The polarisation method and the method of equivalent nodal forces: A comparison with other modal decomposition methods in the analysis of coupled instabilities

The objective of this paper is to validate the newly proposed polarization method (PM) and the method of the equivalent nodal forces (NFM) and to highlight their distinctive features by comparing them with some more established modal decomposition methods, including mainly the generalized beam theory (GBT) and the constrained finite strip method (cFSM). Modal decomposition methods analyse the deformed shapes of a buckled thin-walled structural member by decomposing them into a linear combination of constituent modes (classical local, distortional and global buckling) augmented with shear and transverse extension modes. An overall comparison of the methods is provided, including practical aspects such as how the buckling modes are generated, and the versatility of these methods when applied to various cross-sectional shapes. Specific technical details are discussed for each method, along with numerical examples focusing on the buckling behaviour of thin-walled structural members under compression. Moreover, considerable attention is paid to the discrepancies between the results yielded by different methods, namely the critical stresses associated with pure local, distortional and global buckling. The numerical examples demonstrate that, in spite of the fact that these four methods stem from different theories, they provide essentially the same extended capabilities for examining and understanding thin-walled member stability. Reasons for the discrepancies between the results are discussed and the conclusion is reached that they are attributed to the differences in the criteria adopted in the various methods of mode generation, particularly in the handling of the membrane strains and stresses. In addition, through this comparison features of the newly proposed methods are unveiled such as greater mesh sensitivity, significantly lower critical stress at extremely short half-wavelengths, and different output regarding distortional buckling of hollow-flange sections.