Deformation modes of thin-walled members: A comparison between the method of Generalized Eigenvectors and Generalized Beam Theory

• Comparison between GBT and GE formulation for linear and bucklings analyses of thin walled beams.
• Both approaches are reviewed, emphasizing their differences and similarities.
• The GE/GBT deformation modes for four cross-sections are calculated and examined in detail.
• Simple tests for which also semi-analytical solutions can be obtained are presented.
• The results have been validated using ABAQUS shell FE analyses.

This paper compares two distinct approaches for obtaining the cross-section deformation modes of thin-walled members with deformable cross-section, namely the method of Generalized Eigenvectors (GE) and the Generalized Beam Theory (GBT). First, both approaches are reviewed, emphasizing their differences and similarities, as well as their resulting semi-analytical solutions. Then, the GE/GBT deformation modes for four selected cross-sections are calculated and examined in detail. Subsequently, attention is turned to the efficiency and accuracy of the GE/GBT mode sets in typical benchmark problems, namely the calculation of the global–local–distortional first-order and buckling (bifurcation) behaviors of bars with the previously analyzed cross-sections. It is concluded that GE and GBT, both based on the method of separation of variables, yield accurate results although they use different structural models and mode selection strategies. Therefore they offer complementary advantages, which are put forward in the paper.