Shear deformable shell elements for large strains and rotations

International Journal for Numerical Methods in Engineering

Volumn 40, Issue 23, 1997, Pages 4427-4449

  Bischoff, M ^a   Ramm, E ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Element technology; Enhanced assumed strains; Geometrically non linear shell formulation; Higher order shell formulation; Large rotations; Large strains

Indexed keywords

CONTINUUM MECHANICS; KINEMATICS; ROTATION; SHEAR DEFORMATION; SHELLS (STRUCTURES); STRAIN;

ASSUMED NATURAL STRAIN (ANS); ENHANCED ASSUMED STRAIN (EAS); GREEN LAGRANGE STRAINS; REISSNER MINDLIN KINEMATICS;

FINITE ELEMENT METHOD;

EID: 0031363025     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19971215)40:23<4427::AID-NME268>3.0.CO;2-9     Document Type: Article

References (23)

1. U. Andelfinger and E. Ramm, 'EAS-elements for two-dimensional, three-dimensional, Plate and Shell structures and their Equivalence to HR-EIements', Int. J. Numer. Meth. Engng., 36, 1311-1337 (1993).
2. J. C. Simo and F. Armero, 'Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes', Int. J. Numer. Meth. Engng., 33, 1413-1449 (1992).
3. N. Büchter and E. Ramm, '3D-extension of nonlinear shell equations based on the enhanced assumed strain concept', in Ch. Hirsch (ed.), Computational Methods in Applied Sciences, Elsevier, Amsterdam, 1992, pp. 55-62.
4. T. J. R. Hughes and T. E. Tezduyar, 'Finite elements based upon Mindlin plate theory with particular reference to the four-node isoparametric element', J. Appl. Mech., 48, 587-596 (1981).
5. E. N. Dvorkin and K. J. Bathe, 'A continuum mechanics based four-node shell element for general nonlinear analysis', Engineering Comput., 1, 77-88 (1984).
6. J. C. Simo and S. Rifai, 'A class of mixed assumed strain methods and the method of incompatible modes', Int. J. Numer. Meth. Engng., 29, 1595-1638 (1990).
7. D. Braess, 'Enhanced assumed strain elements and locking in membrane problems', submitted to Comput. Meth. Appl. Mech. Engng., (1997).
8. M. Braun, Nichtlineare Analysen von geschichteten, elastischen Flächentragwerken, Ph.D. Thesis, Institut für Baustatik, Universität Stuttgart, 1994.
9. M. Braun, M. Bischoff and E. Ramm, 'Nonlinear shell formulations for complete three-dimensional constitutive laws including composites and laminates', Comput. Mech., 15, 1-18 (1994).
10. 0-elastoplastic shell element based on assumed covariant strain interpolations', in G. N. Pande and J. Middleton (eds.), Proc. Int. Conf. NUMETA 1987, Swansea, 1987.
11. M. L. Bucalem and K. J. Bathe, 'Higher-order MITC general shell elements', Int. J. Numer. Meth. Engng., 36, 3729-3754 (1993).
12. N. Büchter, E. Ramm and D. Roehl, Three-dimensional extension of nonlinear shell formulation based on the enhanced assumed strain concept', Int. J. Numer. Meth. Engng., 37, 2551-2568 (1994).
13. E. Ramm, M. Bischoff and M. Braun, 'Higher order nonlinear shell formulations - a step back into three dimensions', in K. Bell (ed.), From Finite Elements to the Troll Platform, Dept. of Structural Engineering, Norwegian Institute of Technology, Trondheim, Norway, 1994, pp. 65-88.
14. H. Parisch, 'A continuum-based shell theory for nonlinear applications', Int. J. Numer. Meth. Engng., 38, 1855-1883 (1993).
15. C. Sansour, 'A theory and finite element formulation of shells at finite deformations including thickness change: circumventing the use of a rotation tensor', Arch. Appl. Mech., 10, 194-216 (1995).
16. H. Verhoeven, Geometrisch und physikalisch nichtlineare finite Plattenelemente mit Berücksichtigung der Dickenverzerrung, Ph.D. Thesis, TU Berlin, Shaker, Aachen, 1993.
17. E. Reissner, 'On finite axi-symmetrical deformations of thin elastic shells of revolution', Comput. Mech., 4, 387-400 (1989).
18. P. Betsch, F. Gruttmann and E. Stein, 'A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains', Comput. Meth. Appl. Mech. Engng., 130, 57-79 (1996).
19. T. H. H. Pian and K. Sumihara, 'A rational approach for assumed stress finite elements', Int. J. Numer. Meth. Engng., 20, 1685-1695 (1984).
20. N. Büchter and E. Ramm, 'Shell theory versus degeneration - a comparison in large rotation finite element analysis', Int. J. Numer. Meth. Engng., 34, 39-59 (1992).
21. M. Bischoff and E. Ramm, 'EAS methods for higher order nonlinear shell formulations', 3rd U.S. National Congress on Computational Mechanics (USNCCM) at Dallas, Texas, 1995 (No proceedings).
22. P. Wriggers and S. Reese, 'An note on enhanced strain methods for large deformations', Comput. Meth. Appl. Mech. Engng., 135, 201-209 (1996).
23. T. Belytschko, 'A response to Babuska-Oden recommendations on benchmarks', Int. Assoc. Comput. Mech. (IACM) Bull., 8, 63-64 (1993).