Physically non-linear GBT analysis of thin-walled members

• GBT formulation to perform first-order elastoplastic analyses of thin-walled members.
• Applicable to members exhibiting arbitrary local/distortional/global deformation patterns.
• Numerical results concerning the three steel beams presented and discussed in detail.
• Mechanical insight and numerical efficiency provided by the GBT modal nature illustrated.
• Accuracy of the GBT-based results assessed through comparisons with SFEA values.

This paper presents a formulation of Generalised Beam Theory (GBT) intended to perform first-order elastic–plastic analyses of thin-walled members experiencing arbitrary deformations and made of non-linear materials exhibiting isotropic hardening. After presenting the GBT fundamental assumptions and kinematic relationships, the member non-linear equilibrium equations are derived and a non-linear one-dimensional (beam) finite element is formulated. The arc-length control technique is adopted in the numerical solution of the non-linear equations and J2-flow theory is used to model plasticity in conjunction with the Backward Euler return-mapping algorithm. In order to show the capabilities and potential of the implemented formulation, a set of numerical illustrative examples are presented and discussed. For validation purposes, most of the GBT results obtained (equilibrium paths, modal participation diagrams, displacement profiles, stress distributions and deformed configurations) are compared with values yielded by Abaqus shell finite element analyses.