Aeroelastic Optimization Of Composite Wing Box Structures

Aircraft design is a complex and iterative task, which requires a tradeoff between many conflicting requirements. These include, but are not limited to, high flutter/divergence speeds, adequate static strength and minimum weight. As the material industry develops, composite material plays an important role in aircraft design due to its high specific strength and stiffness. It is a typical aeroelastic optimization problem to address static strength, aeroelastic stability and manufacturing requirements in a global optimization environment.Aeroelastic constraints were conventionally calculated in frequency domain, which produced invalid damping information. The optimization method was usually based on gradient information, which also had many disadvantages, like the convergence to a local optimum. This paper tries to solve these problems by doing the flutter analysis in the Laplace domain and applying the genetic algorithm to the optimization of composite wing structures. The detail contents of the study are listed as follow.1) The mathematical formulation of the aeroelastic stability problem is discussed and the aeroelastic analysis methods based on the k method, pk method, p method, and the root locus method are also explained. Traditional frequency domain solution methods, such as k method and pk method, can efficiently determine the flutter/divergence speed, however, with the damping information either invalid or approximate. Laplace domain method like the p method and root locus method, result in damping information that is valid for all of the speed range of interest and provide better insight into the physical phenomena leading to aeroelastic instability. However, the main difficulty in implementing these methods lies in obtaining the aerodynamic loads for an arbitrary motion in Laplace domain. This problem is circumvented effectively through the use of rational function approximations.2) Mode tracking is one of the key problems in flutter analysis. A method based on orthogonality check, which introduces the left eigenvector, is developed to solve the problem. The numerical results are compared with those of the MAC method and validate that the orthogonality check is more effective in mode tracking. The root locus method is performed using this mode tracking method and the results are compared with those of the pk method to verify its effectiveness.3) The optimization problem of the composite wing structures is mathematically formulated, including the objective function, constrains and the types of variables. To overcome the pitfalls of the traditional gradient-based method, an optimization platform for the design of composite wing structures is built using genetic algorithm. The static strength, aeroelastic stability, and manufacturing requirements are simultaneously addressed in a global optimization environment.4) A wing box structure is considered in three different cases to perform the optimization procedure. In the first case study, the materials of the wing box are defined as metal and the aeroelastic constraint is addressed. The developed platform is verified through this case since the number of variables is small and there are results in literature for direct comparison. In the second case study, the capability of the platform in optimization the composite wing box is demonstrated by replacing the metal skins with composite ones. In the third case study, the aeroelastic constraints is added to the second case. It is shown that a 106% increase in the aeroelastic stability speed is achieved at the cost of 10.9% increase in the total structure weight. The advantage of considering aeroelastic stability constraints at early stages of the design is proved and the capability of the platform in the optimization of composite wing box structures with static strength, aeroelastic stability, and manufacturing constraints is also demonstrated.