A Nonlinear Analysis for One-Way Buckling of a Laterally Loaded Column

Abstract

Recently, the problem of the mechanical buckling of a long beam resting on a frictionless rigid foundation and subjected to a uniform lateral loading was analysed using a linear formulation. The purpose of this paper is to show that the linear analysis is not sufficient for predicting a correct post-buckling response and that a completely nonlinear formulation is needed. The problem is formulated as a variational problem with variable end-points. The resulting nonlinear boundary value problem is solved numerically using the ‘shooting method’. The nonlinear solution indicates the presence of a lower buckling load, before which the only state of equilibrium is the undeformed state.