Postbuckling behaviour of beams with discrete nonlinear restraints

Conference item


McCann, F, Wadee, MA, Pearson, J and Gardner, L (2016). Postbuckling behaviour of beams with discrete nonlinear restraints. 7th International Conference on Coupled Instabilities in Metal Structures. Baltimore 07 - 08 Nov 2016 London South Bank University.
AuthorsMcCann, F, Wadee, MA, Pearson, J and Gardner, L
Abstract

A beam with nonlinearly‐elastic lateral restraints attached at discrete points along its span is investigated via analytical and numerical methods. Previous results for the critical moment and the deflected shape based on an eigenvalue analysis of a similar beam with linearly‐elastic restraints are discussed, along with a validation of these results against an equivalent finite element model and results from numerical continuation. A beam with nonlinearly‐elastic restraints is then analysed with treatments for both quadratic and cubic restraint force–displacement relationships being provided. After formulation of the potential energy functionals, the governing differential equations of the system are derived via the calculus of variations and appropriate boundary conditions are applied. The equations are then solved using the numerical continuation software AUTO‐07p for a standard I‐section beam. The variation in elastic critical buckling moment with the linear component of the restraint stiffness is tracked via a two‐parameter numerical continuation, allowing determination of the stiffness values at which the critical buckling modes changes qualitatively. Using these stiffness values, subsequent analyses are conducted to examine the influence of the nonlinear component of the restraint stiffness, from which post‐buckling equilibrium paths and deformation modes are extracted. The results of these analyses are then compared with an equivalent Rayleigh–Ritz formulation whereby the displacement components are represented by Fourier series. Equilibrium equations are derived by minimizing the potential energy functional with respect to the amplitudes of the constituent harmonics of the Fourier series. The amplitudes are solved for in the post‐buckling range by AUTO‐O7p and equilibrium paths are produced and compared to the equivalent solutions of the differential equations, with good agreement observed.

Year2016
PublisherLondon South Bank University
Accepted author manuscript
License
CC BY 4.0
Publication dates
Print07 Nov 2016
Publication process dates
Deposited18 Jul 2017
Accepted30 Jun 2016
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https://openresearch.lsbu.ac.uk/item/871q3

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