Compositional Aeroelastic Operators for Morphing Flexible Multibody Aircraft: A Geometric Framework with Structural Verification
Morphing flexible multibody aircraft require structural strain, aerodynamic geometry, surface velocity, and generalized loading to remain compatible as joints and flexible components change configuration. A compositional formulation is developed around an assumed material attachment between each lifting surface and a geometrically exact beam. Separating the component root pose from the section field shows that the body strain and elastic potential of a component depend on its own elastic coordinates, while upstream motion enters kinetic terms and external-load pullbacks. At element level, an exact relative logarithm $d$ supplies strain and potential energy, whereas a reference-anchored section coordinate $σ$ supplies deformed section geometry. Finite-order expansions retain the finite reference geometry exactly and truncate only endpoint perturbations. The attachment map then generates surface points, tangents, normals, velocities, and force Jacobians from common section kinematics. Euler--Poincare beam balance, moving-surface potential-flow relations, graph cotangent assembly, and the associated semidiscrete power identity are stated in a common twist--wrench convention. Collocation, pressure, equivalent-load, and structural-station sites are distinguished to expose their approximation errors. Verification gives the expected $N_d+1$ convergence order for degree-$N_d$ relative-log expansions. In a geometrically nonlinear cantilever comparison, a cubic static-manifold correction reduces mean full-record displacement error from $0.479$ to $0.255$ over four completed load cases. These results provide structural and interface-level evidence rather than validation of a complete aircraft aeroelastic prediction.