# Design and Optimization of a Compliant Morphing Trailing Edge for High-Lift Generation
## 1 Introduction  
The aerospace sector is experiencing rapid growth strictly related to some specific factors, such as the market entry of emerging countries as China and India [1; 2], the increase in the e-commerce demand for fast and efficient shipments [3], and the evolution of geopolitical situations (wars, pandemics, etc.) altering the conventional trade routes and demanding new ones [4]. All these aspects dramatically affect the environment and climate through dramatic increase in the emission of pollutants [5; 6]. Many strategies are under investigation to mitigate this problem. A critical role is played by emerging technologies. In this sense, the next generation of sustainable aviation fuels (SAF) is doing well [7; 8]: hydrogen and biofuels are increasingly taking the spotlight despite the challenges that must be faced [9]. Electric propulsion is another strategic technology for the abatement of chemical emissions and acoustic nuisances and for its versatility in the different on-board systems [10; 11; 12]. Other interesting technologies are the natural laminar flow [13; 14; 15] and the morphing of aerodynamic surfaces [16; 17; 18], both having an impact in terms of efficiency improvement of the aircraft. Several studies have been conducted on novel technologies and aircraft configurations [19; 20]. The interest in morphing systems' targeting flow control is widespread in the scientific environment, essentially for the benefits that can be achieved. Among them is the investigation of the unsteady flow behavior of a NACA 0012 airfoil integrated with a bio-inspired morphing trailing edge flap, whose findings indicated that the proposed system can lead to instantaneous lift increases [21]; the numerical study on a flexible leading edge mounted on a NACA 0012 configuration whose actuation led to an increase in the lift coefficient of up to 15% and a reduction in the drag coefficient of up to 10% [22]; the optimization design of a morphing flap for an A320 A/C based on shape-memory alloy technology, providing an architecture capable of replacing a conventional flap [23]; and the numerical predictions about the impact of morphing systems on the take-off and landing performance of the same A/C [24]. A crucial role is played by the identification of the structural architecture matching the prescribed morphed shape. Due to the complexity of the problem, dedicated topology optimization strategies are under investigation; the most common approaches are the variable density and level set methods [25]. The problem of searching for an optimal configuration starting from a pre-defined layout of 1D elements whose edges and thickness can be suitably modified is related to variable density [26]. In this case, the position of the edges can be changed among discrete values. Some examples of topology optimization of morphing structures can be found in [27], where the inner structure of a full-sized morphing trailing edge was sought, or in [28], addressing the topology optimization of a leading and trailing edge. In the last decades, one may distinguish three main waves of funding/action program at the worldwide and European level. The Smart Wing Project (1995-2001) and Morphing Aircraft Structures (MAS) (2003-2007) of DARPA [29; 30] and the European 5 th and 6 th Framework Programmes (1998-2002 and 2002-2006) [31; 32] belonged to the first exploratory wave (late 1990s through the early years of the twenty-first century). The Electric Aircraft Propulsion (EAP) phase 1 (2010-2015) [33] and the Adaptive Compliant Trailing Edge (ACTE) (2014-2018) [34] of NASA as well as the Continuous Lower Energy, Emissions, and Noise (CLEEN) Program, phases 1-2 (2010-2020) [35], were promoted by the FAA and the 7 th Framework Programme (2007-2015). The Clean Sky and Clean Sky 2 programs (2008-2014 and 2014-2020) [36; 37]belonged to the second wave of actions, focusing on the selection of the most promising technologies and on their integration.