Structural Solver

For the computation of the structural deformation, the in-house structural solver “Finite Element Analysis for Aeroelasticity” (FEAFA) is employed. It is a Finite Element (FE) code based on a physically and geometrically linearised formulation, so it is limited to small strains and linear-elastic material behaviour. Over recent years, it has been expanded to offer a range of element types comparable to com­mercial CSD code packages which includes volume and shell elements, spring ele­ments, point masses and multi-freedom constraints. The mainstay for aeroelastic simulations is the multi-axial Timoshenko beam element [8, 9]. Its formulation al­lows for distinct cross-sectional positions of the centre of mass, the shear centre and the centre of bending. Thereby structural coupling between bending and torsional motion can be captured. The consideration of shear deformation in the Timoshenko formulations assures a physically-reasonable wave propagation through the struc­ture, which is important for unsteady simulations. With very few degrees of freedom and thus at low computational cost, such reduced structural models are capable of accurately rendering the elastic and inertial properties of slender structures such as transport aircraft wings. This is not only a significant advantage for unsteady sim­ulations, but also for steady design optimisation tasks, as has been demonstrated in the MEGADESIGN [20] project. During steady simulations, the structural deform­ation is either obtained by direct solution of the linear system of equations resulting from the FE discretisation or by superposition of pre-calculated modes.