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Complementary Energy Based Formulation for Torsional Buckling of Columns |
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| Authors: | R. Emre Erkmen Magdi Mohareb Mark A. Bradford |
| Affiliation: | 1Research Associate, Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, Univ. of New South Wales, UNSW Sydney, NSW 2052, Australia (corresponding author). E-mail: emre.erkmen@unsw.edu.au 2Associate Professor, Dept. of Civil and Environmental Engineering, Univ. of Ottawa, 161 Louis Pasteur, Ottawa, ON, Canada K1N 6N5. E-mail: mmohareb@uottawa.ca 3Scientia Professor and Australian Government Federation Fellow, Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, Univ. of New South Wales, UNSW Sydney, NSW 2052, Australia. E-mail: m.bradford@unsw.edu.au |
| 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. |
| Keywords: | Buckling Torsion Convergence |