Nonlinear flutter and limit-cycle oscillations of damaged highly flexible composite wings

A study on nonlinear flutter of damaged high- wings is presented. Because an undamaged, high- wing is long and slender, it may be properly modeled as a 1D beam, using a geometrically exact beam formulation. However, structural damages in the form of cracks and delaminations are in fact 3D phenomena. Therefore, the area near a crack cannot be accurately modeled as a reduced-dimensional beam. However, finite element analysis of a wing structure modeled entirely as a 3D continuum is computationally expensive. To address this issue, a joined 3D/1D finite element approach has been proposed in which a small area surrounding the crack is regarded as a 3D continuum, and the rest of the wing structure is modeled as a reduced-dimensional 1D beam undergoing large displacements and rotations. The continuity conditions at the intersection between the 3D and 1D models are derived using the variational asymptotic method, by which the two parts are rigorously connected. Hence, the joined 3D/1D method provides a computationally inexpensive, yet accurate, analysis for slender wings. The structural model is then coupled with a reduced-order unsteady aerodynamic model to compute the aerodynamic forces and moments acting on the wing. The resulting nonlinear aeroelastic element is integrated into Abaqus, a commercial finite element computer code as a nonlinear user-defined element. Through nonlinear time-marching, using a generalized α method, limit-cycle oscillations associated with the free response of both undamaged and damaged wings undergoing large deformations are studied, and the differences are highlighted.