Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-07T02:08:04.606Z Has data issue: false hasContentIssue false
  • English
  • Français

On the general theory of the stability of equilibrium of discrete conservative systems

Published online by Cambridge University Press:  04 July 2016

D. J. Allman
D. J. Allman*
Affiliation:
Royal Aerospace Establishment, Farnborough
Get access Rights & Permissions [Opens in a new window]

Summary

The general theory of the stability of equilibrium of discrete conservative systems is reviewed with an eye to implementation in finite element structural analysis. The approach features a natural parameter, such as the applied loading of a system, as the independent variable; all results are thus conveniently established without recourse to any of the artificial parameters advocated by some earlier authors. The criteria for identifying singular (critical) points, which include bifurcation points and limit points, and determining their stability are obtained in simple forms suitable for computation. Numerical results are given for an example problem characteristic of a loaded plate with multiple, stable and unstable, bifurcation points to demonstrate an application of the theory.

Type
Research Article
Information
The Aeronautical Journal , Volume 93 , Issue 921 , January 1989 , pp. 29 - 35
Copyright
Copyright © Royal Aeronautical Society 1989 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Koiter, W. T. Over de Stabiliteit van het Elastisch Evenwicht, Amsterdam: H. J. Paris, 1945.Google Scholar
2. Koiter, W. T. NASA TT F-10833, 1967.Google Scholar
3. Thompson, J. M. T. J Mech Phys Solids, 1963, 11, 13–20.Google Scholar
4. Thompson, J. M. T. J Mech Phys Solids, 1965, 13, 295–310.Google Scholar
5. Sewell, M. J. Proc R Soc A, 1968, 306, 201–223.Google Scholar
6. Sewell, M. J. Proc R Soc A, 1968, 306, 225–238.Google Scholar
7. Thompson, J. M. T. and Hunt, G. W. A General Theory of Elastic Stability, London: John Wiley, 1973.Google Scholar
8. Haftka, R. T., Mallett, R. H. and Nachbar, W. Int J Solids Struct, 1971, 7, 1427–1445.Google Scholar
9. Ortega, J. M. and Rheinboldt, W. C. Iterative Solution of Nonlinear Equations in Several Variables, New York: Academic Press, 1970.Google Scholar
10. Rheinboldt, W. C. and Riks, E. ASME. State-of-the-Art Surveys on Finite Element Technology., (Noor, A. K. and Pilkey, W. D. (Eds)), 1983.Google Scholar
11. Riks, E. ASME. Winter Annual Meeting. Symposium on Innovative Methods for Nonlinear Problems, New Orleans, 1984.Google Scholar
12. Smirnov, V. I. A Course of Higher Mathematics, Vol I, Oxford: Pergamon Press, 1964.Google Scholar
13. Allman, D. J. RAE Technical Report 86053, 1986.Google Scholar