Abstract
Continuation and path following methods have been applied to many nonlinear problems in mathematics and physics. There is less widespread application of these methods, however, to structural systems. Since structural buckling and stability problems are primarily concerned with system behavior as a control parameter (most often the load) varies, they are particularly well suited for continuation methods and bifurcation analysis. In this work, the continuation package AUTO is utilized to calculate post-buckled configurations, natural frequencies, and mode shapes of flat plates. Additionally, the continuation analysis identifies bifurcation points and is also adapted to plate configurations that include slight initial imperfections. Finally, the path following methods are also applied to track the unstable snap-through solution and natural frequencies of post-buckled plates subject to a transverse load.
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Acknowledgements
The authors would like to acknowledge the NASA Graduate Student Researchers Program (GSRP) grant NNX09AJ17H and the Air Force Office of Scientific Research grant FA9550-09-1-0204 for support.
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© 2012 The Society for Experimental Mechanics, Inc. 2012
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Lyman, T.C., Virgin, L.N., Davis, R.B. (2012). Application of Continuation Methods to Nonlinear Post-buckled Structures. In: Adams, D., Kerschen, G., Carrella, A. (eds) Topics in Nonlinear Dynamics, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-2416-1_20
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DOI: https://doi.org/10.1007/978-1-4614-2416-1_20
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