Interpolation functions of a hybrid-Trefftz perforated super-element featuring nodes on the hole boundary

• Interpolation functions of hybrid-Trefftz FE with nodes on the hole boundary are evaluated.
• Its capability to accurately describe the interior displacement/stress fields is assessed.
• Open discussion about the evolution of series-based FE when increasing the order.
• This evolution seems linked to the ill-conditioning of the system.
• Results show that a 16-node perforated FE with eight nodes on its hole boundary can be formulated.

The topic of the paper is related to the macroscopic modelling of riveted assemblies for full-scale aircraft structures subjected to crash/impact loadings. “Super-elements” have been developed to model the rivet and its rupture. However, stress concentrations in riveted assemblies can also initiate cracks from hole boundaries that propagate to the next ones and can lead to the catastrophic loss of the airplane by dismantlement of structural parts. An hybrid-Trefftz perforated super-element has been previously developed by the authors. However, the hole boundary of this super-element is a traction-free analytical boundary, preventing any connection with rivet elements. As a necessary first step to make the connection with the rivet possible, it is proposed to formulate additional nodes on the hole boundary of the perforated super-element. However, increasing the number of nodes implies increasing the super-element interpolation functions series order. Their ability to accurately describe the strain and stress fields is evaluated. It is found that when the series order is increased, the mechanical fields are still well described, but are a little less accurate than lower order interpolation functions. This evolution is discussed and seems to be linked to the ill-conditioning of the system. The accuracy is however still sufficient for the formulation of a 16-node super-element featuring eight nodes on the hole boundary.