# Computational Stability Theory — Its Strategy

• F. Fujii
• S. Okazawa
• S.-X. Gong
Conference paper

## Abstract

The general stability theory developed by Koiter [1], Thompson/Hunt [2] well applies in the theoretical buckling analysis. The mathematical stability theory seems however not always feasible in computational practice. More specifically, use of the higher-order derivatives of the equilibrium equations, for example, is not realistic in existing finite element codes. The computational stability theory will challenge to stability problems from the more practical and computational viewpoint. The present paper describes the fundamental strategies, path-tracing, pinpointing and path-switching [3,4,5,6,7,8,9], in the computational stability theory.

## Keywords

Bifurcation Point Line Search Stability Point Equilibrium Path Primary Path
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. [1]
Koiter, W.T.(1945) On the stability of elastic equilibrium. Thesis, Polytechnic Institute, Delft H.T., Paris, AmsterdamGoogle Scholar
2. [2]
Thompson, J.M.T. and Hunt, G.W. (1973) A general theory of elastic stability, John Wiley & Sons, London, 1973
3. [3]
Ramm, E. (1981), Strategies for tracing the non-linear response near limit points, in “Nonlinear Finite Element Analysis in Structural Mechanics”, edited by Wunderlich, W., Springer-Verlag, Berlin, 63–89
4. [4]
Wriggers, P., Wagner, W. and Miehe, C.,(1988), A Quadratically Convergent Procedure for the Calculation of Stability Points, Computer Methods in Applied Mechanics and Engineering, 70, 329–347Google Scholar
5. [5]
Chan, S. L. (1988), Geometric and material Nonlinear Analysis of Beam-Columns and Frames using the Minimum Residual Displacement Method, Int. J. for Numerical Methods in Engineering, 26, 2657–2669
6. [6]
Fujii, F. (1994), Bifurcation and Path-Switching in Nonlinear Elasticity, Invited Lecture, 3rd WCCM, 1–5 August, JapanGoogle Scholar
7. [7]
Fujii, F. and Choong, K.K. (1992) Branch-switching in Bifurcation of Structures. EM, ASCE, Vol. 118, No. 8, 1578–1595
8. [8]
Fujii, F. and Asada, K. (1993) Branch-switching in simple spatial bifurcation models. SEIKEN-IASS Symposium on Nonlinear Analysis and Design for Shells and Spatial Structures, 515–522, TokyoGoogle Scholar
9. [9]
Fujii, F. and Okazawa, S. (1994), Multi-Bifurcation Models in Nonlinear Elasticity, Vol. II, 583–588, Proceedings of the Int. Conf. on Computational Methods in Structural and Geotechnical Engineering, Hong KongGoogle Scholar
10. [10]
Chatelin, F., Valeurs propres de Matrices, Masson, Paris, 1988

## Authors and Affiliations

• F. Fujii
• 1
• S. Okazawa
• 2
• S.-X. Gong
• 3
1. 1.Gifu UniversityGifuJapan
2. 2.Nagoya UniversityNagoyaJapan