The post-buckling response of a bi-laterally constrained column

Abstract The post-buckling behavior of a linearly elastic column under a bi-lateral constraint is studied experimentally and analytically with an eye toward applications to corrugated sandwich structures. Under a controlled axial displacement, a rather rich sequence of events unfolds, including the formation of discrete or continuous contact zones between the column and the guiding walls and the instantaneous transition of the buckling waveform to a new equilibrium configuration due to local instability. The specific details, which depend on the system parameters as well as on the loading direction, are quantified based on the linearized differential equation of the column and without recourse to imperfections or energy considerations. For a frictionless contact, the response of the column exhibits a degree of statistical variation, but the range of this variation can be bounded. A companion elastica type analysis is also developed to account for large rotations which occur at large end shortenings. Under this condition, the ever repeating mode transition process which is predicted by the small deformation analysis ceases. Other interesting buckling characteristics are found which should be useful for the understanding of more complex contact/stability systems.