Finite element solution of the stability problem for nonlinear undamped and damped systems under nonconservative loading

International Journal of Solids and Structures

Volumn 34, Issue 19, 1997, Pages 2497-2516

  Vitaliani, Renato V ^a   Gasparini, Alessandro M ^a   Saetta, Anna V ^b  

^a UNIVERSITY OF PADOVA   (Italy)

^b Dipto di Costruzione dell'Archit   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; DAMPING; EIGENVALUES AND EIGENFUNCTIONS; ELASTICITY; FINITE ELEMENT METHOD; STIFFNESS; STRUCTURAL ANALYSIS;

ELASTIC STRUCTURES;

BEAMS AND GIRDERS;

EID: 0031188562     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(96)00115-1     Document Type: Article

References (27)

1. Alliney, S. and Tralli, A. (1984). Extended variational formulations and F.E. models for nonlinear beams under nonconservative loading. Computers and Methods in Applied Mechanical Engineering 46, 177-194.
2. Argyris, J. H., Straub, K. and Symeondis, S. (1982). Static and dynamic stability of nonlinear elastic systems under nonconservative forces. Natural approach. Computers and Methods in Applied Mechanical Engineering 32, 59-83.
3. Argyris, J. H. and Symeondis, S. (1981a). A sequel to: nonlinear finite element analysis of elastic systems under nonconservative loading. Natural formulation. Part I Quasistatic problem. Computers and Methods in Applied Mechanical Engineering 26, 377-383.
4. Argyris, J. H. and Symeondis, S. (1981b). Nonlinear finite element analysis of elastic systems under non-conservative loading. Natural formulation. Part I Quasistatic problem. Computers and Methods in Applied Mechanical Engineering 26, 75-123.
5. Bathe, K. J. (1982) Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey.
6. Bolotin, V. V. (1965). Nonconservative Problems of the Theory of Elastic Stability, Pergamon Press, London.
7. Bolotin, V. V. and Zhinzher, N.I. (1969). Effects of damping on stability of elastic system subjected to non-conservative forces. International Journal of Solids and Structures 5, 965-989.
8. Bratus, A. S. (1993). On various cases of instability for elastic nonconservative systems with damping. International Journal of Solids and Structures 30, 3431-3441.
9. El Naschie, M. S. (1990). Stress, Stability and Chaos in Structural Engineering. An Energy Approach, McGraw-Hill, NY.
10. Gasparini, A. M., Saetta, A. V. and Vitaliani, R. V. (1995). On the stability and instability regions of non-conservative continuous system under partially follower forces. Computers and Methods in Applied Mechanical Engineering 124, 63-78.
11. NAFEMS (1990). A Review of Benchmark Problems for Geometric Nonlinear Behaviour of 3D Beams and Shells, Knowles, N. C.
12. Kounadis, A. N. (1991). Some new instability aspects for nonconservative systems under follower loads. International Journal of Mechanical Science 33, 297-311.
13. Kounadis, A. N. (1992). On the paradox of the destabilizing effect of damping in nonconservative systems. International Journal of Non-Linear Mechanics 27, 597-609.
14. Kounadis, A. N. and Avraam, T. (1993). Global stability analysis of a classical non-conservative system under a follower load. Journal of Sound and Vibration 150, 67-82.
15. Kounadis, A. N. and Smitses, G. J. (1993). Local (classical) and global bifurcations in non-linear, non-gradient autonomous dissipative structural systems. Journal of Sound and Vibration, 160, 417-432.
16. Kounadis, A. N. (1994). On the failure of static stability analyses of nonconservative systems in regions of divergence instability. International Journal of Solids and Structures 31, 2099-2120.
17. Krätzig, W. B., Li, L. Y. and Nawrotzki, P. (1991). Stability conditions for non-conservative dynamical systems. Computational Mechanics 8, 145-151.
18. Krätzig, W. B. (1993). Computational Concepts for Kinetic Instability Problems, Corso CISM, Udine, Italy.
19. ○ isoparametric skew beam element. Computers and Structures 29, 437-449.
20. Simo, J. C. and Vu-Quoc, L. (1986). Three-dimensional finite-strain rod model. Part II: computational approach. Computers and Methods of Applied Mechanical Engineering X, 79-116.
21. Simo, J. C. and Vu-Quoc, L. (1988). On the dynamics in space of rods undergoing large motions - a geometrically exact approach. Computers and Methods of Applied Mechanical Engineering X, 125-161.
22. Simo, J. C. and Vu-Quoc, L. (1991). A geometrically exact rod model incorporating shear and torsion-warping deformation. International Journal of Solids and Structures, 27, 371-393.
23. Surana, K. S and Sorem, R. M. (1989). Geometrically nonlinear formulation for three dimensional curved beam elements with large rotations. International Journal of Numerical Methods in Engineering 28, 43-73.
24. Thomsen, J. J. (1993). Chaotic dynamics of the partially follower-loaded elastic double-pendulum, Report no. 455. Technical University of Denmark.
25. Vaccaro, G. (1968). Lezioni di Geometria, vol. 2, Libreria Eredi Virgilio Veschi, Rome.
26. Ziegler, H. (1968). Principles of Structural Stability, Blaisdell Publ. Co, Toronto.
27. Zienkiewicz, O. C. and Taylor, R. L. (1989). The Finite Element Method, fourth edition, vol. 1.