Geometrically non-linear generalised beam theory for elastoplastic thin-walled metal members

This paper presents the formulation and validation of a geometrically and physically (J2 plasticity) non-linear Generalised Beam Theory formulation, intended to calculate accurate non-linear elastoplastic equilibrium paths of thin-walled metal bars and associated collapse loads. This formulation extends previous work (Gonçalves and Camotim, 2011) [1] by including the geometrically non-linear effects. The plate-like bending strains are assumed to be small (as in all GBT formulations), but the membrane strains are calculated exactly. Both stress-based and stress resultant-based GBT approaches are developed and implemented in a 3-node beam finite element. The stress-based formulation is generally more accurate, but the stress resultant-based formulation makes it possible to avoid numeric integration in the through-thickness direction of the walls. In order to show the potential of the proposed formulation and resulting finite element, several numerical results are presented and discussed. For validation purposes, these results are compared with those obtained with standard 2D-solid and shell finite element analyses.