On the role of geometrically exact and second-order theories in buckling and post-buckling analysis of three-dimensional beam structures

Computers and Structures

Volumn 61, Issue 6, 1996, Pages 1101-1114

  Ibrahimbegovic A ^a   Shakourzadeh, H ^a   Batoz, J L ^a   Al Mikdad, M ^a   Guo, Ying Qiao ^a  

^a UNIVERSITÉ DE TECHNOLOGIE DE COMPIÈGNE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BEAMS AND GIRDERS; BUCKLING; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; LOADS (FORCES); MATHEMATICAL MODELS; MATRIX ALGEBRA; PERFORMANCE; ROTATION; THREE DIMENSIONAL; VECTORS;

BEAM MODELS; BUCKLING ANALYSIS; DISPLACEMENT; EXACT BEAM THEORY; NEWTON METHOD BASED CONTINUATION STRATEGY;

STRUCTURAL ANALYSIS;

EID: 0030379932     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/0045-7949(96)00181-2     Document Type: Article

References (36)

1. J. H. Argyris, An excursion into large rotations. Comput. Meth. appl. Mech. Engng 32, 85-155 (1982).
2. J. H. Argyris, H. Balmer, J. St. Doltsinis, P. C. Dunne, M. Haase, M. Kleiber, G. A. Malejannakis, H. P. Mlejnek and D. W. Scharpf, Finite element method - the natural approach. Comput. Meth. appl. Mech. Engng 17/18, 1-106 (1979).
3. T. Belytschko and B. J. Hsieh, Non-linear finite element analysis with convected coordinates. Int. J. numer. Meth. Engng 7, 255-271 (1973).
4. M. A. Crisfield, A consistent co-rotational formulation for non-linear, three-dimesional beam elements. Comput. Meth. appl. Mech. Engng 81, 131-150 (1990).
5. B. Nour-Omid and C. C. Rankin, Finite rotation analysis and consistent linearization using projectors. Comput. Meth. appl. Mech. Engng 93, 353-384 (1991).
6. K. J. Bathe and S. Bolourchi, Large displacement analysis of three-dimensional beam structures. Int. J. numer. Meth. Engng 14, 961-986 (1979).
7. Ph. Jetteur, S. Cescotto, V. de Ville de Goyet and F. Frey, Improved nonlinear finite elements for oriented bodies using an extension of Marguerre's theory. Comput. Struct. 17, 129-137 (1983).
8. J. C. Simo, The (symmetric) Hessian for geometrically nonlinear models in solid mechanics: intrinsic definition and geometric interpretation. Comp. Meth. appl. Mech. Engng 96, 189-200 (1992).
9. J. C. Simo and L. Vu-Quoc, A three-dimensional finite-strain rod model. Part II: computational aspects. Comp. Meth. appl. Mech. Engng 58, 79-116 (1986).
10. E. Reissner, On finite deformations of space curved beams. J. appl. Math. Phys. 32, 734-744 (1981).
11. E. Reissner, Lateral buckling of beams. Comput. Struct. 33, 1289-1306 (1989).
12. A. Ibrahimbegović, On FE implementation of geometrically nonlinear Reissner's beam theory: three-dimensional curved beam elements. Comput. Meth. appl. Mech. Engng 122, 11-26 (1995).
13. A. Cardona and M. Geradin, A beam finite element non-linear theory with finite rotations. Int. J. numer. Meth. Engng 26, 2403-2438 (1988).
14. M. Iura and S. N. Atluri, On a consistent theory, and variational formulation of finitely stretched and rotated 3d space-curved beams. Comput. Mech. 4, 73-88 (1989).
15. A. Ibrahimbegović, F. Frey and I. Kožar, Computational aspects of vector-like parameterization of three-dimensional finite rotations. Int. J. numer. Meth. Engng 38, 3653-3573 (1995).
16. J. L. Batoz and G. Dhatt, Modélisation des structures par éléments finis, I. Solides élastiques, II, Poutres et plaques, III. Coques. Hermes, Paris (1990).
17. W. T. Koiter, On the stability of elastic equilibrium. NASA Report TT-F10.833 (1945).
18. S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability. McGraw-Hill, Maidenhead (1961).
19. B. Budiansky, Theory of buckling and post-buckling behavior of elastic structures. Adv. appl. Mech. 14, 1-65 (1974).
20. H. Ziegler, Principles of Structural Stability. Birkhauser, Basel (1977).
21. T. J. R. Hughes and K. S. Pister, Consistent linearization in mechanics of solids and structures. Comput. Struct. 8, 391-397 (1978).
22. F. Frey and S. Cescotto, Some new aspects of the incremental total Lagrangian description in nonlinear analysis. In: Finite Elements in Nonlinear Mechanics (Edited by P. G. Bergan et al.), pp. 323-343. Tapir, Trondheim (1978).
23. J. E. Marsden and T. J. R. Hughes, Mathematical Foundations of Elasticity, p. 272. Prentice-Hall, Englewoods Cliffs, NJ (1983).
24. E. Riks, An incremental approach to the solution of snapping and buckling problems. Int. J. Solids Struct. 15, 529-551 (1979).
25. W. Rheinboldt, Numerical analysis of continuation methods for nonlinear structural problems. Comput. Struct. 13, 103-113 (1981).
26. S. Yaghmai and E. Popov, Incremental analysis of large deflections of shells of revolution. Int. J. Solids Struct. 7, 1375-1393 (1971).
27. K. J. Bathe, E. Ramm and E. L. Wilson, Finite element formulation for large deformation dynamic analysis. Int. J. numer. Meth. Engng 9, 353-386 (1975).
28. Y. Q. Guo and J. L. Batoz, Displacement fields and large deformation analysis of three-dimensional beams. In: Proc. Shell and Spatial Structures. Computational Aspects (Edited by G. De Roech and M. Van Laethem). Springer, Berlin (1986).
29. Y. Q. Guo, Analyse non linéaire statique et dynamique des poutres tridimensionnelles élasto-plastiques. Doctoral thesis, University of Compiègne, Compiègne (1987).
30. H. Shakourzadeh, Y. Q. Guo, J. L. Batoz and P. Penserini, Modélisation du comportement non linéaire des structures formées des poutres 3D. In: Proc. French National Congress on Structures, Giens (1993).
31. H. Shakourzadeh, Modélisation des structures-poutres tridimensionnelles àparois minces et simulation du comportement non linéaire géométrique et élasto-plastique. Doctoral thesis, University of Compiègne, Compiègne (1994).
32. A. Eriksson, On linear constraints for Newton-Raphson corrections and critical point searches in structural FE problems. Int. J. numer. Meth. Engng 28, 1317-1334 (1989).
33. D. H. Hodges and D. A. Peters, On the lateral buckling of uniform slender cantilever beams. Int. J. Solids Struct. 11, 1269-1280 (1975).
34. H. Lee, D. W. Jung, J. H. Jeong and S. Im, Finite element analysis of lateral buckling of beams. Comput. Struct. 53, 1357-1371 (1994).
35. D. A. DaDeppo and R. Schmidt, Instability of clamped-hinged circular arches subjected to a point load. J. appl. Mech. 97, 894-896 (1975).
36. A. Ibrahimbegović and F. Frey, Finite element analysis of linear and nonlinear planar deformation of elastic initially curved beams. Int. J. numer. Meth. Engng 36, 3239-3258 (1993).