The three-dimensional beam theory: Finite element formulation based on curvature

Computers and Structures

Volumn 81, Issue 18-19, 2003, Pages 1875-1888

  Zupan, D ^a   Saje, M ^a  

^a UNIVERSITY OF LJUBLJANA   (Slovenia)

Author keywords

Curvature; Finite element method; Three dimensional beams; Three dimensional rotations

Indexed keywords

DEFORMATION; FINITE ELEMENT METHOD; STRAIN;

THREE-DIMENSIONAL ROTATION;

BEAMS AND GIRDERS;

EID: 0038790302     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7949(03)00208-6     Document Type: Conference Paper

References (24)

1. Argyris J. An excursion into large rotations. Comput. Methods Appl. Mech. Eng. 32:1982;85-155.
2. Atluri S.N., Cazzani A. Rotations in computational solid mechanics. Arch. Comput. Methods Eng. 2:1995;49-138.
3. Cardona A., Géradin M. A beam finite element non-linear theory with finite rotations. Int. J. Numer. Methods Eng. 26:1988;2403-2438.
4. Crisfield M.A. A consistent co-rotational formulation for non-linear, three-dimensional beam elements. Comput. Meth. Appl. Mech. Eng. 81:1990;131-150.
5. Crisfield M.A. Non-linear finite element analysis of solids and structures. Advanced topics. vol. 2:1997;Wiley & Sons, Chichester.
6. Crisfield M.A., Jelenić G. Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation. Proc. Roy. Soc. London A. 455:1999;1125-1147.
7. DaDeppo D.A., Schmidt R. Instability of clamped-hinged circular arches subjected to point load. ASME J. Appl. Mech. 97:1975;894-896.
8. Géradin M., Rixen D. Parametrization of finite rotations in computational dynamics: a review. Revue européenne des éléments finis. 4:1995;497-553.
9. Ibrahimbegovic A. On the finite element implementation of geometrically non-linear Reissner's beam theory: 3d curved beam element. Comput. Methods Appl. Mech. Eng. 122:1995;11-26.
10. Jelenić G., Saje M. A kinematically exact space finite strain beam model - finite element formulation by generalized virtual work principle. Comput. Methods Appl. Mech. Eng. 120:1995;131-161.
11. Li M. The finite deformation theory for beam, plate and shell. Part III. The three-dimensional beam theory and the FE formulation. Comput. Methods Appl. Mech. Eng. 162:1998;287-300.
12. Planinc I., Saje M., Čas B. On the local stability condition in the planar beam finite element. Struct. Eng. Mech. 12:2001;507-526.
13. Planinc I., Bratina S., Saje F., Saje M. A kinematically exact FE formulation of planar reinforced concrete frames based on pseudocurvature. ZAMM (J. Appl. Math. Mech.). 81:2001;881-882.
14. Reissner E. On finite deformation of space-curved beams. J. Appl. Math. Phys. 32:1981;734-744.
15. Saje M., Turk G., Kalagasidu A., Vratanar B. A kinematically exact finite element formulation of elastic-plastic curved beams. Comput. Struct. 67:1998;197-214.
16. Shabana A.A. Dynamics of multibody systems. 2nd ed. 1998;Cambridge University Press, London.
17. Simo J.C. A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Comput. Methods Appl. Mech. Eng. 49:1985;55-70.
18. Simo J.C., Vu-Quoc L. A three-dimensional finite-strain rod model. Part II: Computational aspects. Comput. Methods Appl. Mech. Eng. 58:1986;79-116.
19. Smoleński W.M. Statically and kinematically exact nonlinear theory of rods and its numerical verification. Comput. Methods Appl. Mech. Eng. 178:1999;89-113.
20. Spurrier R.A. Comment on "Singularity-free extraction of a quaternion from a direction-cosine matrix" J. Spacecraft. 15:1978;255.
21. Tabarrok B., Farshad M., Yi H. Finite element formulation of spatially curved and twisted rods. Comput. Methods Appl. Mech. Eng. 70:1988;275-299.
22. Timoshenko S.P., Gere J.M. Theory of elastic stability. 1961;McGraw-Hill, New York.
23. Troutman J.L. Variational calculus with elementary convexity. 1983;Springer-Verlag, New York.
24. Vratanar B., Saje M. A consistent equilibrium in a cross-section of an elastic-plastic beam. Int. J. Solids Struct. 36:1999;311-337.