Linear buckling analysis of cracked plates by SFEM and XFEM

Journal of Mechanics of Materials and Structures

Volumn 6, Issue 9-10, 2011, Pages 1213-1238

  Baiz, Pedro M ^a   Natarajan, Sundararajan ^b   Bordas, Stéphane P A ^b   Kerfriden, Pierre ^b   Rabczuk, Timon ^c  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b CARDIFF UNIVERSITY   (United Kingdom)

^c BAUHAUS UNIVERSITY WEIMAR   (Germany)

Author keywords

Buckling; Extended finite element method (XFEM); Fracture; Mindlin; Partition of unity methods (PUM); Reissner; Shear deformable plate theory

Indexed keywords

EXTENDED FINITE ELEMENT METHOD; MINDLIN; PARTITION OF UNITY METHODS; REISSNER; SHEAR DEFORMABLE PLATE;

CRACK PROPAGATION; CRACKS; FRACTURE; FUNCTIONS;

BUCKLING;

EID: 84861751388     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2011.6.1213     Document Type: Article

References (41)

1. ABAQUS user's manual, Version 6.9.1, Hibbitt, Karlsson and Sorensen, Pawtucket, Rhode Island, 2009.
2. M. M. Alinia, S. A. A. Hosseinzadeh, and H. R. Habashi, "Numerical modelling for buckling analysis of cracked shear panels", Thin-Walled Struct 45:12 (2007), 1058-1067.
3. P. M. A. Areias and T. Belytschko, "Non-linear analysis of shells with arbitrary evolving cracks using XFEM", Int. J. Numer. Meth. Eng. 62:3 (2005), 384-415.
4. I. Babuška, G. Caloz, and J. E. Osborn, "Special finite element methods for a class of second order elliptic problems with rough coefficients", SIAM J. Numer. Anal. 31:4 (1994), 945-981.
5. M. Bachene, R. Tiberkak, and S. Rechak, "Vibration analysis of cracked plates using the extended finite element method", Arch. Appl. Mech. 79:3 (2009), 249-262.
6. K.-J. Bathe and E. N. Dvorkin, "A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation", Int. J. Numer. Meth. Eng. 21 (1985), 367-383.
7. T. Belytschko and T. Black, "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Meth. Eng. 45:5 (1999), 601-620.
8. T. Belytschko, R. Gracie, and G. Ventura, "A review of extended/generalized finite element methods for material modelling", Model. Simul. Mater. Sci. Eng. 17:4 (2009), 1-31.
9. S. P. A. Bordas and S. Natarajan, "On the approximation in the smoothed finite element method (SFEM)", Int. J. Numer. Meth. Eng. 81:5 (2010), 660-670.
10. S. P. A. Bordas, T. Rabczuk, N. Hung, V. Nguyen, S. Natarajan, T. Bog, D. Quan, and N. Hiep, "Strain smoothing in FEM and XFEM", Comput. Struct. 88:23-24 (2009), 1419-1443.
11. R. Brighenti, "Buckling sensitivity analysis of cracked thin plates under membrane tension or compression loading", Nucl. Eng. Des. 239:6 (2009), 965-980.
12. K. Y. Dai, G. R. Liu, and T. T. Nguyen, "An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics", Finite Elem. Anal. Des. 43:11-12 (2007), 847-860.
13. J. Dolbow, N. Moës, and T. Belytschko, "Modeling fracture in Mindlin-Reissner plates with the extended finite element method", Int. J. Solids Struct. 37:48-50 (2000), 7161-7183.
14. F. Gruttmann and W. Wagner, "A stabilized one-point integrated quadrilateral Reissner-Mindlin plate element", Int. J. Numer. Methods Eng. 61:13 (2004), 2273-2295.
15. S. Hosseini-Hashemi, K. Khorshidi, and M. Amabili, "Exact solution for linear buckling of rectangular Mindlin plates", J. Sound Vibration 315:1-2 (2008), 318-342.
16. C. V. Le, H. Nguyen-Xuan, H. Askes, S. P. A. Bordas, T. Rabczuk, and H. Nuguyen-Vinh, "A cell-based smoothed finite element method for kinematic limit analysis", Int. J. Numer. Meth. Eng. 83:12 (2010), 1651-1674.
17. F. L. Liu, "Differential quadrature element method for buckling analysis of rectangular Mindlin plates having discontinuities", Int. J. Solids Struct. 38:14 (2001), 2305-2321.
18. G. R. Liu, "A G space theory and a weakened weak .W2/form for a unified formulation of compatible and incompatible methods, I: Theory", Int. J. Numer. Meth. Eng. 81:9 (2010), 1093-1126.
19. G. R. Liu, "A G space theory and a weakened weak .W2/form for a unified formulation of compatible and incompatible methods, II: Applications to solid mechanics problems", Int. J. Numer. Meth. Eng. 81:9 (2010), 1127-1156.
20. G. R. Liu, K. Y. Dai, and T. T. Nguyen., "A smoothed finite element method for mechanics problems", Comput. Mech. 39:6 (2007), 859-877.
21. G. R. Liu, T. T. Nguyen, K. Y. Dai, and K. Y. Lam, "Theoretical aspects of the smoothed finite element method (SFEM)", Int. J. Numer. Meth. Eng. 71:8 (2007), 902-930.
22. G. R. Liu, T. Nguyen-Thoi, and K. Y. Lam, "An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids", J. Sound Vibration 320:4-5 (2009), 1100-1130.
23. G. R. Liu, T. Nguyen-Thoi, H. Nguyen-Xuan, and K. Y. Lam, "A node-based smoothed finite element method (N-SFEM) for upper bound solutions to solid mechanics problems", Comput. Struct. 87:1-2 (2009), 14-26.
24. K. Markström and B. Stoṙ akers, "Buckling of cracked members under tension", Int. J. Solids Struct. 16:3 (1980), 217-229.
25. S. Natarajan, S. Bordas, and D. R. Mahapatra, "Numerical integration over arbitrary polygonal domains based on Schwarz-Christoffel conformal mapping", Int. J. Numer. Meth. Eng. 80:1 (2009), 103-134.
26. S. Natarajan, S. P. A. Bordas, and T. Rabczuk, "Linear free flexural vibration of cracked isotropic plates using the extended finite element method", preprint, 2009. Submitted to Algorithms.
27. S. Natarajan, D. R. Mahapatra, and S. P. A. Bordas, "Integrating strong and weak discontinuities without integration subcells and example applications in an XFEM/GFEM framework", Int. J. Numer. Meth. Eng. 83:3 (2010), 269- 294.
28. N. Nguyen-Thanh, T. Rabczuk, H. Nguyen-Xuan, and S. P. A. Bordas, "A smoothed finite element method for shell analysis", Comput. Methods Appl. Mech. Eng. 198:2 (2008), 165-177.
29. H. Nguyen-Xuan, S. Bordas, and H. Nguyen-Dang, "Smooth finite element methods: convergence, accuracy and properties", Int. J. Numer. Meth. Eng. 74:2 (2008), 175-208.
30. H. Nguyen-Xuan, T. Rabczuk, S. Bordas, and J. F. Debongnie, "A smoothed finite element method for plate analysis", Comput. Methods Appl. Mech. Eng. 197:13-16 (2008), 1184-1203.
31. J. Purbolaksono and M. H. Aliabadi, "Dual boundary element method for instability analysis of cracked plates", Comput. Model. Eng. Sci. 8:1 (2005), 73-90.
32. T. Rabczuk and P. Areias, "A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis", Comput. Model. Eng. Sci. 16:2 (2006), 115-130.
33. T. Rabczuk, P. M. A. Areias, and T. Belytschko, "A meshfree thin shell method for non-linear dynamic fracture", Int. J. Numer. Meth. Eng. 72:5 (2007), 524-548.
34. T. Rabczuk, R. Gracie, J.-H. Song, and T. Belytschko, "Immersed particle method for fluid-structure interaction", Int. J. Numer. Meth. Eng. 81:1 (2010), 48-71.
35. E. Reissner, "On bending of elastic plates", Quart. Appl. Math. 5 (1947), 55-68.
36. E. Riks, C. C. Rankin, and F. A. Brogan, "The buckling behavior of a central crack in a plate under tension", Eng. Fract. Mech. 43:4 (1992), 529-548.
37. G. C. Sih and Y. D. Lee, "Tensile and compressive buckling of plates weakened by cracks", Theor. Appl. Fract. Mech. 6:2 (1986), 129-138.
38. B. Stahl and L. M. Keer, "Vibration and stability of cracked rectangular plates", Int. J. Solids Struct. 8 (1972), 69-91.
39. A. Vafai, M. Javidruzi, and H. E. Estekanchi, "Parametric instability of edge cracked plates", Thin-Walled Struct. 40:1 (2002), 29-44.
40. D. Wang and J.-S. Chen, "Locking-free stabilized conforming nodal integration for meshfree Mindlin- Reissner plate formulation", Comput. Methods Appl. Mech. Eng. 193:12-14 (2004), 1065-1083.
41. E. Wyart, D. Coulon, M. Duflot, T. Pardoen, J.-F. Remacle, and F. Lani, "A substructured FE-shell/XFE-3D method for crack analysis in thin-walled structures", Int. J. Numer. Meth. Eng. 72:7 (2007), 757-779.