A discontinuous Galerkin framework for aeroelastic flutter analysis with variable-order structural modeling capability

Abstract

An original computational framework for aeroelastic flutter analysis of wings is proposed. The novelty of the method lies in the combination of a discontinuous Galerkin method (DG) for structural analysis with the unsteady vortex lattice method (UVLM) for aerodynamics. The proposed DG formulation is based on a variable-order kinematic model, which allows adopting different structural theories in the analysis of the lifting wing structure, including beam and plate theories. The UVLM is employed for generating both the geometry of the wake shed by the wing and the flutter equations. The coupling between the methods is performed under the assumptions of small structural and aerodynamic perturbations. The formulation has been implemented and validated against benchmark results obtained by a commercial finite element code or data available in the literature in terms of eigenvalues and eigenvectors for various free-vibration and aeroelastic problems. The obtained results confirm the accuracy and robustness of the proposed methodology and demonstrate that high-order DG approximations may achieve faster convergence rates, in terms of degrees of freedom, with respect to standard finite element schemes, thus making the framework a powerful tool for fast aeroelastic analysis in early-stage aircraft design.