Authors: Rehlicki, Lidija
Janev, Marko 
Novaković, Branislava
Atanacković, Teodor
Title: On Post-Critical Behavior of a Beam on an Elastic Foundation
Journal: International Journal of Structural Stability and Dynamics
Volume: 18
Issue: 6
Issue Date: 1-Jun-2018
Rank: M21
ISSN: 0219-4554
DOI: 10.1142/S0219455418500827
In this paper, we analyze the nonlinear equilibrium equation corresponding to the two-parameter bifurcation problem arising in the stability analysis of an elastic simply supported beam on the Winkler type elastic foundation for the case when bimodal buckling occurs. We perform the bifurcation analysis of the nonlinear problem, by using Lyapunov-Schmidt reduction, thus obtaining the number of the nontrivial solutions to the nonlinear problem and qualitatively characterizing the solution patterns. We also give the formulation of the problem and bifurcation analysis from the total energy viewpoint and determine the energy of each bifurcating solution. We assert that the solution with the smallest energy is the one that will be observed in the post-critical state. For specific choice of parameters, the bifurcating solution in the form of the second buckling mode has the smallest total energy. The numerical results illustrating the theory are also provided.
Keywords: Lyapunov-Schmidt reduction | Simply supported beam | two-parameter bifurcation problem | Winkler foundation
Publisher: World Scientific
Project: Viscoelasticity of fractional type and shape optimization in a theory of rods 
Methods of Functional and Harmonic Analysis and PDE with Singularities 
Provincial Secretariat for Science, Grant 114-451-2098

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