# Aeroelastic Optimization Design of the Global Stiffness for a Joined Wing Aircraft
## 1 Introduction
Flutter involving vehicle motion can be an active constraint [29]. As mentioned above, the aeroelastic analysis of a joined wing is necessary, and as stated earlier, optimization in the preliminary stage of aircraft design is also indispensable; therefore, the aeroelastic optimization of a joined wing is important. A large number of aeroelastic optimizations of joined wings have been explored in precursory studies. The rib thicknesses of a scaled joined wing was studied as a variables, and the scaled natural frequencies and scaled flutter speed of the full-scale vehicle were reproduced after optimization in [14]. An equivalent unsymmetrical beam section was used for structural optimization and was proven to adequately approximate the stiffness and deflection behavior of a real wing in [30]. Aerostructural optimization was carried out in [31; 32]. A panel method and an equivalent beam finite-element model were used for aerostructural optimization with the aerodynamic design variables as the parameters of the geometric configuration, and the thicknesses of the spar wall were added as structural design variables. The application of bacterial foraging optimization to a joined wing was shown in [33] and a hybrid variant was applied to match the aeroelastic responses of a wind tunnel model with a full-scale aircraft. Compared with traditional airplanes, structural optimization and weight estimations for the preliminary design of a joined-wing aircraft lack mature methods. In engineering, traditional wing-box design procedures and empirical formulas for traditional wing stiffness distributions have been frequently used for the preliminary design of a joined wing. However, this approach has three problems. Firstly, as it is a complex overconstrained system, similar external geometric parameters in the layout lead to completely different thicknesses of the internal structures and thus weights. Secondly, to minimize the weight by fixing the topology of the wing box, the material needs to be redistributed differently from what is usually seen in common layouts. As a result, the secondary bending moment tilts the neutral axis, and thus material is more efficiently utilized when distributed far apart to the two opposite corners. Thirdly, because of the interaction of the front wing and the rear wing, the distribution of the bending moment of the joined wing is different from traditional wings; thus, the distribution of the stiffness is different. For these reasons,optimization approaches in regard to stiffness based on traditional wings are not applicable to joined wings. In the conceptual and preliminary design stages, there are many uncertain parameters. Stiffness design requires a large amount of relevant data, such as airfoil, load, structural layout, etc., and this information is often obtained through parallel or subsequent design processes. This lack of information will lead to a decrease in the accuracy of the stiffness design, which will require repeated modifications of the structural stiffness distribution in the subsequent design, resulting in a waste of manpower and time. Furthermore, parametric analysis of the joined wing is even more difficult due to its complex layout compared with the traditional airplane. This leads to the low design efficiency of the detailed finite-element models and nonlinear structure models. Therefore, it is necessary to introduce a simple stiffness model that can describe joined-wing structural characteristics directly and efficiently, so as to provide guidance for the subsequent structural scheme screening, macro-structural layout, and mass distribution. It can be seen from the above that there are few direct studies on the stiffness distribution of joined-wing structures; however, it is necessary to conduct an in-depth study in the preliminary design stage, while considering the aeroelastic problem. In order to solve this problem, this paper introduces three different aeroelastic optimization methods in the preliminary stage to design the stiffness of the joined wing.