Static aeroelastic stiffness optimization of a forward swept composite wing with CFD-corrected aero loads

Abstract

This paper presents an aero load correction strategy applicable to the static aeroelastic optimization of composite wings. The optimization framework consists of a successive convex subproblem iteration procedure, in which a gradient-based optimizer consecutively solves a local approximation problem. Responses are approximated as a linear and/or reciprocal function of the laminate membrane and bending stiffness matrices. Together with the laminate thicknesses h, they constitute the design variables in the optimization process. Internally, the design space is transformed from stiffness matrices to lamination parameters, resulting in a continuous and convex optimization problem. Structural responses considered in the stiffness optimization are strength, local buckling and mass; aileron effectiveness, divergence, and twist constitute the aeroelastic responses. Steady aeroelastic loads are calculated with a doublet lattice method (DLM) embedded in the applied finite element solver, allowing for the generation of response sensitivities that incorporate the effects of displacement-dependent aeroelastic loads. To incorporate flow phenomena that cannot be reproduced with DLM, a higher order aerodynamic method is considered. The developed correction methods and their application are presented in this paper. The correction is twofold, first, aiming at a correction of DLM by means of camber and twist modifications applied directly to the doublet lattice mesh and second, by employing the capabilities of a higher order computational fluid dynamics (CFD) solver, like the DLR-based TAU code. To this end, DLM loads transferred to the structure are rectified by means of the supposedly superior CFD results. The aero load correction method is applied in the stiffness optimization of a forward swept wing. First, a trim application without structural optimization is discussed, to demonstrate the convergence behavior of the correction forces. The results of a wing skin mass minimization with balanced and unbalanced laminates are presented. In particular, the differences between optimizations with and without aero correction are highlighted. Eventually, a stacking sequence optimization based on the continuous optimization results is demonstrated.