A new approach is proposed that seamlessly integrates with current industrial aeroelastic load analysis methods and aims to bring together the complexity of computational models in the production environment of aircraft (normally enhanced with experimental data) and the inherent difficulties associated with geometrically nonlinear analysis. Motivation stems from next-generation, ultra-efficient aircraft exhibiting high aspect-ratio wings.
Efficient incorporation of geometrically-nonlinear effects to standard (linear) approaches –based on generic Finite-Element models and Aerodynamic Influence Coefficient matrices– is accomplished through a two-step process: firstly, a reduction of the structure through dynamic condensation techniques on nodes along the main load paths of the vehicle; and secondly, a manipulation of the resulting condensed stiffness and mass matrices, their linear normal modes, and the nodal coordinates provide the nonlinear modal coefficients of the intrinsic beam equations that describe the dynamics of these load paths. The original model is preserved and effectively augmented with geometric stiffening, variations to the inertia and shortening effects, and aerodynamic follower forces (which naturally rotate in a formulation cast in material coordinates). The approach further caters to multibody and trajectory constraints using Lagrange multipliers on the velocity level set.
Structural and aeroelastic static and dynamic solutions are presented, including rigid-body and multibody dynamics, using the resulting nonlinear modal description. Comparison with full FE calculations of a representative wing illustrates both the accuracy and efficiency of the formulation. Excellent approximation of the flutter instability of a clamped wing is obtained under linear assumptions, while limit-cycle oscillations are found due to structural nonlinearities. Studies on a large transport aircraft configuration show the importance of nonlinear effects on the analysis of manoeuvres, trimmed flight, and dynamic gust loads. Moreover, the flutter speed of the airplane decreases as deflections from a steady angle-of-attack increase; and a first exploration into movable wing-tips is carried out within the multibody framework.