Thin-walled member plastic bifurcation analysis using generalised beam theory

This paper presents the formulation and illustrates the application of a non-linear Generalised Beam Theory (GBT), which makes it possible to calculate bifurcation load factors of thin-walled members made of non-linear elastic–plastic materials and subjected to general loading conditions. This formulation is an extension of the non-linear GBT recently derived by the authors, which was valid for uniformly compressed members only. In order to illustrate the application of the proposed non-linear GBT, a beam finite element is formulated and some numerical results are presented and discussed. These results concern rectangular plates and thin-walled hat-section beams. The material instantaneous elastic moduli are determined on the basis of both the well known J2-flow and J2-deformation small strain plasticity theories.