Cellular buckling from nonlinear mode interaction in unequal-leg angle struts

Abstract

A variational model based on total potential energy principles that describes the nonlinear mode interaction in thin-walled unequal-leg angle struts under pure axial compression is presented. The formulation, which combines continuous displacement functions and generalized coordinates, leads to the derivation of a system of differential and integral equations that describe the static equilibrium response of the strut. Solving the system of equations using numerical continuation techniques reveals, for the first time, progressive cellular buckling (or snaking) represented by a sequence of snap-back instabilities arising from the nonlinear interaction of the weak-axis flexural, strong-axis flexural and torsional buckling modes—the resulting behaviour being highly unstable. For verification purposes, a finite element (FE) model is also devised and the sequential snap-back instabilities are also captured within its framework. Moreover, once an initial geometric perturbation is incorporated within the variational model it compares very well with the FE model.