Sensitivity analysis of a coupled aero-structural system using direct differentiation and adjoint equations

In order to solve a multi-disciplinary optimization problem with strongly coupled disciplines, like the design of a commercial aircraft's wing, an aero-structural design framework is currently under construction. The optimization process is gradient-based and relies on the method of feasible directions. Several constraints can be applied, but only single objective optimization can be performed. The sensitivities of constraints and of the objective function can be computed either using the direct method or the adjoint method. However the adjoint method is far more convenient for high-fidelity parametrizations. The aerodynamic analysis is performed with the state-of-the-art solver elsA developped at ONERA, and the structural analysis is done trough a Euler-Bernoulli beam model