Abstract
• The closed-form analytical solution of torsional buckling load is derived. • The initial post-buckling behaviour is presented. • The non-linear differential equation of torsional buckling is derived and solved. • The effect of non-linear elastic material with comparison to linear one is discussed. • Comparison of analytical results to FEM analysis is presented. The paper concerns torsional buckling and the initial post-buckling of axially compressed thin-walled aluminium alloy columns with bisymmetrical cross-section. It is assumed that the column material behaviour is described by the Ramberg–Osgood constitutive equation in non-linear elastic range. The stationary total energy principle is used to derive the governing non-linear differential equation. An approximate solution of the equation determined by means of the perturbation approach allows to determine the buckling loads and the initial post-buckling behaviour. Numerical examples dealing with simply supported I-column are presented and the effect of material elastic non-linearity on the critical loads and initial post-buckling behaviour are compared to the linear solution.
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