Semi-analytical sensitivity methods for aeroelastic shape optimization

Accurate and efficient sensitivity analysis is fundamental for the convergence of gradient-based optimization techniques. Analytical sensitivity methods are preferred over numerical ones for their accuracy and higher computational efficiency. Although analytical sensitivity methods have been developed for different static structural and purely aerodynamic problems, no methods exist for flutter shape eigensensitivities. This work presents the development of semi-analytical methods for calculating the sensitivity of flutter eigenvalues to variations in the structural and aerodynamic shape simultaneously. A discrete analytical differentiation of the flutter governing equations has been performed. Existing discrete analytical methods are developed for eigenvalue problems formulated in the node set. A novel methodology is introduced to handle flutter equations written in modal coordinates. The technique requires the differentiation of the structural and aerodynamic matrices and the real eigenvectors matrix. The derivative of the structural mass, stiffness, and damping matrices has been calculated analytically with an element-agnostic approach. On the other hand, aerodynamic matrices have been differentiated using finite differences, leading to a semi-analytical sensitivity method. The proposed methodology yields promising results, demonstrating the analytical differentiability of flutter eigenvalues and paving the way to a more accurate aeroelastic tailored design.