An energy-based approach to buckling modal decomposition of thin-walled members with arbitrary cross sections, Part 1: Derivation

This paper presents the generalisation of an energy-based method for the modal decomposition of buckled shapes of thin-walled members. This comprehensive method is derived and validated for fully decomposing the elastic buckling solution of a thin-walled member into the pure buckling mode classes of global, distortional, local, shear and transverse extension. The first three modes are de-facto prerequisites for buckling capacity predictions found in current design standards for thin-walled structures. In the literature, two main methods, namely the generalised beam theory (GBT) and the constrained finite strip method (cFSM), are widely employed for modal decomposition. Recently, an alternative energy-based approach has been presented for the decomposition of buckling modes into the classical local, distortional and global modes. This method is generalised in the present study to achieve a complete decomposition that also accounts for shear and transverse extensional modes in addition to global, distortional and local modes. In this method, each of the buckling classes is separated by imposing constraints that are defined by enforcing specific criteria on the total strain energy of the member. The adopted criteria are based on the fundamental mechanical assumptions of the GBT which were also implemented in the conventional cFSM and later were further detailed for modal classification in the generalised cFSM. This paper is accompanied by a paper in which derivation of a modified global torsion mode for sections with closed loops is presented and the applicability of the proposed method is demonstrated using a series of numerical examples.