Non-linear buckling analysis of thin-walled beams modeled with 7-parameter shell elements

The non-linear quasi-static buckling of thin-walled beams with arbitrary cross-sections is studied by developing coupling strategies between the composing plates (web, flanges). The element adopted for modeling the plates is a 7-parameter shell element using the Enhanced Assumed Strain concept (Büchter et al., 1994). Different nodal shell directors exist at the interface between plates for thin-walled beams with arbitrary cross-sections, requiring appropriate strategies. The coupling between plates first considers Lagrange multipliers at the interface, following the mortar method on the surface between the plates. Second a simplified pre-processing method is proposed by modifying the shell directors of the nodes close to the interface. In the case of the quasi-static buckling of thin-walled beams with L-shaped and I-shaped cross-sections, the two coupling strategies are thoroughly assessed by using three different solution procedures: Newton–Raphson, Newton–Riks and Asymptotic Numerical Method (ANM). The pre-processing method is simple and turns out to be robust and efficient. •Non-linear buckling analysis of thin-walled beams with arbitrary cross-section.•Mortar approach for coupling 7-parameter shell elements (with Enhanced Assumed Strain).•Pre-processing approach for dealing with discontinuity of shell directors.•Comparisons between solving strategies: Newton–Raphson with EAS, Riks, Asymptotic Numerical Method.•Reference computation with hexahedral 20-node elements.