Aeroelastic design optimization of thin-walled subsonic wings against divergence

The present paper deals with aeroelastic design optimization of a slender, thin-walled wing-type structure against divergence. The main goal is to avoid torsional instability, which might occur at critical flow conditions, by maximizing the divergence speed without the penalty of increasing the total structural mass. Divergence provides a useful measure of the general stiffness level of the wing structure. The model formulation considers a large aspect ratio unswept wing of rectangular planform, while the flow conditions are restricted to those of subsonic incompressible ones. Both continuous and piecewise models are analyzed, where exact analytical solutions are obtained within the context of linear elasticity and aerodynamic strip theories. The final optimization problem is formulated as a nonlinear mathematical programming problem solved by implementing the interior penalty function technique, which interacts to eigenvalue calculation routines. Results show that optimum patterns with decreasing wall thickness from the inboard portion toward the outboard one produce significant improvement in the overall torsional stiffness level. It is also shown that global optimality can be achieved from the proposed mathematical model, provided that the wing is constructed from piecewise uniform portions having not-equally spaced lengths and different torsional rigidities.