Iteration-based adjoint method for the sensitivity analysis of static aeroelastic loads

The sensitivity analysis of static aeroelastic loads can be analytically performed by virtue of a modified stiffness matrix. However, introducing a modified stiffness matrix into the calculation will incur extra computational cost. Additionally, the intrinsic drawback of the direct method is disadvantageous for the sensitivity calculation with a large number of design variables. This paper therefore presents a novel iteration-based adjoint method for the sensitivity analysis of static aeroelastic loads acting on flexible wing, the basis of which is the static aeroelastic calculation via loosely coupled iteration between the potential-flow panel model and the structural linear finite element model. By using an iterative approach for evaluating the adjoint variable, modification to the original stiffness matrix can be obviated. Moreover, this method is more competent for the structural sensitivity analysis with a very large number of design variables, since the adjoint variable is unrelated to the designs. A rectangular wing and a swept wing are employed to demonstrate the verification of the algorithms. The design sensitivities of applied nodal forces on the structure, lift per unit span, total lift and root bending moment are calculated and analyzed. The computational cost is also discussed to further demonstrate the efficiency of the proposed method.