Aerostructural Adjoint Method for Flexible Wing Optimization I. Ghazlane ∗ , G. Carrier † and A. Dumont ‡ ONERA, The French Aerospace Lab, 92100 Meudon, France J.-A. D´ esid´ eri § INRIA, Sophia-Antipolis M´ editerann´ ee, 06905 Sophia-Antipolis, France This paper presents the current developments at ONERA on wing optimization via the aero-structural adjoint method. The aero-structural adjoint is the extension of the aero-elastic adjoint already used in aero- dynamic function optimization. 1 The aero-structural adjoint method allows the improvement of both aerody- namic and structural functions in the same design space. The internal structural element thicknesses (spar webs, caps, skins), the structural characteristics (flexibility) and the planform parameters are all variable in the aero-structural adjoint-based design process. A module for structural modelling, wing weight estimation and adjoint-compatible structural sensitivities computation is presented. The material stresses are aggregated into the Kreisselmeier-Steinhauser function to reduce the high number of design structural constraints. The structural module is integrated with the existing aero-elastic environment for adjoint-based optimizations in order to perform drag and weight optimizations. Nomenclature α geom Shape parameters α struct Structural parameters J (α) Cost function X Aerodynamic mesh X b Beam mesh C D Aerodynamic drag coefficient F Flexibility Matrix I Area moment of inertia J Torsion constant L Aerodynamic loads D Structural displacements W Aerodynamic conservative variables on X W ps Structural weight of the primary structure WB Wing box KS Kreisselmeier-Steinhauser function ρ aggregation parameter n g Number of structural constraints σ i Bending stress at section i τ t i Torsion stress at section i σ yield Maximum allowable bending stress τ yield Maximum allowable torsion stress g i Dimensionless structural constraint at section i I. Introduction An optimal wing will be extremely rigid to resists aero-elastic effects and considerably light for economical rea- sons. Unfortunately these two properties evolve monotonously in opposite directions: the wings are flexible because of their high dimension (high aspect ratio), making them stiffer will come at the expense of structural weight. The task of the designer is then to find a balance in the design space, a wing light enough to meet the environmental and economical needs and rigid enough to meet the FAR25 safety standards. Wing structural and aerodynamic behaviour are not only linked through performance. Sobieski shows 2 that a lift resultant located aft on an airfoil, results in an increase in the torque on the wing box and also generates twisting movement of the structure. Therefore, to keep ∗ Applied Aerodynamics Department, Ph.D candidate † Applied Aerodynamics Department, Research Engineer ‡ Applied Aerodynamics Department, Research Engineer § Research Scientist, Head of Opal Research Group 1 of 13 American Institute of Aeronautics and Astronautics