Geometrically and Physically Non-Linear GBT-Based Analysis of Thin-Walled Steel Members

This paper presents and illustrates the application of an elastic-plastic Generalised Beam Theory (GBT) formulation, based on J₂-flow plasticity theory, that makes it possible to perform physically and geometrically non-linear (post-buckling) analyses of prismatic thin-walled members (i) with arbitrary cross-section shapes, (ii) exhibiting any type of deformation pattern (global, local, distortional, warping, shear), (iii) made from non-linear materials with isotropic strain-hardening and (iv) containing initial imperfections, namely residual stresses and/or geometric imperfections, having generic distributions. After providing a brief overview of the main GBT assumptions, kinematical relations and equilibrium equations, the development of a novel non-linear beam finite element (FE) is addressed in some detail. Moreover, its application is illustrated through the presentation and discussion of numerical results concerning the post-buckling behaviour of a fixed-ended I-section steel column exhibiting local initial geometrical imperfections, namely (i) non-linear equilibrium paths, (ii) displacement profiles, (iii) stress diagrams/distributions and (iv) deformed configurations. For validation purposes, the GBT results are also compared with values yielded by Abaqus rigorous shell FE analyses.