A smoothed finite element method for plate analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 13-16, 2008, Pages 1184-1203

  Nguyen Xuan, H ^a   Rabczuk, T ^b   Bordas, Stéphane ^c   Debongnie, J F ^d  

^a UNIVERSITY OF NATURAL SCIENCES   (Viet Nam)

^b UNIVERSITY OF CANTERBURY   (New Zealand)

^c UNIVERSITY OF GLASGOW   (United Kingdom)

^d UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Curvature smoothing; Distorted meshes; Locking free; Plates; SFEM; Smooth finite element method

Indexed keywords

APPROXIMATION THEORY; BENDING (DEFORMATION); BOUNDARY INTEGRAL EQUATIONS; COMPUTER SIMULATION; CURVE FITTING; FINITE ELEMENT METHOD; STIFFNESS MATRIX;

CURVATURE SMOOTHING; DISTORTED MESHES; NON-LOCAL APPROXIMATION; PLATE ANALYSIS; SMOOTHED FINITE ELEMENT METHOD;

PLATES (STRUCTURAL COMPONENTS);

APPROXIMATION THEORY; BENDING (DEFORMATION); BOUNDARY INTEGRAL EQUATIONS; COMPUTER SIMULATION; CURVE FITTING; FINITE ELEMENT METHOD; PLATES (STRUCTURAL COMPONENTS); STIFFNESS MATRIX;

EID: 38349019509     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.10.008     Document Type: Article

References (67)

1. ABAQUS/Standard User's Manual, Version 6.4, Hibbitt, Karlsson and Sorensen, Inc., Rawtucket, Rhode Island, 2004.
2. F. Armero, D. Ehrlich, Finite element methods for the multi-scale modeling of softening hinge lines in plates at failure.
3. Bathe K.J. Finite Element Procedures (1996), Prentice-Hall/MIT, Englewood Cliffs, NJ/MA
4. Bathe K.J., and Dvorkin E.N. A four-node plate bending element based on Mindlin/Reissener plate theory and a mixed interpolation. Int. J. Numer. Methods Engrg. 21 (1985) 367-383
5. Bathe K.J., and Dvorkin E.N. A formulation of general shell elements. the use of mixed interpolation of tensorial components. Int. J. Numer. Methods Engrg. 22 (1986) 697-722
6. J.L. Batoz, G. Dhatt, Modélisation des structures par éléments finis, vol. 2, poutres et plaques, Hermès, 1990.
7. Bazeley G.P., Cheung Y.K., Irons B.M., and Zienkiewicz O.C. Triangular Elements in Plate Bending. Proceedings of the First Conference, on Matrix Methods in Structural Mechanics (1965), Wright-Patterson AFB, Ohio
8. Belytschko T., and Black T. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Engrg. 45 5 (1999) 601-620
9. Belytschko T., Moes N., Usui S., and Parimi C. Arbitrary discontinuities in finite elements. Int. J. Numer. Methods Engrg. 50 4 (2001) 993-1013
10. Bletzinger K., Bischoff M., and Ramm E. A unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput. Struct. 75 (2000) 321-334
11. Bordas S., Conley J.G., Moran B., Gray J., and Nichols E. A simulation-based design paradigm for complex cast components. Engrg. Comput. 23 1 (2007) 25-37
12. S. Bordas, M. Duflot, Derivative recovery and a posteriori error estimation in extended finite element methods, Comput. Methods Appl. Mech. Engrg., in press, http://dx.doi.org/10.1016/j.cma.2007.03.011.
13. S. Bordas, M. Duflot, P. Le, A simple a posteriori error estimator for the extended finite element method, Commun. Numer. Methods Engrg., in press, doi:10.1002/cnm.1001.
14. Bordas S., and Moran B. Enriched finite elements and level sets for damage tolerance assessment of complex structures. Engrg. Fract. Mech. 73 (2006) 1176-1201
15. S. Bordas, V.P. Nguyen, C. Dunant, H. Nguyen-Dang, A. Guidoumm, An extended finite element library, Int. J. Numer. Methods Engrg., doi:10.1002/nme.1966.
16. S. Bordas, T. Rabczuk, G. Zi, Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment, Engrg. Fract. Mech., in press, doi:10.1016/j.engfracmech.2007.05.010.
17. Chen J.S., Wu C.T., Yoon S., and You Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Numer. Methods Engrg. 50 (2001) 435-466
18. Chen W., and Cheung Y.K. Refined quadrilateral element based on Mindlin/Reissner plate theory. Int. J. Numer. Methods Engrg. 47 (2000) 605-627
19. Chinosi C., Lovadina C., and Marini L.D. Nonconforming locking-free finite elements for Reissner-Mindlin plates. Comput. Methods Appl. Mech. Engrg. 195 (2006) 3448-3460
20. Dai K.Y., and Liu G.R. Free and forced vibration analysis using the smoothed finite element method (SFEM). J. Sound Vibration 301 3-5 (2007) 803-820
21. Dai K.Y., Liu G.R., and Nguyen T.T. An n-sided polygonal smoothed finite element method (nSFEM) for solid mechanics. Finite Elements Anal. Design 43 11-12 (2007) 847-860
22. M. Duflot, S. Bordas, An extended global recovery procedure for a posteriori error estimation in extended finite element methods, Int. J. Numer. Methods Engrg., in press.
23. Dunant C., Nguyen P., Belgasmia M., Bordas S., Guidoum A., and Nguyen-Dang H. Architecture trade-offs of including a mesher in an object-oriented extended finite element code. Eur. J. Mech. 16 (2007) 237-258 (special issue on the extended finite element method)
24. Dvorkin E.N., and Bathe K.J. A continuum mechanics based four-node shell element for general nonlinear analysis. Engrg. Comput. (1994)
25. Fraeijs de Veubeke B., and Sander G. An equilibrium model for plate bending. International Journal of Solids Structures (1968), Pergamon Press, London
26. Garcia O., Fancello E.A., Barcellos C.S., and Duarte C.A. Hp clouds in Mindlin's thick plate model. Int. J. Numer. Methods Engrg. 47 (2000) 1381-1400
27. Gruttmann F., and Wagner W. A stabilized one-point integrated quadrilateral Reissener-Mindlin plate element. Int. J. Numer. Methods Engrg. 61 (2004) 2273-2295
28. Hughes T.J.R. The Finite Element Method (1987), Prentice-Hall, Englewood Cliffs, NJ
29. Hughes T.J.R., Cohen M., and Haroun M. Reduced and selective integration techniques in finite element method of plates. Nuclear Engrg. Des. 46 (1978) 203-222
30. Hughes T.J.R., Taylor R.L., and Kanoknukulchai W. Simple and efficient element for plate bending. Int. J. Numer. Methods Engrg. 11 (1977) 1529-1543
31. Hughes T.J.R., and Tezduyar T. Finite elements based upon Mindlin plate theory with particular reference to the four-node isoparametric element. J. Appl. Mech. (1981)
32. Jensen D.D., and Park K.C. Equilibrium constrained assumed natural co-ordinate strain plate elements. Int. J. Numer. Methods Engrg. 38 (1995) 2951-2977
33. Batoz J.L., and Tahar M.B. Evaluation of a new quadrilateral thin plate bending element. Int. J. Numer. Methods Engrg. 18 (1982) 1655-1677
34. Krysl P., and Belytschko T. Analysis of thin plates by the element-free Galerkin method. Comput. Mech. 16 (1995) 1-10
35. Krysl P., and Belytschko T. Analysis of thin shells by the element-free Galerkin method. Int. J. Numer. Methods Engrg. 33 (1996) 3057-3080
36. Lee S.W., and Pian T.H.H. Improvement of plate and shell finite element by mixed formulation. AIAA J. 16 (1978) 29-34
37. Lee S.W., and Wong C. Mixed formulation finite elements for Mindlin theory plate bending. Int. J. Numer. Methods Engrg. 18 (1982) 1297-1311
38. Leissa A.W. Vibration of plates. NASA SP-160 (1969)
39. Li Q., Soric J., Jarak T., and Atluri S.N. A locking-free meshless local Petrov-Galerkin formulation for thick and thin plates. J. Comput. Phys. 208 (2005) 116-133
40. Liu G.R., Dai K.Y., and Nguyen T.T. A smoothed finite element for mechanics problems. Comput. Mech. 39 (2007) 859-877
41. Liu G.R., Nguyen T.T., Dai K.Y., and Lam K.Y. Theoretical aspects of the smoothed finite element method (SFEM). Int. J. Numer. Methods Engrg. 71 8 (2007) 902-930
42. Liu I.W., and Lin C.C. A new conforming quadrilateral plate bending element. Int. J. Numer. Methods Engrg. 36 (1993) 2921-2937
43. Moes N., and Belytschko T. Extended finite element method for cohesive crack growth. Engrg. Fract. Mech. 69 (2002) 813-834
44. Moes N., Dolbow J., and Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Engrg. 46 1 (1999) 133-150
45. Morley L.S.D. Skew Plates and Structures (1963), Pergamon Press, Oxford
46. X.H. Nguyen, S. Bordas, H. Nguyen-Dang, Smooth strain finite elements: selective integration. Collection of Papers from Prof. Nguyen-Dang Hung's former students, Vietnam National University, HCM Publishing House, 2006, pp. 88-106.
47. Nguyen T.T., Liu G.R., Dai K.Y., and Lam K.Y. Selective smoothed finite element method. Tsinghua Sci. Tech. 12 5 (2007) 497-508
48. Pian T.H.H., and Tong P. Basis of finite elements for solids continua. Int. J. Numer. Methods Engrg. 1 (1969) 3-28
49. Prathap G. The Finite Element Method in Structural Mechanics (1993), Kluwer Academic Publishers, Dordrect
50. T. Rabczuk, S. Bordas, G. Zi, A three-dimensional meshfree method for continuous crack initiation, nucleation and propagation in statics and dynamics, Comput. Mech., 2007, doi:10.1007/s00466-006-0122-1.
51. Razzaque A. Program for triangular bending elements with derivative smoothing. Int. J. Numer. Methods Engrg. 6 (1973) 333-345
52. Simo J.C., and Hughes T.J.R. On the variational foundation of assumed strain methods. ASME J. Appl. Mech. 53 (1986) 51-54
53. Simo J.C., and Rifai M.S. A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Numer. Methods Engrg. 29 (1990) 1595-1638
54. Soric J., Li Q., Jarak T., and Atluri S.N. The meshless local Petrov-Galerkin (MLPG) formulation for analysis of thick plates. Comput. Model. Engrg. Sci. 6 (2004) 349-357
55. Taylor R.L., and Auricchio F. Linked interpolation for Reissner-Mindlin plate elements. Part I - A simple triangle. Int. J. Numer. Methods Engrg. 36 (1993) 3056-3066
56. Wang D., and Chen J.S. Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1065-1083
57. Wang D., Dong S.B., and Chen J.S. Extended meshfree analysis of transverse and inplane loading of a laminated anisotropic plate of general planform geometry. Int. J. Solids Struct. 43 (2006) 144-171
58. Washizu K. Variational Methods in Elasticity and Plasticity. third ed. (1982), Pergamon Press, New York
59. Weissman S.L., and Taylor R.L. Resultant fields for mixed plate bending elements. Comput. Methods Appl. Mech. Engrg. 79 (1990) 321-355
60. E. Wyart, Three-dimensional crack analysis in aeronautical structures using the Substructured Finite Element/Extended Finite Element Method, PhD thesis, Université catholique de Louvain, 2007.
61. E. Wyart, D. Coulon, M. Duflot, T. Pardoen, J.-F. Remacle, F. Lani, A substructured fe shell/xfe 3d method for crack analysis. Int. J. Numer. Methods Engrg., in press.
62. E. Wyart, D. Coulon, P. Martiny, T. Pardoen, J.-F. Remacle, F. Lani, A substructured fe/xfe method for stress intensity factors computation in an industrial structure, Rev. Eur. Mécanique Numérique, in press.
63. E. Wyart, M. Duflot, D. Coulon, P. Martiny, T. Pardoen, J.-F. Remacle, F. Lani, Substructuring fe-xfe approaches applied to rack propagation, J. Comput. Appl. Math., in press.
64. Yoo J.W., Moran B., and Chen J.S. Stabilized conforming nodal integration in the natural-element method. Int. J. Numer. Methods Engrg. 60 (2004) 861-890
65. Zienkiewicz O.C., Zeng L.F., Xu Z., Samuelsson A., and Wiberg N.E. Linked interpolation for Reissner-Mindlin plate elements: Part i-a simple quadrilateral. Int. J. Numer. Methods Engrg. 36 (1993) 3043-3056
66. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method. fifth ed. (2000), Butterworth-Heinemann, Oxford
67. Zienkiewicz O.C., Taylor R.L., and Too J.M. Reduced integration technique in general analysis of plates and shells simple and efficient element for plate bending. Int. J. Numer. Methods Engrg. 3 (1971) 275-290