A Nonlinear Extensible 4-Node Shell Element Based on Continuum Theory and Assumed Strain Interpolations

Journal of Nonlinear Science

Volumn 6, Issue 2, 1996, Pages 169-199

  Betsch, P ^a   Stein, E ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001317365     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02434053     Document Type: Article

References (37)

1. J. C. Simo and F. Armero, Geometrically nonlinear enhanced strain mixed methods and the method of incompatible modes, Int. J. Num. Meth. Eng. 33 (1992) 1413-1449.
2. E. Ramm, Geometrisch nichtlineare Elastostatik und finite Elemente, Habilitation, Bericht Nr. 76-2, Institut für Baustatik, Universität Stuttgart, (1976).
3. T. J. R. Hughes and W. K. Liu, Nonlinear finite element analysis of shells: Part I. Three-dimensional shells, Comp. Meth. Appl. Mech. Eng. 26 (1981) 331-362.
4. J. C. Simo, D. D. Fox and M. S. Rifai, On a stress resultant geometrically exact shell model. Part III: Computational aspects of the nonlinear theory, Comp. Meth. Appl. Mech. Eng. 79 (1990) 21-70.
5. F. Gruttmann, W. Wagner, P. Wriggers, A nonlinear quadrilateral shell element with drilling degrees of freedom, Archive Appl. Mech. 62 (1992) 474-486.
6. Y. Basar, Y. Ding and W. B. Krätzig, Finite-rotatation shell elements via mixed formulation, Comp. Mech. 10 (1992) 289-306.
7. J. C. Simo, M. S. Rifai and D. D. Fox, On a stress resultant geometrically exact shell model. Part IV: Variable thickness shells with through-the-thickness stretching, Comp. Meth. Appl. Mech. Eng. 81 (1990) 91-126.
8. N. Büchter and E. Ramm, 3d-extension of nonlinear shell equations based on the enhanced assumed strain concept, Comp. Meth. Appl. Sci. (1992) 55-62.
9. N. Büchter, E. Ramm and D. Roehl, Three-dimensional extension of nonlinear shell formulations based on the enhanced assumed strain concept, Int. J. Num. Meth. Eng. 37 (1994) 2551-2568.
10. P. Steinmann, P. Betsch and E. Stein, FE plane stress analysis incorporating arbitrary 3d large strain constitutive models, submitted to Eng. Comp. (1994).
11. P. Betsch, F. Gruttmann and E. Stein, A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains, to appear in Comp. Meth. Appl. Mech. Eng. (1994).
12. 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, 65 (1995) 194-216.
13. A. Kühhorn and H. Schoop, A nonlinear theory for sandwich shells including the wrinkling phenomenon, Arch. Appl. Mech. 62 (1992) 413-427.
14. H. Parisch, A continuum-based shell theory for non-linear applications, Int. J. Num. Meth. Eng. 38 (1995) 1855-1883.
15. H. Schoop, A simple nonlinear flat element for large displacement structures, Computers & Structures 32 (1989) 379-385.
16. J. C. Simo and M. S. Rifai, A class of mixed assumed strain methods and the method of incompatible modes. Int. J. Num. Meth. Eng. 29 (1990) 1595-1638.
17. E. N. Dvorkin and K.-J. Bathe, A continuum mechanics based four-node shell element for general nonlinear analysis, Eng. Comput. 1 (1984) 77-88.
18. 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. Num. Meth. Eng. 21 (1985) 367-383.
19. N. Stander, A. Matzenmiller and E. Ramm, An assessment of assumed strain methods in finite rotation shell analysis, Eng. Comput. 6 (1989) 58-66.
20. H. Parisch, An investigation of a finite rotation four-node assumed strain shell element, Int. J. Num. Meth. Eng. 31 (1991) 127-150.
21. P. Betsch and E. Stein, An assumed strain approach avoiding artificial thickness straining for a nonlinear 4-node shell element, Comm. Num. Meth. Eng. 11 (1995) 899-909.
22. J. C. Simo and T. J. R. Hughes, On the variational foundations of assumed strain methods, J. Appl. Mech. 53 (1986) 51-54.
23. B. D. Reddy and J. C. Simo, Stability and convergence of a class of enhanced strain methods, preprint (1994).
24. P. M. Naghdi, The theory of plates and shells, in Handbuch der Physik, Band VIa/2 (Springer, Berlin, 1972) 425-640.
25. E. L. Wilson, R. L. Taylor, W. P. Doherty and J. Ghaboussi, Incompatible Displacement Models, Numerical and Computer Models in Structural Mechanics, eds. S. J. Fenves, N. Perrone, A. R. Robinson and W. C. Schnobrich. New York: Academic Press (1973) 43-57.
26. J. C. Simo, F. Armero and R. L. Taylor, Improved versions of assumed enhanced strain tri-linear elements for 3D finite deformation problems, Comp. Meth. Appl. Mech. Eng. 110 (1993) 359-386.
27. A. E. Green and W. Zerna, Theoretical Elasticity (Oxford University Press, London, 1954).
28. T. J. R. Hughes, The Finite Element Method (Prentice Hall, Englewood Cliffs, NJ, 1987).
29. O. C. Zienkiewicz and R. L. Taylor, The Finite Element Method, Volume 1, Basic Formulation and Linear Problems (McGraw-Hill, London, 1989).
30. C. Miehe, Aspects of the formulation and finite element implementation of large strain isotropic elasticity, Int. J. Num. Meth. Eng. 37 (1994) 1981-2004.
31. J. C. Simo, R. L. Taylor and K. S. Pister, Variational and projection methods for the volume constraint in finite deformation elasto-plasticity, Comp. Meth. Appl. Mech. Eng. 51 (1985) 177-208.
32. R. H. MacNeal and R. L. Harder, A proposed standard set of problems to test finite element accuracy, Finite Elements in Analysis and Design 1 (1985) 3-20.
33. J. C. Simo, D. D. Fox and M. S. Rifai, On a stress resultant geometrically exact shell model. Part II: The linear theory; Computational aspects, Comp. Meth. Appl. Mech. Eng. 73 (1989) 53-92
34. T. J. R. Hughes and E. Carnoy, Nonlinear finite element shell formulation accounting for large membrane strains, Comp. Meth. Appl. Mech. Eng. 39 (1983) 69-82.
35. H. Parisch, Efficient non-linear finite element shell formulation involving large strains, Eng. Comput. 3 (1986) 121-128.
36. K. Schweizerhof and E. Ramm, Displacement dependent pressure loads in nonlinear finite element analyses, Comput. Struct. 18 (1984) 1099-1114.
37. F. Gruttmann and R. L. Taylor, Theory and finite element formulation of rubberlike membrane shells using principal stretches, Int. J. Num. Meth. Eng. 35 (1992) 1111-1126.