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