Download Keynote Lecture, CFRAC, Barcelona, June 6, 2011

2013 Conference of the ASCE Engineering Mechanics Institute, August 4 – 7, 2013
Northwestern University, Evanston, IL
Analytical modelling of cellular buckling in stiffened plates
M. Ahmer Wadeea* and Maryam Farsia
a
Imperial College London, London, UK
* corresponding author: [email protected]
Abstract:
An analytical model that describes the behaviour of a structural component, which is known to
suffer from interactive buckling, is presented. In certain circumstances, the results from
numerical modelling (e.g. from the finite element method) of structural components that exhibit
complex instability phenomena can obscure the underlying mechanics. Typical features that may
be lost include symmetry breaking from modal interactions, the localization of post-buckling
modes and progressive cellular buckling. The mathematical model in the current work,
formulated using variational principles, is used to describe the behaviour of thin-walled stiffened
plates under compression where global and local buckling modes interact.
Modal descriptions using the Rayleigh–Ritz method are combined with continuous displacement
functions and Timoshenko beam theory to formulate total potential energy. The energy is
minimized and results in the description of equilibrium states by means of a system of
differential and integral equations. For the stiffened plate components, the interaction is between
overall flexural (Euler) buckling about the weak axis in combination with the local buckling of
the stiffener. The cases where either global buckling is critical is focused upon.
Numerical continuation software, such as AUTO-07P, which can solve nonlinear problems
numerically without losing the intrinsic mathematical structure of the solutions, switch
equilibrium paths and trace solution branches, is used. The initial eigenmode is shown to be
destabilized at a secondary bifurcation point when the conditions for interactive buckling being
triggered are met. Progressive cellular buckling is then observed in the stiffened plate since there
is an interaction between the weakly stable overall mode and strongly stable local buckling
mode. The interaction causes the initial localized buckling deformation to spread in stages
throughout the component with a sequence of snap-back instabilities. This sequence of
progressive destabilization leads to a reduction in the load-carrying capacity of the component.
The analytical approach has been shown previously to provide excellent predictive capabilities
for the actual physical behaviour. It has been shown to be particularly valuable in cases where
there are a significant number of co-existing equilibrium configurations and where it may not be
immediately apparent which state would be observed in practice. The results from the present
model are being validated against the commercial finite element package ABAQUS and shows
very positive results for the interactive buckling profiles and the actual load-carrying capacities.