Complementary Energy Based Formulation for Torsional Buckling of Columns
This article has been corrected.
VIEW CORRECTIONPublication: Journal of Engineering Mechanics
Volume 135, Issue 12
Abstract
A unique formulation for the elastic torsional buckling analysis of columns is developed in this paper based on the principle of stationary complementary energy. It is well known that in displacement based numerical formulations, discretization errors lead to stiffer behavior; hence convergence from above. On the other hand, discretization errors in complementary energy based numerical formulations lead to softer behavior in linear elasticity problems, which is a desired feature from the engineering view point. However, complementary energy based formulations can only overpredict the buckling loads for the flexural buckling problems of columns unless the physical conditions are compromised. In this study a formulation based on the principle of stationary complementary energy is considered for the elastic torsional buckling analysis of columns. The complementary energy expression is obtained from the well known total potential energy functional by using Frederichs’ transformation. In contrast to flexural buckling analysis of columns, it is shown that when the principle of stationary complementary energy is used, the torsional buckling loads can be underpredicted. A mathematical proof is provided to elucidate this property. The convergence behavior of the approximate solutions is illustrated through numerical examples for several columns with different boundary conditions.
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Published In
Journal of Engineering Mechanics
Volume 135 • Issue 12 • December 2009
Pages: 1420 - 1426
Copyright
© 2009 ASCE.
History
Received: Jul 10, 2008
Accepted: May 19, 2009
Published online: May 20, 2009
Published in print: Dec 2009
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