Multiplicative updating of the rotation tensor in the finite element analysis of rods and shells - A path independent approach

Computational Mechanics

Volumn 31, Issue 1-2 SPEC., 2003, Pages 153-162

  Sansour, C ^a   Wagner, W ^b  

^a UNIVERSITY OF ADELAIDE   (Australia)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Finite elements; Multiplicative updating; Path independency; Rods; Rotation group; Shells

Indexed keywords

FINITE ELEMENT METHOD; INTERPOLATION; NUMERICAL METHODS; SHELLS (STRUCTURES); TENSORS;

RODS; ROTATION TENSOR;

COMPUTATIONAL FLUID DYNAMICS;

EID: 0037818736     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-002-0401-4     Document Type: Article

References (26)

1. Antman SS (1995) Nonlinear problems of elasticity, Springer, Berlin Heidelberg New York
2. Başar Y, Ding Y (1992) Finite rotation shell elements for the analysis of finite-rotation shell problems. Int. J. Numer. Meth. Eng. 34: 165-169
3. Borri M, Bottasso CL (1994) An intrinsic beam model based on a helicoidal approximation- Part II: linearization and finite element implementation, Int. J. Numer. Meth. Eng. 37: 2291-2309
4. Cardona A, Geradin M (1988) A beam finite element non-linear theory with finite rotations. Int. J. Numer. Meth. Eng. 26: 2403-2438
5. Choquet-Bruhat Y, DeWitt-Merette C, Dillard-Bleick M (1982) Analysis, Manifolds and Physics Part I. North-Holland, Amsterdam
6. Cohen H, DeSilva KN (1966) Nonlinear theory of elastic directed surfaces. J. Math. Phys. 7: 960
7. Dubrovin BA, Fomenko AT, and Novikov SP (1984) Modern Geometry-Methods and Applications I. Springer-Verlag, New York
8. Ericksen JL, Truesdell C (1957) Exact theory of stress and strain in rods and shells. Arch. Rat. Mech. Anal. 1: 295-323
9. Eringen AC, Kafadar CB (1976) Polar field theories. In: Continuum Physics IV, Eringen AC (ed.) Academic Press, New York, pp. 1-73
10. Green AE, Naghdi PM, Wainwright WL (1965) A general theory of a Cosserat surface. Arch. Rat. Mech. Anal. 20: 287-308
11. Gruttmann F, Sauer R, Wagner W (1998) A geometrical non-linear eccentric 3d-beam element with arbitrary cross-sections. Comput. Meth. Appl. Mech. Eng. 160: 383-400
12. Hestens D (1986) New foundations for classical mechanics, Reidel, Dordrecht
13. Hjalmars S (1982) Non-linear micropolar theory. In: Mechanics of Micropolar Media, Brulin O, Hsieh RKT (eds).l World Scientific, Singapore, pp. 147-185
14. Ibrahimbegovic A (1995) On finite element implementation of geometrically nonlinear Resissner's beam theory: three-dimensional curved beam elements. Comput. Meths. Appl. Mech. Eng. 122: 11-26
15. Jelenic G, Crisfield MA (1999) Geometrically exact 3D beam theory: implementation of a strain-invariant finite element for static and dynamics. Comput. Meths. Appl. Mech. Eng. 171: 141-171
16. Libai A, Simmonds JG (1983) Nonlinear elastic shell theory. In: Advances in Applied Mechanics, Hutchinson, Wu (eds) 23, Academic Press, New York, pp. 271-371
17. McRobie FA, Lasenby J (1999) Simo-Vu Quoc rods using Clifford Algebra. Int. J. Numer. Meth. Eng. 45: 337-398
18. Naghdi PM (1972) The theory of shells, In: Handbuch der Physik VI/2 Flügge S (ed) Springer, Berlin Heidelberg New York
19. Reissner E (1981) On finite deformations of space-curved beams. J. Appl. Math. Phys. (ZAMP) 35: 734-377
20. Rubin MB (2000) Cosserat theories: Shells, rods and points. Kluwer, Dordrecht
21. Sansour C, Bednarczyk H (1995) The Cosserat surface as a shell model, theory and finite-element formulation. Comput. Meths. Appl. Mech. Eng. 120: 1-32
22. Sansour C, Bufler H (1992) An exact finite rotation shell theory, its mixed variational formulation, and its finite element implementation. Int. J. Numer. Meth. Eng. 34: 73-115
23. Simo JC, Fox DD (1989) On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization, Comput. Meths. Appl. Mech. Eng. 72: 267-304
24. Simo JC, Vu-Quoc L (1986) A three-dimensional finite-strain rod model. Part II: Geometric and computational aspects. Comput. Meths. Appl. Mech. Eng. 58: 79-116
25. Simo JC, Tarnow N, Doblare M (1995) Non-linear dynamics of three-dimensional rods: exact energy and momentum conservation algorithms. Int. J. Numer. Meth. Eng. 38: 1431-1473
26. Trindade M, Sampaio R (2002) Dynamics of beams undergoing large rotations accounting for arbitrary axial deformation. Journal of Guidance, Control, and Dynamics 25: 634-643