Buckling instabilities of thick elastic beams subjected to axial stresses

Abstract

Buckling instabilities of a simply supported thick elastic beam subjected to axial stresses are studied. Taking into account the effects of shear deformations and thickness changes, buckling loads and buckling displacement modes of thick beams are obtained. Based on the power series expansion of displacement components, a set of fundamental equations of a one-dimensional higher-order beam theory is derived through the principle of virtual displacement. Several sets of truncated approximate theories are applied to solve the eigenvalue problems of a thick beam. The convergence properties of the buckling loads of a simply supported thick beam are examined in detail and comparison of the results with previously published ones is also made. The same asymptotic buckling load appears at higher displacement modes with wrinkling instabilities for the axial and bending problems. It is noticed that the present approximate theories can predict the buckling loads of an extremely thick beam more accurately compared to other refined theories and classical beam theory.