Limit point buckling of a finite beam on a nonlinear foundation

Romain Lagrange

doi:10.1063/2.1403101

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arXiv · 2101.12125

Limit point buckling of a finite beam on a nonlinear foundation

Romain Lagrange

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Abstract

In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from $1$ to $k$ as the beam deflection increases. Periodic equilibrium solutions are found analytically and are in good agreement with a numerical resolution, suggesting that localized buckling does not appear for a finite beam. The equilibrium paths may exhibit a limit point whose existence is related to the imperfection size and the stiffness parameter $k$ through an explicit condition. The limit point decreases with the imperfection size while it increases with the stiffness parameter. We show that the decay/growth rate is sensitive to the restoring force model. The analytical results on the limit load may be of particular interest for engineers in structural mechanics

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Romain Lagrange. 2021-01-28. Limit point buckling of a finite beam on a nonlinear foundation. https://doi.org/10.1063/2.1403101

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