Analysis of interacting cracks using the generalized finite element method with global-local enrichment functions

Journal of Applied Mechanics, Transactions ASME

Volumn 75, Issue 5, 2008, Pages 0511071-05110712

  Kim, Dae Jin ^a   Duarte, Carlos Armando ^a   Pereira, Jeronymo Peixoto ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONING; GENERALIZED FINITE ELEMENT METHOD; GLOBAL APPROXIMATION; GLOBAL DOMAINS; GLOBAL-LOCAL; GLOBAL-LOCAL ANALYSIS; LOCAL PROBLEMS; NUMERICAL EXPERIMENTS; ORDER-OF MAGNITUDES; PARTITION OF UNITY; SCALE SIZES; STRESS INTENSITY FACTORS;

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CHLORINE COMPOUNDS; DIFFERENTIAL EQUATIONS; EXPERIMENTS; FRACTURE FIXATION; FRACTURE MECHANICS; INITIAL VALUE PROBLEMS; MATERIALS SCIENCE; NUMERICAL METHODS; SPEED; STRENGTH OF MATERIALS; STRESSES; STRUCTURAL ANALYSIS; THREE DIMENSIONAL;

FINITE ELEMENT METHOD;

EID: 52649150385     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2936240     Document Type: Conference Paper

References (34)

1. Kayama, M., and Totsuka, N., 2002, "Influence of Interaction Between Multiple Cracks on Stress Corrosion Crack Propagation," Corros. Sci., 44, pp. 2333-2352 (2002).
2. Kayama, M., and Kitamura, T., 2004, "A Simulation on Growth of Multiple Small Cracks Under Stress Corrosion," Int. J. Fract., 130, pp. 787-801.
3. Kebir, H., Roelandt, J. M., and Chambon, L., 2006, "Dual Boundary Element Method Modelling of Aircraft Structural Joints With Multiple Site Damage," Eng. Fract. Mech., 73, pp. 418-434.
4. Seyedi, M., Taheri, S., and Hild, F., 2006, "Numerical Modeling of Crack Propagation and Shielding Effects in a Striping Network," Nucl. Eng. Des., 236, pp. 954-964.
5. Felippa, C. A., 2004, "Introduction to Finite Element Methods," Course Notes, Department of Aerospace Engineeing Sciences, University of Colorado at Boulder, available at http://www.colorado.edu/engineering/Aerospace/ CAS/courses.d/IFEM.d/.
6. Noor, A. K., 1986, "Global-Local Methodologies and Their Applications to Nonlinear Analysis," Finite Elem. Anal. Design, 2, pp. 333-346.
7. Diamantoudis, A. Th., and Labeas, G. N., 2005, "Stress Intensity Factors of Semi-Elliptical Surface Cracks in Pressure Vessels by Global-Local Finite Element Methodology," Eng. Fract. Mech., 72, pp. 1299-1312.
8. Duarte, C. A., Kim, D.-J., and Babusška, I., 2007, Advances in Meshfree Techniques (Computational Methods in Applied Sciences, Vol. 5), V. M. A. Leitão. C. J. S. Alves, and C. A. Duarte, eds., Springer, The Netherlands, pp. 1-26.
9. Duarte, C. A., and Kim, D.-J., 2008, "Analysis and Applications of a Generalized Finite Element Method With Global-Local Enrichment Functions," Comput. Methods Appl. Mech. Eng., 197(6-8), pp. 487-504.
10. Civelek, M. B., and Erdogan, F., 1982, "Crack Problems for a Rectangular Plate and an Infinite Strip," Int. J. Fract., 19, pp. 139-159.
11. Sun, C. T., and Mao, K. M., 1988, "A Global-Local Finite Element Method Suitable for Parallel Computations," Comput. Struct., 29, pp. 309-315.
12. Babuška, I., and Strouboulis, T., 2001, The Finite Element Method and its Reliability (Numerical Mathematics and Scientific Computation) Oxford Science, New York.
13. Babuška, I., and Melenk, J. M., 1997, "The Partition of Unity Finite Element Method," Int. J. Numer. Methods Eng., 40, pp. 727-758.
14. Duarte, C. A., Babuška, I., and Oden, J. T., 2000, "Generalized Finite Element Methods for Three Dimensional Structural Mechanics Problems," Comput. Struct., 77, pp. 215-232.
15. Oden, J. T., Duarte, C. A., and Zienkiewicz, O. C., 1998, "A New Cloud-Based hp Finite Element Method," Comput, Methods Appl. Mech. Eng., 153, pp. 117-126.
16. Strouboulis, T., Copps, K., and Babuška, I., 2001, "The Generalized Finite Element Method," Comput. Methods Appl. Mech. Eng., 190, pp. 4081-4193.
17. Duarte, C. A., Kim, D.-J., and Quaresma, D. M., 2006, "Arbitrarily Smooth Generalized Finite Element Approximations," Comput. Methods Appl. Mech. Eng., 196, pp. 33-56.
18. Oden, J. T., and Duarte, C. A., 1997, Recent Developments in Computational and Applied Mechanics, B. D. Reddy, ed., International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, pp. 302-321.
19. Oden, J. T., and Duarte, C. A. M., 1996, The Mathematics of Finite Elements and Applications-Highlights 1996, J. R. Whiteman, ed., Wiley, New York, Chap. 2, pp. 35-54.
20. Duarte, C. A., Hamzeh, O. N., Liszka, T. J., and Tworzydlo, W. W., 2001, "A Generalized Finite Element Method for the Simulation of Three-Dimensional Dynamic Crack Propagation," Comput. Methods Appl. Mech. Eng., 190, pp. 2227-2262.
21. Moes, N., Dolbow, J., and Belytschko, T., 1999, "A Finite Element Method for Crack Growth Without Remeshing," Int. J. Numer. Methods Eng., 46, pp. 131-150.
22. Sukumar, N., Moes, N., Moran, B., and Belytschko, T., 2000, "Extended Finite Element Method for Three-Dimensional Crack Modelling," Int. J. Numer. Methods Eng., 48(11), pp. 1549-1570.
23. Wells, G. N., and Sluys, L. J., 2001, "A New Method for Modeling Cohesive Cracks Using Finite Elements," Int. J. Numer. Methods Eng., 50, pp. 2667-2682.
24. Simone, A., 2004, "Partition of Unity-Based Discontinuous Elements for Interface Phenomena," Int. J. Math. Model., 20, pp. 465-478.
25. Duarte, C. A., Reno, L. G., and Simone, A., 2007, "A High-Order Generalized FEM for Through-The-Thickness Branched Cracks," Int. J. Numer. Methods Eng., 72(3), pp. 325-351.
26. Strouboulis, T., Zhang, L., and Babuška, I., 2003, "Generalized Finite Element Method Using Mesh-Based Handbooks: Application to Problems in Domains With Many Voids," Comput. Methods Appl. Mech. Eng., 192, pp. 3109-3161.
27. Szabo, B. A., and Babuška, I., 1988, "Computation of the Amplitude of Stress Singular Terms for Cracks and Reentrant Corners," Fracture Mechanics: Nineteenth Symposium, T A. Cruse, ed., American Society for Testing and Materials, Philadelphia, pp. 101-124, ASTM STP, 969.
28. Pereira, J. P., and Duarte, C. A., 2005, "Extraction of Stress Intensity Factors From Generalized Finite Element Solutions," Eng. Anal. Boundary Elem., 29, pp. 397-413.
29. Pereira, J. P., and Duarte, C. A., 2004, "Computation of Stress Intensity Factors for Pressurized Cracks Using the Generalized Finite Element Method and Superconvergent Extraction Techniques," XXV Iberian Latin-American Congress on Computational Methods in Engineering, Recife, PE, Brazil, Nov., P. R. M. Lyra, S. M. B. A. da Silva, F. S. Magnani, L. J. do, N. Guimaraes, L. M. da Costa, and E. Parente, Jr., eds.
30. Babuška, I., and Andersson, B., 2005, "The Splitting Method as a Tool for Multiple Damage Analysis," SIAM J. Sci. Comput. (USA), 26, pp. 1114-1145.
31. Yohannes, A., Cartwright, D. J., and Collins, R. A., 1996, "Application of a Discontinuous Strip Yield Model to Multiple Site Damage in Stiffened Sheets," The 1996 Forth International Conference on Computer-Aided Assesment and Control, Fukuoka, Japan, pp. 565-572.
32. Wang, L., Brust, F. W., and Atluri, S. N., 1997, "The Elastic-Plastic Finite Element Alternating Method (EPFEAM) and the Prediction of Fracture Under WFD Conditions in Aircraft Structures," Comput. Mech., 19, pp. 356-369.
33. Stern, M., Becker, E. B., and Dunham, R. S., 1976, "A Contour Integral Computation of Mixed-Mode Stress Intensity Factors," Int. J. Fract., 12, pp. 359-368.
34. Pereira, J. P., and Duarte, C. A., 2006, "The Contour Integral Method for Loaded Cracks," Int. J. Math. Model., 22(5), pp. 421-432.