# Aeroelastic Optimization Design of the Global Stiffness for a Joined Wing Aircraft
## 1 Introduction  
Aircraft design includes complex aeroelastic problems; therefore, it is necessary to use structural optimization techniques for a compromising primary design scheme, in order to solve issues related to the coupling between different disciplines, e.g., structural, aerodynamics, control, etc., and meeting aeroelastic performance requirements. A design under aeroelastic constraints is called an aeroelastic optimization. In the overall design of aeroelastic problems, the primary issue for determining the influence of structural deformation on the aerodynamic characteristics is designing a reasonable stiffness distribution for the wing structure [1], and this is also an essential basis for subsequent designs [2]. To obtain more accurate results that satisfy the aeroelastic performance requirements, it is necessary to design a wing stiffness distribution using design optimization technology, which can preferably guide the selection of the structural scheme and the arrangement of the macrostructure stiffness and mass distribution [3]. Joined-wing airplanes have been widely explored and studied in many different disciplines since [PERSON] introduced the concept in 1976 [4]. A joined-wing airplane can be defined as an airplane that incorporates tandem wings arranged to form diamond shapes in both the plan and front views, and the fuselage can be seen as the connecting diagonal of the diamond frame. The advantages of a joined wing include light weight, high stiffness, low induced drag, good transonic area distribution, high-trimmed CLmax (maximum trimmed lift coefficient), reduced wetted area and parasite drag, direct lift control, side force control capability, excellent stability and controllability [5]. However, the connection between the front wing and the rear wing leads to dissimilarity in the structural and aerodynamic characteristics compared with a traditional layout, and the interconnectedwings form a complex overconstrained system, which increases the difficulty of analysis and increases the design space of different disciplines [6; 7]. This leads to integrated design changes becoming the key problem, as the authors in [8] noted that basic aeroelastic investigations must be introduced early in the design process of a joined-wing aircraft, and a stiffness distribution design is also necessary. Aeroelasticity research has been accompanied by the development of the joined wing. [PERSON] and his team performed a series of studies on the aeroelasticity of a joined wing during the first decade of the 21 st century. Different structural models of joined wings were studied, including high-fidelity finite elements method (FEM)-based weight models [8], embedded antenna models [9; 10], nonlinear structure models [11; 12], sensor craft models [13; 14], scale models [15; 16; 17; 18], a beam model [19], and a wind tunnel model [20]. Nearly half of the research dealt with linear structural integrated design and optimization, whereas the other half dealt with the nonlinearity of the joined-wing models. [PERSON] et al. also performed great research on the aeroelasticity of joined wings. Their research focused mainly on the nonlinear problems of joined wings. The evaluation of aeroelastic characteristics of the joined wing was undertaken in the early design stages in [21]; both reduced-order models [22; 23] and full-order models [24] were used to analyze the nonlinearity of joined wings; and post-critical phenomena were researched in [25; 26]. However, the aeroelastic optimization of the models has hardly been taken into account. Preliminary analyses on joined wings showed that aerodynamic loads at the tip of the wing were sensitive to the modeling with reference to efforts [27; 28]; moreover, aeroelastic analyses showed large differences in the predicted flutter speeds. Thus, it was speculated that by attributing the forces in the tip regions largely to the bending moment, the overall aeroelastic response was significantly affected by the redistribution.