## 1 Introduction  
Adaptive aircraft structures can provide many benefits related to the capability of continuously modifying and optimizing the aerodynamic wing shape across the flight envelope. According to the classification of morphing [1], one of the most pursued concepts is active camber morphing, which aims to replace conventional flight control surfaces installed on fixed wing aircraft. Substituting classical hinged or slotted leading and trailing edge devices with flexible structures is an attractive goal due to the effective benefits that can be achieved in terms of flight and aerodynamic performances. The main goal is the reduction of fuel consumption and acoustic emissions during the mission [2, 3]. The design of conventional aircraft wings is the result of an optimization process based on a single flight condition, typically the cruise, at a given speed and altitude. Aircraft performances are suboptimal in the other conditions. If there was the possibility of changing the wing shape on demand, near-optimal performances for different conditions could be achieved. This goal is the idea behind the morphing concept, which is based on adaptive structures. According to the NATO RTO Technical Team on Morphing Vehicles, morphing is the \"real-time adaptation to enable multi-point optimized performance\" [4]. [PERSON] [5] suggested that \"morphing aircraft are multi-role aircraft\" that can change their external shape to adapt to a changing mission environment during flight. Most real-world aeronautical design problems involves multiple load conditions. In the case of the design of adaptive structures, there is also a need to combine conflicting structural requirements. This complexity can be summarized in the morphing paradox: the same structure must be sufficiently stiff to withstand its external loads without suffering appreciable deformations, and it must be flexible enough to change its shape into the required shape [6]. In this sense, many authors have described the morphing challenge. The design of adaptive structures becomes critical when it concerns control surfaces, because they must be designed as aeronautical structures that can achieve large deformations that are localized in small regions of the wing. On the one hand, they must be able to change the aerodynamic performance at different conditions of the flight envelope and to provide highly variable aerodynamics distributions, as required by the design manoeuvres. On the other hand, when the morphing device is actuated, the adaptive structure must be able to change its shape while being insensitive to load variations. The multi-load-bearing capability of the control surfaces implies that the external shape cannot be affected by the load variation. Adaptive structures are used as control surfaces, but they must be designed as structures, and thus the determination of the loads acting on the aircraft is one of the main tasks during their design. The knowledge of loads is important for structural design, prediction of the performance, and certification. [PERSON] and [PERSON] [7] wrote: \"Aircraft are subject to a range of static and dynamic loads resulting from flight manoeuvres, ground manoeuvres and gust/turbulence encounters.\" These load cases influence the structural design and should be recomputed for each considered mass state across the flight envelope [8]. Considering all of the load cases is not possible due to computational constraints, and thus some type of downselection must be implemented to identify a reduced set of critical load cases. Different approaches have been proposed in the literature. The most common methods are load envelopes, which are typically based on maximum and minimum criteria. More recent methods are based on using singular value decomposition to derive a set of characteristic loads that approximate all of the global load distributions [9]. For a realistic design, internal loads must be calculated for a few tens of characteristic loads rather than thousands of real load cases.