Finite-Element based modeling for flight dynamics and aeroelasticity of flexible aircraft

Fully-coupled equations of rigid-body and structural dynamics of flexible aircraft are deduced from the weak formulation of Cauchy equation for an unconstrained elastic continuum. An appropriate choice of the body coordinate system enables to describe inertial coupling using a reduced set of coefficients, which are estimated for complex configurations via Finite Element Method (FEM) discretization. A fully-coupled linearized formulation around aeroelastic trim conditions is presented and implemented using data from a generic FEM solver. Small-disturbance, fully-unsteady aerodynamics is modeled in frequency domain via Doublet Lattice Method (DLM) and recast in time-domain state-space form by means of a rational function approximation. A state-space representation of the linearized system is ultimately obtained which simultaneously includes rigid-body, elastic, and aerodynamic state variables. Numerical results for two representative configurations are presented and discussed to point out the influence of inertial and aerodynamic coupling on integrated flight dynamic/aeroelastic stability and response.