GBT-based structural analysis of elastic–plastic thin-walled members

Structural systems made of high-strength and/or high-ductility metals are usually also rather slender, which means that their structural behaviour and ultimate strength are often governed by a combination of plasticity and instability effects. Currently, the rigorous numerical analysis of such systems can only be achieved by resorting to complex and computationally costly shell finite element simulations. This work aims at supplying to designers/researchers with an efficient and structurally clarifying alternative to assess the geometrically and/or materially non-linear behaviour (up to and beyond the ultimate load) of prismatic thin-walled members, such as those built from cold-formed steel. The proposed approach is based on Generalised Beam Theory (GBT) and is suitable for members exhibiting arbitrary deformation patterns (e.g., global, local, distortional, shear) and made of non-linear isotropic materials (e.g., carbon/stainless steel grades or aluminum alloys). The paper begins by providing an overview of the physically and geometrically non-linear GBT formulation recently developed and validated by the authors, which is followed by the presentation and thorough discussion of several illustrative numerical results concerning the structural responses of 5 members (beams and columns) made of distinct (linear, bi-linear or highly non-linear) materials. The GBT results consist of equilibrium paths, modal participation diagrams and amplitude functions, stress contours, displacement profiles and collapse mechanisms – some of which are compared with Abaqus shell finite element analysis (SFEA) values. An excellent correlation is found in all cases and, moreover, it is shown that GBT analyses including judiciously selected deformation mode sets involve only 25% (on average) of the number of d.o.f. required by similarly accurate SFEA. Moreover, it is clearly evidenced that the GBT modal nature makes it possible to acquire in-depth knowledge on the member behavioural mechanics in the elastic and elastic–plastic regimes.