Multi-objective robust design optimization (MORDO) of an aeroelastic high-aspect-ratio wing

In this paper, a new approach for multi-objective robust optimization of flutter velocity and maximum displacement of the wing tip are investigated. The wing is under the influence of bending-torsion coupling and its design variables have different levels of uncertainty. In designing and optimizing wings with a high aspect ratio, the optimization process can be done in such a way to increase the flutter velocity, but this can increase the amplitude of the wing tip displacement to a point that leads to the wings damage and structural failure. Therefore, single-objective design optimization may lead to infeasible designs. Thus, for multi-objective optimization, modeling is based on the Euler-Bernoulli cantilever beam model in quasi-steady aerodynamic condition. Using the Galerkin's techniques, the aeroelastic equations are converted to ODE equations. After validating the results, the system time response is obtained by the numerical solution of the governing equations using 4th Runge-Kutta method and the flutter velocity of the wing is obtained using the theory of eigenvalues. Subsequently, by choosing bending and torsional rigidity and mass per unit wing length as the optimization variables, using Monte Carlo-Latin hypercube (MC-LH) simulation and 4th polynomial chaos expansion (PCE), the effect of uncertainty on these variables is modeled in modeFRONTIER (TM) software coupled with MATLAB (TM) and optimization is performed by genetic algorithm. Finally, by plotting the Pareto front, it is observed that with an acceptable increase in flutter velocity, the maximum wing displacement amplitude is reduced as much as possible. The results of the multi-objective robust optimization show more feasible results compared with deterministic optimization.