Torsional Buckling of Columns by the Lyapunov Method

Abstract

The paper presents an application of Lyapunov's direct method to torsional and torsional-flexural buckling of columns. A metric space and a Lyapunov functional are proposed for each of the problems. Making use of Zubov's stability theorem and appropriate eigenvalue inequalities, the functionals yield the expressions for the buckling loads for simple and fixed supports. Of particular interest is the relative ease with which the expressions are derived, especially in the torsional-flexural buckling case, where it has not been necessary to seek the roots of the traditional cubic equation which governs the critical loads of the member.