Combining shell and GBT-based finite elements: Plastic analysis with adaptive mesh refinement

In a recent work [1], the authors proposed a versatile and computationally efficient method to model thin-walled members with complex geometries, which combines standard shell and GBT-based (beam) finite elements. In the present paper, the approach is extended to the physically non-linear case (in particular, J₂ plasticity), by using an adaptive mesh refinement strategy that updates the finite element model such that the plastic zones are handled by the shell elements, whereas the elastic prismatic beam parts are dealt with using standard GBT-based elements with a minimum number of deformation modes (hence a minimum number of DOFs). This proposed approach offers two advantages: (i) versatility, in the sense that non-prismatic zones can be easily modelled, using shell elements, and (ii) computational efficiency, since the adaptive plastic zones are confined to the shell substructures, which require a much lower computational cost than GBT elements in handling physically non-linearity, whereas the elastic zones are most efficiently dealt with by GBT elements. For illustrative purposes, three examples are presented to demonstrate the capabilities of the proposed approach. These examples concern (i) a simply supported hat section beam, (ii) a lipped channel cantilever with two long holes in the web and (iii) a plane frame with I-section members. For comparison and validation purposes, full shell finite element model solutions are provided. It is concluded that, in all cases, the proposed approach leads to excellent results throughout the load-displacement range considered.