Generalised beam theory-based finite elements for elastoplastic thin-walled metal members

This paper addresses the formulation and validation of GBT-based beam finite elements, intended to analyse the physically non-linear (plastic zone) behaviour of thin-walled metal members. Both stress-based and stress resultant-based elastoplastic formulations are developed. The stress-based formulation is generally more accurate, but the stress resultant-based formulation, which employs the Ilyushin yield function, leads to significant computational savings, namely (i) numeric integration in the through-thickness direction is not required and (ii) constraints to the stress resultant and work-conjugate strain field, typical of linear elastic GBT-type formulations, are straightforwardly enforced. The choice of interpolation functions and the cross-section discretization procedure are also discussed. In order to illustrate the application, provide validation and demonstrate the capabilities of the proposed finite elements, several numerical results are presented and discussed. These results are compared with those obtained with standard 2D-solid and shell finite element analyses.