An improvement of the EDI method in linear elastic fracture mechanics by means of an a posteriori error estimator in G

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 4, 2004, Pages 533-558

  Giner, E ^a   Fuenmayor, F J ^a   Tarancon J E ^a  

^a UNIVERSITAT POLITÈCNICA DE VALÈNCIA   (Spain)

Author keywords

Design sensitivity analysis; EDI method; Error estimation; Finite element method; Fracture mechanics; Strain energy release rate

Indexed keywords

ERROR ANALYSIS; STRAIN; STRESS INTENSITY FACTORS;

ERROR ESTIMATOR; NUMERICAL PROBLEMS; SHAPE DESIGN SENSITIVITY ANALYSIS (SDSA);

FRACTURE MECHANICS;

FINITE ELEMENT METHOD;

EID: 0442280854     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.889     Document Type: Article

References (50)

1. Banks-Sills L. Application of the finite element method to linear elastic fracture mechanics. Applied Mechanics Reviews (ASME) 1991; 44(10):447-461.
2. Parks DM. A stiffness derivative finite element technique for determination of crack tip stress intensity factors. International Journal of Fracture 1974; 10:487-502.
3. Li FZ, Shih CF, Needleman A. A comparison of methods for calculating energy release rates. Engineering Fracture Mechanics 1985; 21(2):405-421.
4. Hellen TK. On the method of virtual crack extensions. International Journal for Numerical Methods in Engineering 1975; 9:187-207.
5. Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 1968; 35:379-386.
6. deLorenzi HG. On the energy release rate and the J-integral for 3-D crack configurations. International Journal of Fracture 1982; 19:183-193.
7. deLorenzi HG. Energy release rate calculations by the finite element method. Engineering Fracture Mechanics 1985; 21(1):129-143.
8. Shih CF, Moran B, Nakamura T. Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture 1986; 30:79-102.
9. Rybicki EF, Kanninen MF. A finite element calculation of stress intensity factors by a modified crack closure integral. Engineering Fracture Mechanics 1977; 9:931-938.
10. Shivakumar KN, Tan PW, Newman Jr JC. A virtual crack closure technique for calculating stress intensity factors for cracked three dimensional bodies. International Journal of Fracture 1988; 36:R43-R50.
11. Banks-Sills L, Sherman D. On the computation of stress intensity factors for three-dimensional geometries by means of the stiffness derivative and J-integral methods. International Journal of Fracture 1992; 53: 1-20.
12. Giner E, Fuenmayor FJ, Besa AJ, Tur M. An implementation of the stiffness derivative method as a discrete analytical sensitivity analysis and its application to mixed mode in LEFM. Engineering Fracture Mechanics 2002; 69(18):2051-2071.
13. Lim IL, Johnston IW, Choi SK. Comparison between various displacement-based stress intensity factor computation techniques. International Journal of Fracture 1992; 58:193-210.
14. Bittencourt TN, Barry A, Ingraffea AR. Comparison of mixed-mode stress intensity factors obtained through displacement correlation. J-integral formulation and modified crack-closure integral. In Fracture Mechanics: 22nd Symposium, Atluri SN, Newman Jr JC, Raju IS, Epstein JS (eds). ASTM STP 1131: Philadelphia, 1992; 69-82.
15. Xiao D, Dexter RJ. Finite element calculation of applied J-integral for cracked ship structural details. Engineering Fracture Mechanics 1998; 60(1):59-82.
16. Babuška I, Miller A. The post-processing approach in the finite element method. Part 1: Calculation of displacements, stresses and other higher derivatives of the displacements. International Journal for Numerical Methods in Engineering 1984; 20:1085-1109.
17. Babuška I, Miller A. The post-processing approach in the finite element method. Part 2: The calculation of stress intensity factors. International Journal for Numerical Methods in Engineering 1984; 20:1111-1129.
18. Babuška I, Miller A. The post-processing approach in the finite element method. Part 3: A posteriori error estimates and adaptive mesh selection. International Journal for Numerical Methods in Engineering 1984; 20:2311-2324.
19. Fuenmayor FJ, Oliver JL, Ródenas JJ. Extension of the Zienkiewicz-Zhu error estimator to shape sensitivity analysis. International Journal for Numerical Methods in Engineering 1997; 40:1413-1433.
20. Fuenmayor FJ, Domínguez J, Giner E, Oliver JL. Calculation of the stress intensity factor and estimation of its error by a shape sensitivity analysis. Fatigue and Fracture of Engineering Materials and Structures 1997; 20(5):813-828.
21. Strouboulis T, Babuška I, Datta DK, Copps K, Gangaraj SK. 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 factor. Computer Methods in Applied Mechanics and Engineering 2000; 181: 261-294.
22. Ainsworth M, Oden JT. A Posteriori Error Estimation in Finite Element Analysis. Wiley-Interscience: New York, 2000.
23. Stone TJ, Babuška I. A numerical method with a posteriori error estimation for determining the path taken by a propagating crack. Computer Methods in Applied Mechanics and Engineering 1998; 160:245-271.
24. Ingraffea AR, Manu C. Stress-intensity factor computation in three dimensions with quarter-point elements. International Journal for Numerical Methods in Engineering 1980; 15:1427-1445.
25. Yehia NAB, Shephard MS. On the effect of quarter-point element size on fracture criteria. International Journal for Numerical Methods in Engineering 1985; 21:1911-1924.
26. Aliabadi MH, Rooke DP. Numerical Fracture Mechanics. Computational Mechanics Publications: Solid Mechanics and its Applications. Kluwer Academic Publishers: UK, 1991.
27. Zienkiewicz OC, Zhu JZ. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal for Numerical Methods in Engineering 1987; 24:337-357.
28. Giner E. Estimación del Error de Discretización en el Cálculo del Factor de Intensidad de Tensiones mediante Elementos Finitos. Ph.D. Thesis, Universidad Politécnica de Valencia: Valencia, Spain, 2001.
29. Haug EJ, Choi KK, Komkov V. Mathematics in Science and Engineering, Design sensitivity analysis of structural systems. vol. 177, Academic Press Inc.: Orlando, FL, 1986.
30. Sussman T, Bathe KJ. The gradient of the finite element variational indicator with respect to nodal point coordinates: an explicit calculation and applications in fracture mechanics and mesh optimization. International Journal for Numerical Methods in Engineering 1985; 21:763-774.
31. Taroco E, de Las Casas EB, Cimini Jr CA. Fracture mechanics via sensitivity analysis and numerical evaluation of J integral in cracked sheets. Journal of Constructional Steel Research 1994; 28:153-165.
32. Taroco E. Shape sensitivity analysis in linear elastic fracture mechanics. Computer Methods in Applied Mechanics and Engineering 2000; 188:697-712.
33. Feijóo RA, Padra C, Saliba R, Taroco E, Vénere MJ. Shape sensitivity analysis for energy release rate evaluation and its application to the study of three-dimensional cracked bodies. Computer Methods in Applied Mechanics and Engineering 2000; 188:649-664.
34. Eshelby JD. The elastic energy-momentum tensor. Journal of Elasticity 1975; 5(3-4):321-335.
35. Choi KK, Chang KH. A study of design velocity field computation for shape optimal design. Finite Elements in Analysis and Design 1994; 15:317-341.
36. El-Sayed MEM, Zumwalt KW. Efficient design sensitivity derivatives for multi-load case structures as an integrated part of finite element analysis. Computers and Structures 1991; 40(6):1461-1467.
37. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique. International Journal for Numerical Methods in Engineering 1992; 33:1331-1364.
38. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery and a posteriori error estimates. Part 2: Error estimates and adaptivity. International Journal for Numerical Methods in Engineering 1992; 33:1365-1382.
39. Zienkiewicz OC, Taylor RL. The Finite Element Method: The Basis (5th edn), vol. 1. Butterworth-Heinemann: UK, 2000.
40. Babuška I, Strouboulis T, Upadhyay CS. A model study of the quality of a posteriori error estimators for finite element solutions of linear elliptic problems, with particular reference to the behavior near the boundary. International Journal for Numerical Methods in Engineering 1997; 40:2521-2577.
41. Fuenmayor FJ, Oliver JL. Criteria to achieve nearly optimal meshes in the h-adaptive finite element method. International Journal for Numerical Methods in Engineering 1996; 39:4039-4061.
42. Yang RJ, Botkin ME. Comparison between the variational and implicit differentiation approaches to shape design sensitivities. AIAA Journal 1986; 24:1027-1032.
43. Giner E, Fuenmayor FJ, Besa AJ, Tur M. A discretization error estimator associated with the energy domain integral method in linear elastic fracture mechanics. In Computational Fluid aid Solid Mechanics, Bathe KJ (ed). Proceedings of the 1st MIT Conference, vol. 1. Elsevier: Cambridge, MA, 2001; 206-210.
44. Babuška I, Yu D. Asymptotically exact a posteriori error estimator for biquadratic elements. Finite Elements in Analysis and Design 1987; 3:341-354.
45. Szabó BA, Babuška I. Finite Element Analysis. Wiley: New York, 1991.
46. Szabó BA, Mehta AK. p-convergent finite element approximations in fracture mechanics. International Journal for Numerical Methods in Engineering 1978; 12:551-560.
47. Kelly DW, Gago JP, Zienkiewicz OC, Babuška, I. A posteriori error analysis and adaptive processes in the finite element method: Part I-error analysis. international Journal for Numerical Methods in Engineering 1983; 19:1593-1619.
48. Tada H, Paris PC, Irwin GC (eds). The Stress Analysis of Cracks Handbook (2nd edn). Paris Productions, Inc.: St Louis, Missouri, 1985.
49. Ainsworth M, Zhu JZ, Craig AW, Zienkiewicz OC. Analysis of the Zienkiewicz-Zhu a posteriori error estimator in the finite element method. International Journal for Numerical Methods in Engineering 1989; 28:2161-2174.
50. Zienkiewicz OC, Zhu JZ. The superconvergent patch recovery (SPR) and adaptive finite element refinement. Computer Methods in Applied Mechanics and Engineering 1992; 101:207-224.