Topics in Nonlinear Dynamics, Volume 3

Part of the series Conference Proceedings of the Society for Experimental Mechanics Series pp 245-254


Application of Continuation Methods to Nonlinear Post-buckled Structures

  • T. C. LymanAffiliated withDepartment of Mechanical Engineering and Materials Science, Duke University Email author 
  • , L. N. VirginAffiliated withDepartment of Mechanical Engineering and Materials Science, Duke University
  • , R. B. DavisAffiliated withNASA Marshall Space Flight Center

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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.


Buckling Post-buckling Continuation Nonlinear Snap through