English

Limit point buckling of a finite beam on a nonlinear foundation

Classical Physics 2021-01-29 v1

Abstract

In this paper, we consider an imperfect finite beam lying on a nonlinear foundation, whose dimensionless stiffness is reduced from 11 to kk 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 kk 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

Keywords

Cite

@article{arxiv.2101.12125,
  title  = {Limit point buckling of a finite beam on a nonlinear foundation},
  author = {Romain Lagrange},
  journal= {arXiv preprint arXiv:2101.12125},
  year   = {2021}
}