Aeroelastic analysis of highly flexible aircraft structures under large deformations

Kurzfassung

Some classes of aircraft are characterized by highly flexible airframes undergoing large structural deformations in steady and maneuvering flight. In most cases this flexibility is pronounced by the wings of the aircraft as the result of a high aspect ratio, forced by dedicated design criteria such as the reduction of the induced drag. The design and the analysis of highly flexible aircraft put high demands on the methods and tools employed. Multidisciplinary analysis taking into account aerodynamics, flight mechanics, and structural dynamics is indispensable where nonlinearities due to large rigid-body motions and large structural deflections are inherent in each of these disciplines. For the structural part, only few methods exist so far for the calculation of general aircraft structures subjected to large deformations. Commercial finite element solvers are mostly limited to clamped structures in their nonlinear solution capabilities, i.e. concurrent rigid-body motions are inadmissible. On the other hand, sophisticated methods incorporating nonlinear rigid-body and elastic motions have been developed mainly for beam-type structural models within academic institutions. In aeroelasticity, the modal approach is a well-established and elegant method for simulating and analyzing the dynamic behavior of aircraft structures. However, its applicability is limited to small structural deformations and an extension into the nonlinear regime with respect to large geometric deflections would be desirable. In this work we present an extension of the modal approach towards large geometric deformations. The modifications include generalized stiffness terms up to the third order to account for nonlinear force-displacement relations as well as quadratic, cubic, and fourth-order modal components for the calculation of the geometrically nonlinear displacement field. The method is shown to be applicable to different kinds of structural (finite element) aircraft models composed of beam and shell elements with anisotropic material properties. Furthermore, an integrated set of equations based on these extensions is presented that allows the nonlinear time-domain simulation of the free-flying elastic aircraft in steady and unsteady maneuvering flight with large structural deformations. The method is applied to different test cases with increasing complexity. A beam structural model in static structural response and a very flexible, maneuvering HALE-type unmanned aerial vehicle demonstrate the method's capabilities and limits.