Formulation of a new shell-like reduced order model finite element for layered structures

Abstract

This paper presents a weak work-based kinematic coupling formulation between layered Reissner-Mindlin (RM) shell models and non-overlapping contiguous solid models. This approach relies on the interface definition proposed by the Mixing Dimensional Coupling (MDC) method, extending it to layered cross-sections. To achieve this, additional weak kinematic conditions are added to the work and reaction equilibrium in order to ensure deformation compatibility along the coupling interface and through the laminate in its thickness direction. The first outcome of the presented work is the development of efficient hybrid models, which employ conventional shell elements in regions with uniform lamination and solid models in areas with discontinuities. This enables accurate capture of the structural stiffness while focusing computational resources on regions where the kinematic assumptions of shell elements are insufficient. Secondly, this work introduces a procedure for defining multi-nodal Shell-Like Reduced Order Models (SLROMs) that are compatible with conventional Reissner Mindlin shell elements. These SLROMs are derived from solid model representations of regions with laminates or discontinuities, such as holes, thickness variations, or laminate transitions. Once analyzed, they enable efficient shell-only analyses while still providing detailed solid model stress distribution. Both the coupling formulation and the SLROM approach are evaluated through illustrative numerical examples.

This research has been supported by the European Union’s Horizon 2020 programs under grant agreements No. 101006860 (FIBRE4YARDS project) and No. 952966 (FIBREGY project), and by the TOMAT project (PID2023-153213NA-I00) funded by the Spanish Ministry of Science, Innovation and Universities. Furthermore, it has been carried out within the framework of an FI doctoral grant awarded by the Generalitat de Catalunya and co-financed by the European Union. The authors appreciate these supports.

Peer Reviewed

Postprint (published version)