On the compatibility between Reissner–Mindlin shell and GBT-based finite elements

Abstract

This technical note discusses aspects related to the combination of standard Reissner–Mindlin shell and GBT-based (beam) finite elements, with the purpose of modelling, efficiently (with degree-of-freedom economy) and accurately, the structural behaviour of thin-walled members and frames with complex geometry, undergoing global-local-distortional deformation. Following the approach previously proposed by the authors (Manta et al., 2020 [1]; 2021 [2]; 2020 [3]), each element type is employed where it is most efficient: (i) GBT-based elements in the prismatic zones and (ii) shell elements in the geometrically complex zones (e.g., tapered, joints, etc.). While lack of compatibility obviously leads to over-flexible solutions, it is shown that full compatibility can lead to locking. Consequently, a well-balanced compatibility statement is proposed. Several numerical examples are presented to show the advantages of the proposed approach over the previous one, in linear static and buckling (bifurcation) analyses.