A force-based method for identifying the deformation modes of thin-walled members

There are three kinds of fundamental deformation of thin-walled members, namely global, distortional and local modes. A set of identification criteria based mainly on the characteristics of forces rather than conventional deformation shapes are proposed. The three newly defined deformation modes based on these criteria cover the entire deformation field of a thin-walled member, including those parts triggered by shear strains and transverse membrane strains. Moreover, it is proved that the three deformation modes are orthogonal to each other with respect to the elastic stiffness, which indicates the accuracy of the corresponding separation of the total strain energy, the portion of which is then designated as the participation factor of the individual mode, which is widely considered to be more physically appealing. Theoretically, the proposed criteria impose no restriction on cross-sectional types or geometric/loading boundary conditions. The proposed criteria are utilised to decompose the buckling results of several examples calculated by Finite Element Method. The resulting participation factors of each buckling mode are compared with those from the base functions of the constrained Finite Stripe Method (cFSM). The comparisons between the results of the two methods indicate the validity of the proposed criteria.