A variable-order accurate framework for finite-strain static aeroelastic analysis

In this work, a novel computational framework for nonlinear elastic and aeroelastic analysis of highly flexible wings is presented. The proposed approach couples a discontinuous Galerkin (DG) formulation for finite-strain, total Lagrangian three-dimensional elasticity with a non-planar Vortex Lattice Method (VLM) for aerodynamic modeling. The structural formulation employs a variable-order approximation of the displacement field, allowing independent tuning of the accuracy along the three spatial directions. The aerodynamics is evaluated on the deformed configuration using a non-planar VLM, where the vortices location follows the large deformations of the wing structure. The DG-VLM coupling is achieved by considering the forces generated by the vortices as energetically equivalent body forces acting on the structure. A series of numerical tests is performed to investigate the influence of the approximation order of the displacement field on the aeroelastic response of the analyzed wings. The obtained results show good agreement with analytical, numerical and experimental benchmark data, confirming the accuracy and robustness of the proposed framework and its potential as a valuable tool for capturing nonlinear aeroelastic effects in conceptual design.