Finite element theory for curved and twisted beams based on exact solutions for three-dimensional solids. Part 1: Beam concept and geometrically exact nonlinear formulation

Computer Methods in Applied Mechanics and Engineering

Volumn 165, Issue 1-4, 1998, Pages 43-92

  Petrov, E ^a   Geradin M ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; ELASTICITY; FINITE ELEMENT METHOD; KINEMATICS; MATRIX ALGEBRA; ROTATION; STRUCTURAL ANALYSIS; STRUCTURAL FRAMES; TENSORS;

TRANSLATIONAL DISPLACEMENT;

BEAMS AND GIRDERS;

EID: 0038959155     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(98)00061-9     Document Type: Article

References (33)

1. [1] J.H., Argyris, P.C. Dunne, and D.W. Scharpf, On large displacements-small strain analysis of structures with rotational degrees of freedom, Comput. Methods Appl. Mech Engrg, 14 (1978) 401-451.
2. [2] J.H. Argyris and Sp. Symeonidis, Nonlinear finite element analysis of elastic system under nonconservative loading - natural formulation. Part 1. Quasistatic problems, Comput. Methods Appl. Mech. Engrg. 26 (1981) 75-123.
3. [3] K.-J. Bathe, E. Ramm, and E.L. Wilson, 'Finite element formulations for large deformation dynamic analysis, Int. J. Numer. Methods Engrg. 9 (1975) 353-386.
4. [4] K.-J. Bathe and S. Bolourchi, Large displacement analysis of three-dimensional beam structures, Int. J. Numer. Methods Engrg. 14 (1979) 961-986.
5. [5] M. Borri and C. Botasso, An intrinsic beam model based on a helicoidal approximation - Part 1: Formulation, Int. J. Numer. Methods Engrg. 37 (1994) 2267-2389.
6. [6] A. Cardona and M. Géradin, A beam finite element non-linear theory with finite rotations, Int. J. Numer. Methods Engrg. 26 (1988) 2403-2438.
7. [7] M. Géradin and A. Cardona, Kinematics and dynamics of rigid and flexible mechanisms using finite elements and quaternion algebra, Comput. Mech. 4 (1989) 115-135.
8. [8] M.A. Crisfield, A consistent co-rotational formulation for non-linear, three-dimensional, beam elements, Comput. Methods Appl. Mech. Engrg. 81 (1990) 131-150.
9. [9] L.A. Crivelli and C.A. Felippa, A three-dimensional non-linear Timoshenko beam based on the core-congruential formulation, Int. J. Numer. Methods Engrg. 26 (1993) 3647-3673.
10. [10] E.N. Dvorkin, E. Oñate and J. Oliver, On a non-linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments, Int. J. Numer, Methods Engrg. 26 (1988) 1597-1613.
11. [11] M. Géradin and D. Rixen, Parametrization of finite rotations in computational dynamics: a review, in: Revue Européene des Éléments Finis (1995) 497-553.
12. [12] D.H. Hodges, Torsion of pretwisted beams due to axial loading, Trans. ASME, J. Appl. Mech. 47 (1980) 393-397.
13. [13] D.H. Hodges, Nonlinear flexure and torsion of rotating beams, with application to helicopter rotor blades - 1. Formulation, Vertica 10(2) (1986) 151-169.
14. [14] D.H. Hodges, Nonlinear beam kinematics for small strains and finite rotations, Vertica 11(3) (1987) 573-589.
15. [15] J.T. Holden, On the finite deflections of thin beams, Int. J. Solids Struct. 8 (1972) 1051-1055.
16. [16] J.C. Houbolt and W. Brooks, Differential equations of motion for combined flapwise bending, chordwise bending, and torsion of twisted nonuniform rotor blades, NACA Report 1346, 1958.
17. [17] A. Ibrahimbegovic, F. Frey and I. Kozar, Computational aspects of vector-like parametrization of three-dimensional finite rotations, Int. J. Numer. Methods Engrg. 38 (1995) 3653-3673.
18. [18] M. Iura and S.N. Atluri. On consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams, Comput. Mech. 4 (1989) 73-88.
19. [19] G.U. Janelidze, Kirchhoff's relations for pretwisted beams and their applications, Transactions of Leningrad Politechnic University, No 1 (1946) 23-32 (in Russian).
20. [20] A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity (Cambridge Press, 1952).
21. [21] A.I. Lur'e, Theory of Elasticity, (Nauka, Publisher, Moscow, 1970) (in Russian).
22. [22] B.M. Quadrelli and S.N. Atluri, Primal and mixed variational principles for dynamics of spatial beams, AIAA J. 34(11) (1996) 2395-2401.
23. [23] A.T. Noël and B.A. Szabó, Formulation of geometrically non-linear problems in the spatial reference frame, Int. J. Numer. Methods Engrg. 40 (1997) 1263-1280.
24. [24] D.F. Parker, The role of Saint-Venant's solutions in rod and beam theories, Trans. ASME. J. Appl. Mech. 46 (1977) 861-866.
25. [25] D. Petersen, Interaction of torsion and tension in beam theory, Vertica 6 (1982) 311-325.
26. [26] A. Rosen, Theoretical and experimental investigation of the nonlinear torsion and extension of initially twisted bars, Trans. ASME, J. Appl. Mech. 50 (1983) 321-326.
27. [27] I. Sharf, Geometrically non-linear beam element for dynamic simulation of multibody systems, Int. J. Numer. Methods Engrg. 28 (1996) 763-786.
28. [28] J.C. Simo, A finite strain beam formulation. The three-dimensional dynamic problem. Part 1, Comput. Methods Appl. Mech. Engrg. 49 (1985) 55-70.
29. [29] J.C. Simo and L.Vu-Quoc, A three-dimensional finite-strain rod model. Part 2: Computational aspects, Comput. Methods Appl. Mech. Engrg. 58 (1986) 79-116.
30. [30] J.C. Simo and L. Vu-Quoc, A geometrically-exact rod model incorporating shear and torsion-warping deformation, Int. J. Solids Struct. 27 (1991) 371-393.
31. [31] R.A. Spurrer, Comment on 'Singularity-free extraction of quaternion from a direct-cosine matrix', J. Aircraft 15(4) (1978) 255.
32. [32] K.S. Surana K.S and R.M. Sorem, Geometrically non-linear formulation for three dimensional curved beam elements with large rotations, Int. J. Numer. Methods Engrg. 28 (1989) 43-73.
33. [33] B.F. Shorr, Bending-torsion vibrations of pretwisted compressor blades, Strength Dyn. Aviation Engines 1 (1964) 15-27 (in Russian).