volumn 20, Issue 5, 1997, Pages 813-828

  Fuenmayor, J ^a   Dominguez J ^b   Giner, E ^a   Oliver, J L ^a  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

^b UNIVERSITY OF SEVILLE   (Spain)

Author keywords

Discretization error estimation; Finite element method; SIF calculation

Indexed keywords

ERROR ANALYSIS; ESTIMATION; FINITE ELEMENT METHOD; SENSITIVITY ANALYSIS;

SHAPE SENSITIVITY ANALYSIS; ZIENKIEWICS ZHU DISCRETIZATION ERROR ESTIMATOR;

STRESS INTENSITY FACTORS;

EID: 0030655794     PISSN: 8756758X     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1460-2695.1997.tb00310.x     Document Type: Article

References (34)

1. S. K. Chang, I. S. Tuba and W. K. Wilson (1970) On the finite element method in linear elastic fracture mechanics. Engng Fract. Mech. 2, 1-17.
2. S. E. Benzley (1974) Representation of singularities with isoparametric finite elements. Int. J. Numer. Meth. Engng 8, 537-545.
3. P. Tong, T. H. H. Pian and S. J. Lasry (1973) A hybrid element approach to crack problems in plane elasticity. Int. J. Numer. Meth. Engng 7, 297-308.
4. R. D. Henchell and K. G. Shaw (1975) Crack tip finite elements are unnecessary. Int. J. Numer. Meth. Engng 9, 495-507.
5. R. S. Barsoum (1976) On the use of isoparametric finite elements in linear fracture mechanics. Int. J. Numer. Meth. Engng 10, 25-37.
6. I. S. Raju and J. C. Newmann, Jr. (1977) Three-dimensional finite-element analysis of finite-thickness fracture specimens. NASA TN D-8414.
7. D. M. Parks (1974) A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int. J. Fract. 10, 487-502.
8. B. Moran and C. F. Shih (1987) A general treatment of crack tip contour integrals. Int. J. Fract. 35, 295-310.
9. C. F. Shih, B. Moran and T. Nakamura (1986) Energy release rate along a three-dimensional crack front in a thermally stressed body. Int. J. Fract. 30, 79-102.
10. L. Banks-Sills (1991) Application of the finite element method to linear elastic fracture mechanics. Appl. Mech. Rev. 44, 447-461.
11. L. Banks-Sills and D. Sherman (1992) On the computation of stress intensity factors for three dimensional geometries by means of the stiffness derivate and J-integral methods. Int. J. Fract. 53, 1-20.
12. T. Sussman and K. J. Bathe (1985) The gradient of the finite element variational indicator with respect to nodal point co-ordinates: An explicit calculation and applications in fracture mechanics and mesh optimization. Int. J. Numer. Meth. Engng 21, 763-774.
13. E. J. Haug, K. K. Choi and V. Komkov (1986) Design sensitivity analysis of structural systems. Math. Sci. Engng 177, Academic Press, pp. 180-254.
14. Barthelemy and R. T. Haftka (1990) Accuracy analysis of the semi-analytical method for shape sensitivity calculation. Mech. Struct. Mach. 18(3), 407-432.
15. S. Kibsgaard (1992) Sensitivity analysis-the basis for optimization. Int. J. Numer. Meth. Engng 34, 901-932.
16. S. H. Wang, Y. Sun and R. H. Gallagher (1985) Sensitivity analysis in shape optimization of continuum structures. Comput. Struct. 33, 1089-1093.
17. M. E. M. El-Sayed and K. W. Zumwalt (1991) Efficient design sensitivity derivatives for multi-load case structures as an integrated part of finite element analysis. Comput. Struct. 40, 1461-1467.
18. O. C. Zienkiewicz and J. Z. Zhu (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int. J. Numer. Meth. Engng 24, 337-357
19. K. Salmenjoki and P. Neittaanmäki (1989) Comparison of various techniques for shape design sensitivity analysis. In: Computer Aided Optimum Design of Structures: Recent Advances (Edited by C. A. Brebbia and S. Hernandez), Springer-Verlag, pp. 367-377.
20. R. J. Yang and M. E. Botkin (1986) Comparison between the variational and implicit differentation approaches to shape design sensitivities. AIAA J. 24, 1027-1032.
21. R. T. Haftka and B. Barthelemy (1989) On the accuracy of shape sensitivity. In: Computer Aided Optimum Design of Structures: Recent Advances (Edited by C. A. Brebbia and S. Hernandez), Springer-Verlag, pp. 327-366.
22. K. K. Choi, J. L. T. Santos and T. M. Yao (1988) Recent advances in design sensitivity analysis and its use in structural design process. SAE Technical Paper, 880783.
23. H. G. Seong and K. K. Choi (1987) Boundary-layer approach to shape design sensitivity analysis. Mech. Struct. Mach. 15(2), 241-263.
24. M. Ainsworth, J. Z. Zhu, A. V. Craig and O. C. Zienkiewicz (1989) Analysis to the Zienkiewicz-Zhu a posteriori error estimator in the finite element method. Int. J. Numer. Meth. Engng 28, 2161-2174.
25. M. S. Shepard, Q. Niu and P. L. Baehmann (1989) Some results using stress projectors for error indication and estimation. Technical Report No. 89013, Rensselaer Polytechnic Institute, Troy, New York.
26. J. L. Oliver and F. J. Fuenmayor (1993) Analysis of the effectivity of the Zienkiewicz-Zhu error estimator. In: Optimization of Structural Systems and Applications, Elsevier, pp. 309-324.
27. O. C. Zienkiewicz and J. Z. Zhu (1992) The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. Int. J. Numer. Meth. Engng 33, 1331-1364.
28. O. C. Zienkiewicz and J. Z. Zhu (1992) The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. Int. J. Numer. Meth. Engng 33, 1365-1382.
29. A. W. Craig, M. Ainsworth, J. Z. Zhu and O. C. Zienkiewicz (1989) h and h-p version error estimation and adaptive procedures from theory to practice. Engineering with Computers 5, 221-234.
30. B. A. Szabo (1986) Estimation and control of error based on p-convergence. In: Accuracy Estimates and Adaptive Refinements in Finite Elements Computations (Edited by I. Babuska, O. C. Zienkiewicz, J. Gago and E. R. de A. Oliveira), John Wiley & Sons, pp. 61-78.
31. O. C. Zienkiewicz, J. Z. Zhu and N. G. Gong (1989) Effective and practical h-p-version adaptive a nalyis procedures for the finite element method. Int. J. Numer. Meth. Engng 28, 879-891.
32. F. J. Fuenmayor and J. L. Oliver (1993) Criteria to achieve optimal meshes in the h-adaptive finite element method. In: World Congress on Optimal Design of Structural Systems, STRUCTURAL OPTIMIZATION 93, pp. 259-266.
33. B. A. Szabo and A. K. Mehta (1978) p-convergence finite element approximations in fracture mechanics. Int. J. Numer. Meth. Engng 12, 551-560.
34. M. F. Kanninen and C. H. Popelar (1985) Advanced Fracture Mechanics. Oxford Engineering Science Series. Oxford University Press, p. 152.