## 4 Actuation System
### Finite Element Modeling of the Actuation System  
The mechanical behaviour of the morphing leading edge system was analysed using an FE model. It includes the flexible composite structure of the skin as well as all moving parts of the kinematic system, which were modelled using kinematic constraints. It also includes the sliding contact which closes the gap at the bottom of the MLE (see Section 6). The FE model is depicted in Figure 15. It represents a MLE section of 1.3 m span. Figure 14: Distribution of inverse reserve factor in the skin of the morphing leading edge. Figure 15: FE (finite element) model of the morphing leading edge (MLE) system shown from two different perspectives: (**a**) side view, (**b**) rear view. In Figure 15a, all components of the drive mechanism are highlighted in red, which move in the x-z-plane. In Figure 15b, those components of the drive mechanism are highlighted in red, which move in the plane of the bell crank and the linear actuator. The hinges with a fixed position are supposed to be connected to the support structure. All parts of the drive mechanism are modeled as rigid parts, whereas skin and stringers are deformable with the local material properties and ply stack sequence assigned. The actuator is represented by a \"translator\" feature, changing its length in order to move the MLE into the desired position. This movement drives the bell crank on the left hand side of Figure 15b. A connection rod between the two bell cranks makes them move synchronously. The sliding contact at the rear bottom end of the leading edge was modeled using frictionless perpendicular behaviour. Abaqus was used as FE software for this model. Skin and stringers were discretised using quadratic quadrilateral shell elements (S8). The bending stiffness of the shell elements representing the stringers are set equal to the bending stiffness of the stringer profiles described in Section 3.2. This allows us to model the behaviour of the stringers without modeling details of their geometry. Stringers and skin are modelled as one part in the FE model. This part has been meshed with an average element size of 10 mm \(\times\) 10 mm. In total, the mesh contains 22,976 Elements and 66,320 nodes. A static general procedure was used with an implicit solver, considering geometric nonlinearity. In this FE model, the aerodynamic pressure loads for different flight conditions, which have been computed via CFD analyses (see Section 2.4), are applied to the skin surface. In Table 4, these different load conditions are listed. * The initial condition \"0\" corresponds to the unloaded MLE in the stress-free manufacturing shape, which is depicted in Figure 15.
* Step no. 1 corresponds to the installation of the MLE to the wing. While installing the MLE, the sliding surface for the gap closure is prestressed by pushing it up against the bottom wing contour (see Section 6). For all subsequent steps, the rear bottom edge of the MLE slides on this contour. The prestressing of this sliding contact is maintained for all subsequent steps. * Steps no. 2 and 3 correspond to a test of the MLE on the ground without pressure loads. In step no. 2, the MLE is deformed into cruise aerofoil S4 without pressure loads. * In step no. 3, the MLE is deformed into the position for take-off and landing S5, still without pressure loads. * In step no. 4, pressure loads are applied assuming that now the plane takes off with MLE remaining in position S5 (Case S5 I in Table 3). As shown in the results of CFD analyses (Section 2.4), the highest pressure loads at the MLE occur for the flight conditions with retracted flap. This may partly be due to the fact that a higher AoA is allowed with retracted flaps. In Section 2.4, it is also shown that the highest pressure loads at the MLE occur at the highest allowed AoA. Hence, the flight condition with the highest AoA, the highest true air speed at that AoA and with retracted flaps is used as the most critical case in position S5. * In step no.