A Hybrid-Displacement POD-based finite element formulation: Application to a linear elastic perforated plate

Riveted assemblies play a crucial role in the strength and failure of aeronautical structures subjected to shock and impact. The finite element evaluation of stress concentrations in these zones necessitate accurate modeling of both the full-scale structure and the local assembly zone to evaluate the structure survivability. To address this challenge, an approach based on the modeling of the assembly zones using Hybrid-Trefftz Displacement super-elements was considered. However, the main drawback of this approach was its restriction to linear problems caused by the use of Kolosov-Muskhelishvili (perforated membrane) analytical solution in the formulation process. To overcome this limitation, we propose to replace the analytical basis functions with numerical ones and to explore the integration of a Proper Orthogonal Decomposition basis into a finite element formulation. The results obtained in single and multi-hole problems show the cost-effectiveness and versatility of the Hybrid-Displacement POD-based finite element formulation. Guidelines are provided to build an efficient and versatile Hybrid-Displacement POD-based finite element formulation. Future work will focus on extending the proposed finite element formulation to non-linear problems.