Morphing aircraft offer many benefits. However, the design of stiff yet flexible structures still provides many obstacles to fully exploring and realizing morphing structures. Due to this, many morphing challenges remain open. Topology optimization is a type of structural optimization that optimizes the material layout of a structure based on imposed boundary conditions and load paths. This type of optimization is promising for solving morphing design challenges but many of the optimized structures are not suited for traditional manufacturing and material arrangements. Multi-material additive manufacturing is an emerging technology that can produce a single structure with many different materials integrated in custom geometries. This could be the solution to realizing topology optimized structures. Despite the rich amount of current research in morphing aircraft, many challenges still remain open and topology of morphing structures could provide the solution to these morphing challenges. / Master of Science / Morphing aircraft offer many benefits. However, the design of stiff yet flexible structures still provides many obstacles to fully exploring and realizing morphing structures. Due to this, many morphing challenges remain open. Topology optimization is a type of structural optimization that optimizes the material layout of a structure based on imposed boundary conditions and load paths. This type of optimization is promising for solving morphing design challenges but many of the optimized structures are not suited for traditional manufacturing and material arrangements. Multi-material additive manufacturing is an emerging technology that can produce a single structure with many different materials integrated in custom geometries. This could be the solution to realizing topology optimized structures. Despite the rich amount of current research in morphing aircraft, many challenges still remain open and topology of morphing structures could provide the solution to these morphing challenges.

Morphing aircraft are envisioned to have multirole capability where the ability to change shape allows for adaptation to a changing mission environment. In order to calculate the properties of many wing configurations efficiently and rapidly, a model of a morphing aircraft is needed. This paper develops an aerodynamic model and a dynamic model of a morphing flying wing aircraft. The dynamic model includes realistic aerodynamic forces, consisting of lift, drag, and pitching moment about the leading edge, calculated using a constant strength source doublet panel method. The panel method allows for the calculation of aerodynamic forces due to large scale shape changing effects. The aerodynamic model allows for asymmetric configurations in order to generate rolling and yawing moments. The dynamic model calculates state information for the morphing wing based on the aerodynamic forces from the panel method. The model allows for multiple shape changing degrees-of-freedom for the wing, including thickness, sweep, dihedral angle, and chord length. Results show the model provides a versatile and computationally efficient tool for calculating the aerodynamic forces on the morphing aircraft and using these forces to show the associated states.

The research presented in this thesis examines the use of an estimated "actuator work" value as a performance parameter for the comparison of various aerodynamic control device configurations. This estimated "actuator work," or practical work as it will be referred to as in this thesis, is based on the aerodynamic and structural resistance to a control surface deflection. It is meant to represent the actuator energy cost required to deflect a general configuration of conventional or unconventional control surface. Thin airfoil theory is used to predict the aerodynamic load distribution required for this work calculation. The details of applying thin airfoil theory to many different types of control surface arrangements are presented. Convenient equations for the aerodynamic load distributions and aerodynamic coefficients are obtained. Using the developed practical work equations, and considering only the aerodynamic load component, the practical work required for a given change in lift is compared between different control surface arrangements. For single control surface cases, it is found that a quadratic (morphing) trailing edge flap requires less practical work than a linear flap of the same size. As the angle of attack at which the change in lift occurs increases, the benefit of the quadratic flap becomes greater. For multiple control surface cases, it is necessary to determine the set of control deflections that require the minimum practical work for a given change in lift. For small values of the initial angle of attack, it is found that a two-segment quadratic trailing edge flap (MTE) requires more work than a two-segment linear flap (TETAB). But, above a small value of angle of attack, the MTE case becomes superior to the TETAB case. Similar results are found when a 1-DOF static aeroelastic model is included in the calculation. The minimum work control deflections for the aeroelastic cases are shown to be strongly dependent on the dynamic pressure. / Master of Science

The following work is directed towards an evaluation of aircraft that undergo structural shape change for the purpose of optimized flight and maneuvering control authority. Dynamical equations are derived for a morphing aircraft based on two primary representations; a general non-rigid model and a multi-rigid-body. A simplified model is then proposed by considering the altering structural portions to be composed of a small number of mass particles. The equations are then extended to consider atmospheric flight representations where the longitudinal and lateral equations are derived. Two aspects of morphing control are considered. The first is a regulation problem in which it is desired to maintain stability in the presence of large changes in both aerodynamic and inertial properties. From a baseline aircraft model various wing planform designs were constructed using Datcom to determine the required aerodynamic contributions. Based on nonlinear numerical evaluations adequate stabilization control was demonstrated using a robust linear control design. In maneuvering, divergent characteristics were observed at high structural transition rates. The second aspect considered is the use of structural changes for improved flight performance. A variable span aircraft is then considered in which asymmetric wing extension is used to effect the rolling moment. An evaluation of the variable span aircraft is performed in the context of bank-to-turn guidance in which an input-output control law is implemented. / Ph. D.

Morphing an aircraft wingtip can provide substantial performance improvement. Most civil transport aircraft are optimized for range but for other flight conditions such as take-off and climb they are used as constraints. These constraints could potentially reduce the performance of an aircraft at cruise. By altering the shape of the wingtip, we can force the load distribution to adapt to the required flight condition to improve performance. Using a Variable Geometry Truss Mechanism (VGTM) concept to morph the wingtip of an aircraft with a Multidisciplinary Design Optimization (MDO) framework, the current work will attempt to find an optimal wing and wingtip shape to minimize fuel consumption for multiple morphing stages during cruise. This optimization routine was conducted with a Particle Swarm Optimization (PSO) algorithm using different fidelity tools to analyze the aerodynamic and structural disciplines.

Morphing an aircraft wingtip can provide substantial performance improvement. Most civil transport aircraft are optimized for range but for other flight conditions such as take-off and climb they are used as constraints. These constraints could potentially reduce the performance of an aircraft at cruise. By altering the shape of the wingtip, we can force the load distribution to adapt to the required flight condition to improve performance. Using a Variable Geometry Truss Mechanism (VGTM) concept to morph the wingtip of an aircraft with a Multidisciplinary Design Optimization (MDO) framework, the current work will attempt to find an optimal wing and wingtip shape to minimize fuel consumption for multiple morphing stages during cruise. This optimization routine was conducted with a Particle Swarm Optimization (PSO) algorithm using different fidelity tools to analyze the aerodynamic and structural disciplines.

Os recentes desenvolvimentos na tecnologia de sistema aeronáutico de geometria variável têm sido motivados principalmente pela necessidade de melhorar o desempenho de aeronaves. O conceito de Morphing Aircraft, por meio da variação da linha de arqueamento, representa uma alternativa para sistemas aeronáuticos mais eficientes. No entanto, para aeronaves de alto desempenho, projetos com estes novos conceitos podem gerar reações aeroelásticas adversas, o que representa uma questão importante e pode vir a limitar esses novos projetos. A compreensão adequada do comportamento aeroelástico devido à variação da linha de arqueamento, particularmente em regimes transônico, compreende uma questão importante. Este trabalho consiste num estudo preliminar das consequências aeroelásticas de um sistema aeronáutico de geometria variável. O objetivo desse trabalho é explorar as repostas aeroelásticas transônicas de um aerofólio com arqueamento variável no tempo. A metodologia para análise aeroelástica é baseada num modelo de seção típica. A integração no tempo do sistema aeroelástico é obtida pelo método de Runge-Kutta de quarta ordem. A representação do escoamento transônico não estacionário foi computada por um código CFD em um contexto de malhas não estruturadas com uma formulação dada pelas equações de Euler-2D. Esses resultados preliminares podem fornecer aos projetistas informações importantes sobre as respostas aeroelásticas de um sistema aeronáutico com variação da linha de arqueamento, permitindo estabelecer um quadro adequado para futuras investigações de controle aeroelástico de sistema aeronáutico de geometria variável. / Recent developments on aircraft variable geometry technologies have been mainly motivated by the need for improving the flight performance. The morphing wing concept, by means of variable camber, represents an alternative towards more efficient lifting surfaces. However, for higher performance aircraft, this technology may lead to designs that create unsteady loads, which may result in adverse aeroelastic responses, which represents an important and limiting issue. Proper understanding of the aeroelastic behavior, particularly in transonic flight regimes, due to variations in camber comprises an important matter. This work is a primary study of aeroelastic consequences of an real-time adaptive aircraft. The objective of this work is to investigate prescribed variations to airfoil camberline and their influence to the aeroelastic response in transonic flight regime. The methodology is based on computational simulations of typical section with unsteady transonic aerodynamics solved with a Computational Fluid Dynamics (CFD) code. The time integration of the aeroelastic system is obtained by Runge-Kutta fourth order. The unsteady transonic flow was computed by a CFD code based on the 2D-Euler equations with unstructured mesh. Prescribed camber variation of a symmetrical airfoil is transferred to the CFD mesh, and aeroelastic responses and loading is assessed. These preliminary results may provide the designers valuable information on the interaction between changes in camber during airfoil aeroelastic reactions, allowing establishing an adequate framework for further aeroelastic control investigations of morphing wings.

Os recentes desenvolvimentos na tecnologia de sistema aeronáutico de geometria variável têm sido motivados principalmente pela necessidade de melhorar o desempenho de aeronaves. O conceito de Morphing Aircraft, por meio da variação da linha de arqueamento, representa uma alternativa para sistemas aeronáuticos mais eficientes. No entanto, para aeronaves de alto desempenho, projetos com estes novos conceitos podem gerar reações aeroelásticas adversas, o que representa uma questão importante e pode vir a limitar esses novos projetos. A compreensão adequada do comportamento aeroelástico devido à variação da linha de arqueamento, particularmente em regimes transônico, compreende uma questão importante. Este trabalho consiste num estudo preliminar das consequências aeroelásticas de um sistema aeronáutico de geometria variável. O objetivo desse trabalho é explorar as repostas aeroelásticas transônicas de um aerofólio com arqueamento variável no tempo. A metodologia para análise aeroelástica é baseada num modelo de seção típica. A integração no tempo do sistema aeroelástico é obtida pelo método de Runge-Kutta de quarta ordem. A representação do escoamento transônico não estacionário foi computada por um código CFD em um contexto de malhas não estruturadas com uma formulação dada pelas equações de Euler-2D. Esses resultados preliminares podem fornecer aos projetistas informações importantes sobre as respostas aeroelásticas de um sistema aeronáutico com variação da linha de arqueamento, permitindo estabelecer um quadro adequado para futuras investigações de controle aeroelástico de sistema aeronáutico de geometria variável. / Recent developments on aircraft variable geometry technologies have been mainly motivated by the need for improving the flight performance. The morphing wing concept, by means of variable camber, represents an alternative towards more efficient lifting surfaces. However, for higher performance aircraft, this technology may lead to designs that create unsteady loads, which may result in adverse aeroelastic responses, which represents an important and limiting issue. Proper understanding of the aeroelastic behavior, particularly in transonic flight regimes, due to variations in camber comprises an important matter. This work is a primary study of aeroelastic consequences of an real-time adaptive aircraft. The objective of this work is to investigate prescribed variations to airfoil camberline and their influence to the aeroelastic response in transonic flight regime. The methodology is based on computational simulations of typical section with unsteady transonic aerodynamics solved with a Computational Fluid Dynamics (CFD) code. The time integration of the aeroelastic system is obtained by Runge-Kutta fourth order. The unsteady transonic flow was computed by a CFD code based on the 2D-Euler equations with unstructured mesh. Prescribed camber variation of a symmetrical airfoil is transferred to the CFD mesh, and aeroelastic responses and loading is assessed. These preliminary results may provide the designers valuable information on the interaction between changes in camber during airfoil aeroelastic reactions, allowing establishing an adequate framework for further aeroelastic control investigations of morphing wings.

Shape Memory Alloy actuators can be used for morphing, or shape change, by controlling their temperature, which is effectively done by applying a voltage difference across their length. Control of these actuators requires determination of the relationship between voltage and strain so that an input-output map can be developed. In this research, a computer simulation uses a hyperbolic tangent curve to simulate the hysteresis behavior of a virtual Shape Memory Alloy wire in temperature-strain space, and uses a Reinforcement Learning algorithm called Sarsa to learn a near-optimal control policy and map the hysteretic region. The algorithm developed in simulation is then applied to an experimental apparatus where a Shape Memory Alloy wire is characterized in temperature-strain space. This algorithm is then modified so that the learning is done in voltage-strain space. This allows for the learning of a control policy that can provide a direct input-output mapping of voltage to position for a real wire. This research was successful in achieving its objectives. In the simulation phase, the Reinforcement Learning algorithm proved to be capable of controlling a virtual Shape Memory Alloy wire by determining an accurate input-output map of temperature to strain. The virtual model used was also shown to be accurate for characterizing Shape Memory Alloy hysteresis by validating it through comparison to the commonly used modified Preisach model. The validated algorithm was successfully applied to an experimental apparatus, in which both major and minor hysteresis loops were learned in temperature-strain space. Finally, the modified algorithm was able to learn the control policy in voltage-strain space with the capability of achieving all learned goal states within a tolerance of +-0.5% strain, or +-0.65mm. This policy provides the capability of achieving any learned goal when starting from any initial strain state. This research has validated that Reinforcement Learning is capable of determining a control policy for Shape Memory Alloy crystal phase transformations, and will open the door for research into the development of length controllable Shape Memory Alloy actuators.

Shape morphing in aerospace structures has the potential to reduce noise, improve efficiency, and increase the adaptability of aircraft. Among the many challenges in developing morphing technologies is finding suitable wing skin materials that can be both stiff to support the structural loads, while being elastic and compliant to support this shape morphing an minimize actuation energy. This remains an open challenge, but many possible solutions have been found in smart materials, namely shape memory alloys and polymers. Of these, shape memory polymers have received more attention for wing skins due to their low density and cost, and high elastic limits in excess of 100% strain, but they suffer from generally low overall moduli. Shape memory polymer composites have been considered to address this, typically in the form of particulate/nanoscale reinforcements or by using them as matrix materials in laminate composites. While these can serve to increase the stiffness of the composite, there is still a present need for reinforcement strategies that can also maintain the large changes in stiffness of shape memory polymers. An alternative shape memory composite relies on honeycomb materials with shape memory polymer infills. Previous research has shown that polymer filled honeycombs exhibit greater in-plane moduli greater than the infill or honeycomb alone, but there has been little research focused on understanding this behavior. Moreover, while most engineered cellular structures are comprised of symmetric and periodic cells, cellular structures in nature are commonly spatially varying, asymmetric networks, which have not been considered in these composites. Motivated by these challenges in designing materials for shape morphing, this work seeks to explore the use of shape memory polymer-filled honeycomb composites for use as variable stiffness materials. First, the interaction between infill and the honeycomb, and the relationship between the honeycomb geometry and the effective composite properties is not well understood. This research first investigates the mechanisms of stiffening in these composites through both unit cell finite element models and through experimental characterization. Parametric studies are completed for selected honeycomb geometry design variables, and three key mechanisms of stiffening are identified. Next, these mechanisms are further supported by experimental studies, and comparisons are made showing the limitations of the few existing analytic models. With the knowledge gained from these studies, shape memory polymer infills are considered to create variable stiffness composites. In the first study, sizing design variables are selected to parametric the honeycomb cell geometry, with the designs constrained to be symmetric in-plane. A constrained multiobjective design optimization is completed for two chosen performance objectives, and corresponding local sensitivity studies are completed as well. The results predict that these composites meet and exceed the current bounds of both shape memory polymers and their composites, but also variable stiffness materials in general. A great degree of tailorability is demonstrated, and the model predictions are validated against experimental results from fabricated honeycomb composite samples. Next, generally asymmetric cell geometries are considered by defining shape design variables for the cell geometry. These cells are constrained to be periodic but not symmetric, allowing for the possible benefits of asymmetric to be investigated. Additionally, interconnected and spatially varying multicell unit cells are considered, further allowing for the study of spatially varying cell geometries. Multiobjective optimizations are completed for two unit cell cases, and Pareto fronts are identified. The results are compared to both those from the sizing optimization study and to the current state of the art, and are similarly found to demonstrate high performance and a great degree of tailorability in effective properties. / Doctor of Philosophy / Vehicle shape morphing, the smooth, continuous change of an aircraft's external shape, can greatly improve the efficiency and reduce noise in modern and future vehicles. Among the is challenges in this field is finding suitable skin materials that can be both stiff to support the forces exerted on an aircraft, while being soft and compliant to support this shape morphing. Smart materials, namely shape memory polymers, present many attractive options for this need, but generally need to have a higher stiffness to be suitable for large scale applications. To address this, adding reinforcements to shape memory polymers has been of interest, and current work has largely been focused on using long fiber composites or particulate and nano-reinforcements. As an alternative to these strategies, inspiration can be found in nature where polygon cells are a common means of reinforcement in both plants and animals. Motivated by the current state of the art and the promise of shape morphing structures, this work seeks to investigate cellular structures in the form of hexagonal honeycombs as a means of increasing the stiffness of shape memory polymer infills. This is done by first improving the understanding of more general polymer-filled honeycomb, which exhibit effective stiffnesses greater than the honeycomb or polymer alone. With a working understanding of how the honeycomb stiffens the infill and how the cell geometry influences this behavior, variable modulus infills are next considered. First, sizing design variables (i.e. the lengths and thicknesses of the honeycomb geometry) are selected to describe cell geometries. Design optimization problems are considered and used to estimate the bounds of possible performance for these composites. Relationships between the design variables and the composite performance are investigated, and an improved understanding of these composites is developed. Next, shape design variables are selected to allow for the asymmetry and spatial variation found in natural cellular structures, and similar design optimizations are completed. The results of this work are experimentally validated, and demonstrate that these composites allow for combinations of stiffness and stiffness change that meet and exceed the current state of the art. Furthermore, tailoring the cell geometry allows for an easy means of changing the behavior of the composite. This work represents a great improvement and an important step in overcoming the challenges in developing shape morphing systems.