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.

The role of extensibility in the birth of a ruck in a rug

“…Figure 3 shows the results of experimental measurements of the dimensionless ruck height D = d/ g as a function of the end-end compression ∆L. The ruck height is easier to measure experimentally than the region over which contact is lost, L; eqn (14) gives that…”

“…This divergence in the compressive force needed to form a ruck has been known for almost thirty years [12]. Previous authors have attempted to explain it as a result of a breakdown of the linearized beam theory used to obtain (1) and (2) [13,14,15] while [16] confirmed the validity of the linearized approach and showed decisively that a critical buckling load does not exist for a perfect, infinite, continuous horizontal heavy elastica. Here, we show using a combination of theory and experiment that the paradox is resolved by incorporating the finite extensibility of the material.…”