A smoothed finite element method for shell analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 198, Issue 2, 2008, Pages 165-177

  Nguyen Thanh, N ^a   Rabczuk, Timon ^b   Nguyen Xuan, H ^c   Bordas, Stéphane P A ^d  

^a VIETNAM NATIONAL UNIVERSITY   (Viet Nam)

^b UNIVERSITY OF CANTERBURY   (New Zealand)

^c SINGAPORE MIT ALLIANCE   (Singapore)

^d UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

MITC4 elements; Shell elements; Smoothed finite elements (SFEM)

Indexed keywords

FINITE ELEMENT METHOD; INTERPOLATION; SHELLS (STRUCTURES); STIFFNESS MATRIX;

ACCURATE; BENDING; COMPUTATIONALLY INEXPENSIVE; INTERPOLATION FUNCTIONS; LOCKING; MEMBRANE ELEMENTS; MEMBRANE STIFFNESSES; MINDLIN; MITC4 ELEMENTS; MIXED INTERPOLATIONS; NATURAL COORDINATES; NUMERICAL EXAMPLES; PLATE BENDING; REISSNER THEORIES; SHELL ANALYSIS; SHELL ELEMENTS; SMOOTHED FINITE ELEMENT METHODS; SMOOTHED FINITE ELEMENTS (SFEM); SMOOTHING;

BENDING (DEFORMATION);

EID: 55049125442     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2008.05.029     Document Type: Article

References (43)

1. P.M.A. Areias, J.H. Song, T. Belytschko, A simple finite-strain quadrilateral shell element. Part I: Elasticity, Int. J. Numer. Methods Engrg., in press.
2. Areias P.M.A., Song J.H., and Belytschko T. Analysis of fracture in thin shells by overlapping paired elements. Int. J. Numer. Methods Engrg. 195 (2006) 5343-5360
3. Bathe K.J. Finite Element Procedures (1996), Prentice-Hall, Massachusetts (MIT), Englewood Cliffs, NJ
4. Bathe K.J., and Dvorkin E.N. A four-node plate bending element based on Mindlin/Reissner 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. Batoz J.L., and Dhatt G. Modélisation des structures par éléments finis. Poutres et Plaques vol. 2 (1990), Hermès
7. Belytschko T., and Leviathan I. Physical stabilization of the 4-node shell element with one-point quadrature. Comput. Methods Appl. Mech. Engrg. 113 (1994) 321-350
8. M. Bischoff, Theorie und Numerik einer dreidimensionalen Schalenformulierung, Ph.D. thesis, University Stuttgart, 1999.
9. Bischoff M., and Ramm E. Shear deformable shell elements for large strains and rotations. Int. J. Numer. Methods Engrg. (1997)
10. Bletzinger K.U., Bischoff M., and Ramm E. A unified approach for shear-locking-free triangular and rectangular shell finite elements. Comput. Struct. (2000)
11. 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
12. Cook R.D., Malkus D.S., Plesha M.E., and Witt R.J. Concepts and Applications of Finite Element Analysis. fourth ed. (2001), John Wiley and Sons
13. Duddeck H. Die biegetheorie der flachen hyperbolischen paraboloidschale z = cxy. Ing. Archiv 31 (1962) 44-78
14. Dvorkin E., and Bathe K.J. A continuum mechanics based four-node shell element for general nonlinear analysis. Engrg. Comput. (1984)
15. Wagner W., and Gruttmann F. A linear quadrilateral shell element with fast. Comput. Methods Appl. Mech. Engrg. 194 (2005) 4279-4300
16. Flores F.G., and Estrada C.F. A rotation-free thin shell quadrilateral. Comput. Methods Appl. Mech. Engrg. 196 (2007) 2631-2646
17. Guzey S., Stolarski H.K., Cockburn B., and Tamma K.K. Design and development of a discontinuous Galerkin method for shells. Comput. Methods Appl. Mech. Engrg. 195 (2006) 3528-3548
18. Hughes T.J.R. The Finite Element Method (1987), Prentice-Hall, Englewood Cliffs, NJ
19. Hughes T.J.R., Cohen M., and Haroun M. Reduced and selective integration techniques in finite element method of plates. Nucl. Engrg. Des. 46 (1978) 203-222
20. Hughes T.J.R., and Liu W.K. Nonlinear finite element analysis of shells. Part II: Two dimensional shells. Comput. Methods Appl. Mech. Engrg. 27 (1981) 167-182
21. 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
22. 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)
23. K. Kansara, Development of membrane, plate and flat shell elements in java, Master's thesis, Virginia Polytechnic Institute and State University, 2004.
24. Chapelle D., Bathe K.J., and Iosilevich A. An evaluation of the MITC shell elements. Comput. Struct. 75 (2000) 1-30
25. Liu G.R., Dai K.Y., and Nguyen T.T. A smoothed finite element for mechanics problems. Comput. Mech. 39 (2007) 859-877
26. 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 (2007) 902-930
27. Lyly M., Stenberg R., and Vihinen T. A stable bilinear element for Reissner-Mindlin plate model. Comput. Methods Appl. Mech. Engrg. 110 (1993) 343-357
28. McNeal R.H., and Harder R.L. A proposed set of problems to test finite element accuracy. Finite Elem. Anal. 1 (1985) 3-20
29. H. Nguyen-Xuan, S. Bordas, H. Nguyen-Dang, Smooth finite element methods: convergence, accuracy and properties, Int. J. Numer. Methods Engrg., in press, DOI:10.1002/nme.2146.
30. Nguyen-Xuan H., Rabczuk T., Bordas S., and Debongnie J.F. A smoothed finite element method for plate analysis. Comput. Methods Appl. Mech. Engrg. 197 (2008) 1184-1203
31. Rabczuk T., and Areias P. A meshfree thin shell for arbitrary evolving cracks based on an external enrichment. Comput. Model. Engrg. Sci. 16 2 (2006) 115-130
32. Rabczuk T., Areias P.M.A., and Belytschko T. A meshfree thin shell for large deformation, finite strain and arbitrary evolving cracks. Int. J. Numer. Methods Engrg. 72 5 (2007) 524-548
33. Rabczuk T., and Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int. J. Numer. Methods Engrg. 61 13 (2004) 2316-2343
34. Rabczuk T., and Belytschko T. Adaptivity for structured meshfree particle methods in 2D and 3D. Int. J. Numer. Methods Engrg. 63 11 (2005) 1559-1582
35. Rabczuk T., Belytschko T., and Xiao S.P. Stable particle methods based on Lagrangian kernels. Comput. Methods Appl. Mech. Engrg. 193 (2004) 1035-1063
36. R. Sauer, Eine einheitliche Finite-Element-Formulierung fur Stab- und Schalentragwerke mit endlichen Rotationen, Bericht 4 (1998), Institut fur Baustatik, Universitat Karlsruhe (TH), 1998.
37. Scordelis A.C., and Lo K.S. Computer analysis of cylindrical shells. J. Am. Concrete Inst. 61 (1964) 539-561
38. Simo J.C., Fox D.D., and Rifai M.S. On a stress resultant geometrically exact shell model. Part II: The linear theory; computational aspects. Comput. Methods Appl. Mech. Engrg. 73 (1989) 53-92
39. Taylor R.L. Finite element analysis of linear shell problems. In: Whiteman J.R. (Ed). The Mathematics of Finite Elements and Applications VI (MAFELAP 1987) (1988), Academic Press, London
40. Taylor R.L., and Kasperm E.P. A mixed-enhanced strain method. Comput. Struct. 75 (2000) 237-250
41. 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
42. Zienkiewicz O.C., and Taylor R.L. The Finite Element Method. fifth ed. (2000), Butterworth Heinemann, Oxford
43. Zienkiewicz O.C., Taylor R.L., and Too J.M. Reduced integration technique in general analysis of plates and shells. Int. J. Numer. Methods Engrg. 3 (1971) 275-290