FEM model

To reduce computational time and complexity a simplified models of the panels were used. The aim of the simulation was to determine difference in mechanical properties of the joint between the stringer and the panel. Thus, the simulation was performed on a sample of the panel and attached stringer. The part of the panel where the simulation was performed is shown on Figure 19.

Figure 19: Scheme of the placement of the sample used for FEM simulation

As shown, the investigated part is from the centre of the panel where use the benefit of symmetry which simplifies the computations. The asymmetry caused by the cut-outs placed in different distance from the axis of symmetry can be neglected, because they do not significantly influence the stress and deformation distribution in the examined area.     Riveted sample dimensions

Figure 20 shows the dimensions and rivet placement of the riveted sample used for simulation. The stringer’s bending axis is coincident with the axis of the panel plate sample.

Figure 20: Scheme of riveted FEM sample     FS welded sample dimensions

Figure 21 shows dimensions and weld location for the FS welded sample.

Figure 21: Scheme of FS welded FEM sample     Mesh creation parameters for riveted panel

Meshing parameters were chosen in order to assure sufficient fidelity in load transfer between the rivets and the stringer. As the rivet joint was the focal point of our interest, each of the rivet models has over 800 elements and appropriate contact surface constrains on the panel plate and stringer. The panel plate is modelled by elements with lower density and there are no rapid changes in stress and strain are expected.

With respect to the set parameters of the mesh, we can expect that, in the area close to the rivets with dense meshing, the simulation showed where stress concentration peaks appeared on the real part. However the meshing is not detailed enough to figure out the value of the stress peaks with a level of certainty needed for conclusions about the fatigue life of the real part. Meshing is shown on Figure 22.

Figure 22: Meshing of the riveted panel sample used for FEM simulations     Mesh creation parameters for FS welded panel

Meshing on the FS welded panel is much simpler as the welded joint is simulated as a fixed bond between the panel plate and stringer. The simulation of the joint properties does not involve heat introduced and structural change introduced residual stresses after welding as well as the fact that the surface of the stringer touching the panel would not be fully welded throughout its width. Thus, the simulation would not reveal stress concentration points in the joint area. The meshing is shown on Figure 23.

Figure 23: Meshing of the FS welded panel sample used for FEM simulations     Contact surfaces of riveted panel

All the contact surfaces between the panel, stringer and the rivets are set as bonded, which means that the neighbouring elements share the same position after deformation. To simulate the rivet joint between the stringer and the panel plate with higher fidelity the contact surface between them was modelled as frictionless (Figure 24). We did not choose the frictional type of the contact region because it would raise the computational requirements dramatically and the friction has negligible influence on the resulting stress and strain.

Figure 24: Frictionless contact region between the panel plate and the stringer; the other contact regions are set as bonded.     Contact surfaces of FS welded panel

There is only one contact region in the model of the FS welded panel (Figure 25). To simulate the FS weld the contact region properties were set as bonded. The more sophisticated simulation of the weld joint could not be used because we did not have more detailed FEM model of the weld zone and the TMAZ available. The accuracy of the currently used model is sufficient for the intended purpose of comparing the mechanical properties of the two distinct joining methods.


Figure 25: Contact region between the panel plate and the stringer was set as bonded     Riveted panel sample constrains

The constraints were chosen to assure the behaviour of the sample to be the same as if it was still a part of the whole panel.

Constraint 1 was set as fixed support, which means that all the nodes on the selected surface of the stringer always remain in their initial position. This constraint can be used as the surface lies in the plane of symmetry of the riveted panel.

The Constraint 2, frictionless support allowing points in the surface to move only within the plane they belong in undeformed stage, was assigned to the surfaces shown on Figure 26. The surface laying the plane of symmetry could be also assigned the fixed support constraint but using the frictionless support allowed us to take the potential instability of the thin plate into account in the simulation. The outer surfaces with the constraint 2 belong to the plane of symmetry between stringers. There is an inaccuracy introduced by this presumption because the stringers, due to their L shape, do not create perfectly symmetrical pattern but for this purpose, we considered the middle line between the bend axes of the stringers as the line in the plane of symmetry allowing us to use frictionless support to constraint these surfaces.

The constraint 3 keeps the nodes of the stringer and the panel plate in the same plane where the loads are applied perpendicular to the neutral plane.

Figure 26: Constraints on riveted sample: 1. Fixed support, 2. Frictionless support, 3. plane constraint     FS welded sample constraints

The constraints for the FS welded panel sample are set in the same way as described for the riveted panel sample and shown in Figure 27. However, in this case there is the symmetry of the stringers existing thus, the constraints simulate the real panel sample environment better.

27: Constraints on FS welded sample: 1. Fixed support, 2. Frictionless support, 3. Plane constraint