PSI - Issue 17

T. Martins et al. / Procedia Structural Integrity 17 (2019) 878–885 Martins, T., Infante, V., Sousa, L., Antunes, P.J., Moura, A.M., Serrano, B./ Structural Integrity Procedia 00 (2019) 000 – 000 3

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3.1. Construction of a FE model of Frame 2

Since CAD geometry for the component in question was unavailable at the start of this work, a model had to be constructed using direct measurement and observation of the structure. From this geometry a finite element mesh was constructed using ABAQUS © . Initially, the objective was to use exclusively hexahedral elements, however certain features of added complexity required the use of tetrahedrals, making the final mesh predominantly hexahedral except for these instances. The material properties for aluminum alloy 2024-T3 were obtained from available bibliography.

Fig. 2. Mesh convergence on Frame 2. In b) is the convergence plot from the 1 st mode of vibration, in a) the converged mesh.

A mesh convergence study was performed on the geometry by constructing several meshes of varying element overall size and performing a modal analysis of the unconstrained structure (Fig. 2.b)). The frequency of the first mode of vibration was chosen as the convergence criterion. This study found that for an overall mesh size of 6mm a variation smaller than 0.02% existed regarding solutions from more refined meshes. Therefore, this mesh (Fig. 2.a)) was used on the following analysis. The boundary conditions applied to the model were varied to obtain the results that most accurately depicted real observations. Pin joints are used to carry the aerodynamic loads generated in the wings to the frame, which then cause the acceleration of the aircraft. To accurately determine the load on these the lift distribution around the wing surface should be determined. With this information unavailable, this distribution was modelled as elliptical, and formulae from bibliography used to determine it.

Fig. 3. Free body diagram of wing spar transmitting loads to the frame by the pinned joints. The elliptical distribution is the ideal one to minimize drag and increase efficiency of aircraft and is used many times as a design goal. From Brederode [4], the lift distribution ( ) for minimum drag was derived for the wings' geometrical properties: f(y) = sin [ −1 ( )] (1)