Finite deformation theory for beam, plate and shell. Part V. The shell element with drilling degree of freedom based on Biot strain

Computer Methods in Applied Mechanics and Engineering

Volumn 189, Issue 3, 2000, Pages 743-759

  Li, Mingrui ^a   Zhan, Fuliang ^a  

^a CHINA AGRICULTURAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

BEAMS AND GIRDERS; DEGREES OF FREEDOM (MECHANICS); PLATES (STRUCTURAL COMPONENTS); SHELLS (STRUCTURES);

BIOT STRAIN; FINITE DIFFERENCE THEORY;

DEFORMATION;

EID: 0034274136     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(99)00327-8     Document Type: Article

References (37)

1. O.C. Zienkicwicz, The Finite Element Method, third ed., McGraw-Hill, UK, 1979
2. D.J. Allman A compatible triangular element including vertex rotations for plane elasticity analysis Comput. Struct. 19 1984 1 8
3. P.G. Bergan C.A. Felippa A triangular membrane element with rotational degrees of freedom Comput. Methods Appl. Mech. 50 1985 25 69
4. D.J. Allman A quadrilateral finite element including vertex rotations for plane elastic problems Int. J. Numer. Methods Engrg. 26 1988 717 739
5. R.D. Cook On the Allman triangle and a related quadrilateral element Comput. Struct. 22 1986 1065 1067
6. R.D. Cook A plane hybrid element with rotational d.o.f. and adjustable stiffness Int. J. Numer. Methods Engrg. 24 1987 1499 1508
7. S. Jaamei, F. Frey, Ph. Jetteur, Nonlinear thin shell finite element with six degrees of freedom per node, in: Seventh International Symposium on Computing methods in Applied Science and Engineering, Versailles, 1987
8. Ph. Jetteur F. Frey A four node Marguerre element for non-linear analysis Engrg. Comput. 3 1986 276 282
9. R.H. MacNeal R.L. Harder A refined four-node membrane element with rotational degrees of freedom Comput. Struct. 28 1988 75 88
10. A. Ibrahimbegovic R.L. Taylor E. Wilson A robust quadrilateral membrane finite element with drilling degrees of freedom Int. J. Numer. Methods Engrg. 30 1990 445 457
11. T.J.R. Hughes On drilling degrees of freedom Comput. Methods Appl. Mech. 72 1989 105 121
12. A. Ibrahimbegovic F. Frey Variational principles and membrane finite elements with drilling rotations for geometrically nonlinear elasticity Int. J. Numer. Methods Engrg. 38 1995 1885 1900
13. J.C. Simo D.D. Fox T.J.R. Hughes Formulation of finite elasticity with independent rotations Comput. Methods Appl. Mech. Engrg. 95 1992 277 288
14. A. Ibrahimbegovic F. Frey Quadrilateral membrane elements with rotational degrees of freedom Engrg. Fract. Mech. 43 1992 13 24
15. A. Ibrahimbegovic Mixed finite element with drilling rotations for plane problems in elasticity Comput. Methods Appl. Mech. Engrg. 107 1993 225 238
16. A. Ibrahimbegovic F. Frey Geometrically nonlinear method of incompatible modes in application to finite elasticity with independent rotations Int. J. Numer. Methods Engrg. 36 1993 4185 4200
17. M. Li The finite deformation of beam, plate and shell structures. Part II. The kinematic model and the Green-Lagrangian strains Comput. Methods Appl. Mech. Engrg. 156 1998 247 257
18. M. Li The finite deformation of beam, plate and shell structures. Part IV. The FE formulation of Mindlin Plate and shell based on Green-Lagrangian strain Comput. Methods Appl. Mech. Engrg. 182 2000 187 203
19. J.H. Argyris An excursion into large rotations Comput. Methods Appl. Mech. Engrg. 32 1982 85 155
20. M.A. Biot Mechanics of Incremental Deformation 1965 Wiley New York
21. J.H. Argyris P.C. Dunne D.W. Scharpf On large displacement-small strain structures with rotational degrees of freedom Comput. Methods Appl. Mech. Engrg. 14 1978 401 451
22. J.H. Argyris O. Hilpert G.A. Malejannakis D.W. Scharpf On the geometrical stiffness of a beam in space-A consistent V.W. approach Comput. Methods Appl. Mech. Engrg. 20 1979 105 131
23. H. Ziegler, Principles of Structural Stability, second ed., Birkshauser, Verlag, Stuttgart, Germany, 1977
24. C. Sansour H. Bufler An exact finite rotation shell theory, its mixed variational formulation and its finite element implementation Int. J. Numer. Method Engrg. 34 1992 73 115
25. W. Kanok-Nukulchai R.L. Taylor T.J.R. Hughes A large deformation formulation for shell analysis by the finite element method Comput. Struct. 13 1981 19 27
26. H. Parish A continuum based shell theory for non-linear applications Int. J. Numer. Methods 38 1995 1855 1883
27. M. Li The finite deformation theory for beam, plate and shell. Part III. The three-dimensional beam theory and the FE formulation Comput. Methods Appl. Mech. Engrg. 162 1998 287 300
28. Y. Basar Y. Ding Finite rotation elements for the nonlinear analysis of thin shell structures Int. J. Solids Struct. 26 1990 83 87
29. J.F. Mescal Large deflection of spherical shells under concentrated loads J. Appl. Mech. 32 1965 936 938
30. K.J. Bathe Finite element formulations for large deformation dynamic analysis Int. J. Numer. Methods Engrg. 9 1975 353 386
31. R.H. MacNeal R.L. Harder A proposed standard set of problems to test finite element accuracy Finite Element Analysis and Design 1 1985 3 20
32. D.W. White Testing of shell finite element accuracy and robustness Finite Element Analysis and Design 6 1989 129 151
33. N. Buechter E. Ramm Shell theory versus degeneration – a comparison in large rotation finite element analysis Int. J. Numer. Methods Engrg. 34 1992 39 59
34. J.C. Simo D.D. Fox M.S. Rifai On a stress resultant geometrically exact shell model. Part III. Computational aspects of the nonlinear theory Comput. Methods Appl. Mech. Engrg. 79 1990 21 70
35. J. Chroscielewski J. Makowski H. Stump Genuinely resultant shell finite elements accounting for geometric and material non-linearity Int. J. Numer. Methods 35 1992 63 94
36. P. Betsch F. Gruttmann E. Stein A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains Comput. Methods Appl. Mech. Engrg. 130 1996 57 79
37. T.J.R. Hughes, F. Brezzi, A. Masud, I. Harai, Finite elements with drilling degrees of freedom: theory and numerical evaluations, in: R. Gruber et al. (Eds.), Proceedings of the Fifth International Symposium on Numerical Methods, Springer, Berlin, 1989, pp. 3–18