On a geometrically exact curved/twisted beam theory under rigid cross-section assumption

Computational Mechanics

Volumn 30, Issue 5-6, 2003, Pages 428-443

  Kapania, R K ^a   Li, J ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

Curved beam element; Curved beam theory; Finite rotation; Finite strain; Geometrically exact; Orthonormal frame; Rigid cross section

Indexed keywords

ELASTICITY; EQUATIONS OF MOTION; FINITE ELEMENT METHOD; STRAIN; STRESSES;

CURVED BEAM ELEMENT; CURVED BEAM THEORY; FINITE ROTATION; FINITE STRAIN; ORTHONORMAL FRAME; PIOLA-KIRCHHOFF STRESSES; RIGID CROSS SECTION;

BEAMS AND GIRDERS;

EID: 0038157324     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-003-0421-8     Document Type: Article

References (24)

1. Argyris J (1982) An excursion into large rotations. Comput. Meth. Appl. Mech. Eng. 49: 85-155
2. Atluri SN, Cazzani A (1995) Rotations in computational solid mechanics. Arch. Comput. Meth. Eng. 2(1): 49-138
3. Cardona A, Geradin M (1988) A beam finite element non-linear theory with finite rotations. Int. J. Numer. Meth. Eng. 26: 2403-2438
4. Franchi CG, Montelaghi F (1996) A weak-weak formulation for large displacements beam statics: a finite volumes approximation. Int. J. Numer. Meth. Eng. 39: 585-604
5. Ibrahimbegović A (1995) On finite element implementation of geometrically nonlinear Reissner's beam theory: three dimensional curved beam elements. Comput. Meth. Appl. Mech. Eng. 122: 11-26
6. Ibrahimbegović A, Frey F (1994) Stress resultant geometrically nonlinear shell theory with drilling rotations - Part II. Computational aspects. Comput. Meth. Appl. Mech. Eng. 118: 285-308
7. Ibrahimbegović A, Frey F, Kožar I (1995) Computational aspects of vector-like parametrization of three-dimensional finite rotations. Int. J. Numer. Meth. Eng. 38: 3653-3673
8. Iura M, Atluri SN(1988) Dynamic analysis of finitely stretched and rotated three-dimensional space-curved beams. Comput. Struct. 29: 875-889
9. Iura M, Atluri, SN (1989) On a consistent theory, and variational formulation of finitely stretched and rotated 3-D space-curved beams. Comput. Mech. 4: 73-88
10. Jelenićc G, Saje M (1995) A kinematically exact space finite strain beam model - finite element formulation by generalized virtual work principle. Comput. Meth. Appl. Mech. Eng. 120: 131-161
11. Kapania RK, Li J (1998) A Four-Noded 3-D geometrically non-linear curved beam element with large displacements/rotations. In: Modeling and Simulation Based Engineering, Atluri SN, O'Donoghue PE (eds), Technology Science Press, pp. 679-684
12. Li J, Kapania RK (2000) A geometrically exact curved beam theory and its finite element formulation/implementation, VPI-AOE-269, Report Submitted to the Army Research Office, Aerospace Engineering, Blacksberg, VA, 2001
13. Ogden RW (1997) Non-linear Elastic Deformations, Dover Publications, Inc., New York
14. Pimenta PM (1996) Geometrically exact analysis of Initially Curved Rods. In: Advances in Computational Techniques for Structural Engineering, Edinburgh, UK vol. 1, pp. 99-108
15. Pimenta PM, Yojo J (1993) Geometrically-exact analysis of spatial frames. Appl. Mech. Rev. ASME 46(11): 118-128
16. Reissner E (1972) On one-dimensional finite-strain beam theory: the plane problem. J. Appl. Math. Phys. 23: 795-804
17. Reissner E (1973) On one-dimensional large displacement finite beam theory. Stud. Appl. Mech. 52: 87-95
18. Reissner E (1981) On finite deformations of space curved beams. J. Appl. Math. Phys. 32: 734-744
19. Saje M (1991) Finite element formulation of finite planar deformation of curved elastic beams. Comput. Struct. 19: 327-337
20. Sandhu JS, Stevens KA, Davies GAO (1990) A 3-D, co-rotational, curved and twisted beam element. Comput. Struct. 35: 69-79
21. Simo JC (1985) A finite strain beam formulation: the three-dimensional dynamics. Part I. Comput. Meth. Appl. Mech. Eng. 49: 55-70
22. Simo JC, Tarnow, N, Doblare M (1995) Non-linear dynamics of three-dimensional rods: exact energy and momentum conserving algorithms. Int. J. Numer. Meth. Eng. 38: 1431-1473
23. Simo JC, Vu-Quoc L (1986) A three dimensional finite-strain rod model. Part II: computational aspects.Comput. Meth. Appl. Mech. Eng. 58: 79-116
24. Simo JC, Vu-Quoc L (1991) A geometrically-exact rod model incorporating shear and torsion-warping deformation. Int. J. Solids Struct. 27: 371-393