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Computer Methods in Applied Mechanics and Engineering, 1997
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Analysis of post‐buckling branches at multiple symmetric bifurcations
International Journal for Numerical Methods in Engineering, 2001AbstractA method to analyse and solve symmetric bifurcations by establishing the bifurcation equations using an asymptotic expansion method is presented. The bifurcation equations are obtained using a decomposition of the spaces by means of the theory of Lyapunov–Schmidt. To solve the bifurcation equations an asymptotic expansion method along the lines
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Bifurcation theory applied to buckling states of a cylindrical shell
ZAMP Zeitschrift f�r angewandte Mathematik und Physik, 1995Inextensible elastic tubes are subjected to a uniform external pressure. Their stability is analysed on the basis of the Lyapunov-Schmidt decomposition and the bifurcation theorem of simple multiplicity. Nontrivial solutions have been found for the critical values of pressure.
J. Chaskalovic, S. Naili
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Periodic Motions and Bifurcation Trees in a Buckled, Nonlinear Jeffcott Rotor System
International Journal of Bifurcation and Chaos, 2015In this paper, analytical solutions for period-m motions in a buckled, nonlinear Jeffcott rotor system are obtained. This nonlinear Jeffcott rotor system with two-degrees of freedom is excited periodically from the rotor eccentricity. The analytical solutions of period-m solutions are developed, and the corresponding stability and bifurcation are also
Jianzhe Huang, Albert C. J. Luo
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Bifurcation Criterion and Plastic Buckling of Plates and Columns
Journal of the Aeronautical Sciences, 1950If a bifurcation of equilibrium paths occurs as the loading is varied on a conservative system, the preferred path is usually obtained by use of a stability criterion. However, even if the definition of stability is modified so as no longer to depend on the existence of a potential energy function, a stability criterion may not be useful if the system ...
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Response Variability of Structures Subjected to Bifurcation Buckling
Journal of Engineering Mechanics, 1992The paper presents a new analytical method for the investigation of the response variability of structures subjected to bifurcation buckling. The method is applied to the buckling of the axialy compressed thin cylindrical shell. The study demonstrates the conceptual simplicity of the method, its numerical efficiency, and its capability to account for ...
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Stability, Bifurcation and Postbuckling Analysis
1998Liapunov theory is first presented and discrete mechanical systems are in particular analysed. Then buckling and postbuckling analysis of continuous mechanical systems due to Koiter are discussed in some detail following Budiansky presentation. Finally, the influence of multiple interactive buckling modes on postbuckling behaviour is analysed in some ...
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An Introduction to Compound and Coupled Buckling and Dynamic Bifurcations
1998This Part I is a general introduction to the subject matter of the Volume, spanning over some of the main « theoretical aspects ».
G. Augusti, V. Sepe, A. Paolone
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