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The digital transformation of engineering design processes is essential for the aerospace industry to remain competitive in the global market. Multidisciplinary design optimization (MDO) frameworks play a crucial role in this transformation by integrating various engineering disciplines and enabling the optimization of complex spacecraft structures. Since the design team consists of multiple entities from different domains working together to build the final product, the design and analysis tools must be readily available and compatible. An integrated approach is required to handle the problem's complexity efficiently. Additionally, most aerospace structures are made from composite panels. It is challenging to optimize such panels as they require the satisfaction of constraints where the design ply thicknesses and orientations can only take discrete values prescribed by the manufacturers. Heuristics such as particle swarm or genetic algorithms are inefficient because they provide sub-optimal solutions when the number of design variables is large. They also are computationally expensive in handling the combinatorial nature of the problem. To overcome these challenges, this work proposes a two-fold solution that integrates multiple disciplines and efficiently optimizes composite spacecraft structures by building a rapid design framework. The proposed model-based design framework for spacecraft structures integrates commercially available software from Siemens packages such as NX and HEEDS and open-source Python libraries. The framework can handle multiple objectives, constraint non-linearities, and discrete design variables efficiently using a combination of black-box global optimization algorithms and Mixed Integer Programming (MIP)-based optimization techniques developed in this work. Lamination parameters and MIP are adopted to optimize composite panels efficiently. The framework integrates structural, thermal and acoustic analysis to optimize the spacecraft's overall performance while satisfying multiple design constraints. Its capabilities are demonstrated in optimizing a small spacecraft structure for required structural performance under various static and dynamic loading conditions when the spacecraft is inside the launch vehicle or operating in orbit. Doctor of Philosophy The design of new spacecraft takes several years and requires significant resources. The primary design objective is to minimize spacecraft mass/cost while satisfying the mission requirements. This is done by altering the structure's geometric and material properties. Most spacecraft panels are made from composite materials where the orientations of fiber paths and the thickness of the panel determine its strength and stiffness. Finding the best values for these parameters cannot be done efficiently using existing optimization algorithms, as several combinations of orientations can give a similar performance which can be subpar. In this dissertation, mathematical programming is adopted for fast evaluation of optimum panel properties, thereby saving a significant amount of resources compared to conventional techniques. Moreover, the requirements that govern the design process are handled one at a time in an organization. This leads to discrepancies in the various teams' designs that satisfy all requirements. A framework is built to integrate all requirements to account for their conflicting nature and quickly give the best possible spacecraft structural design configuration.

Energy-shaping techniques are used to expand the range of autonomous motion of unmanned aerial systems without prohibitively {color{black}increasing the computational cost of the resultant controller}. Passivity-based control presents a method to implement a static, nonlinear state feedback control law that stabilizes the motion of an aircraft with a large region of attraction. {color{black} The energy-based control scheme is applied to both multirotor and fixed-wing aircraft}. Multirotor aircraft dynamics are cast into a port-Hamiltonian System and the concept of trajectory tracking using canonical feedback transformation is implemented to construct a cross-track controller. Fixed-wing aircraft dynamics are cast in port-Hamiltonian form and a passivity-based nonlinear control law for steady, wings-level flight of a fixed-wing aircraft to a specified inertial velocity (speed, course, and climb angle) is constructed. Results in simulations and experiments suggest robustness, and a large region of attraction of the controller. The control law extended to support time-varying inertial velocity tracking that incorporates banking to turn. The results are extended by including a line-of-sight guidance law and varying the direction as a function of position relative to a desired path, rather than as a function of time. The control law and the associated proof of stability follow similarly to that of the time-varying directional stabilization problem. The results are supported with simulations as well as experimental flight tests. Doctor of Philosophy This dissertation presents an alternative but intuitive approach to regulate unmanned aerial vehicles' flight that would allow for more maneuverability {color{black} than conventional methods}. This scheme relies on modifying the energy of the system to achieve the desired motion and leverages the properties of the aircraft rather than eliminating them and imposing different properties. This approach is applied to both fixed-wing and aircraft and quadcopters. Simulations and experimental flights have show the efficacy of this approach compared to other more established methods.

Slotted Waveguide Antenna Stiffened Structures (SWASS) offer a new way to integrate the antennas used by many aircraft systems in modern aircraft. Looking at the weather radars used by current aircraft and using the loading estimates of the X-47B from Northrop Grumman, the designs went through several stages in the optimization procedure. The first stage centered around accounting for the stress concentrations present at the corners of the slots. These points led to local failure around the slots prior to the buckling of the overall structure, but the development of a concentration factor curve fit accounted for these in the optimization procedure and filled in a gap in the current literature. The models are then optimized, exposing a weakness in that these stress concentrations would lead to failure well before buckling in most designs with a loaded copper insert. To avoid this and shift most of the load to the supporting material, an initial gap is implemented in the eigenvalue buckling analysis, thus allowing for the simple 1-D models to be rapidly optimized without the need for contact modelling upon the gap's closure. The waveguide designs are then analyzed to ensure that the optimization of the individual waveguides is not prioritizing the structural performance to the detriment of the electromagnetic performance. Multiple points along the optimized Pareto front are tested and showed that their electromagnetic performance was consistent across the various regions of the front, and that the desired frequency of 10 GHz used by weather radars was within the optimal operational range for the various designs. Continuing from the individual waveguides now to larger panels, high fidelity models were used to develop another curve fit that relates the buckling of a panel simply supported on all four sides to the buckling of a single constituent waveguide simply supported on both ends. This curve fit is then used to validate the larger panel's performance against anticipated flight loads, without the need to model entire panels during the optimization procedure. Doctor of Philosophy Modern aircraft utilize antennas for a variety of purpose, ranging from the weather radars in the nose of passenger airlines, to the communications antennas mounted on the exterior of military aircraft, and even the targeting radars used by weapons systems in modern military craft. However, these systems often require large empty spaces within the aircraft or interfere with the profile of the aircraft if mounted externally. Slotted Waveguide Antenna Stiffened Structures (SWASS) aims to eliminate these issues by integrating these antennas into the skin of the aircraft but uses the antennas themselves to help strengthen the structures, thereby eliminating the need to reroute the loads around them and making the aircraft lighter. These designs consist of a slotted metallic waveguide enclosed within supporting composite materials, which are substituted in place of the standard aircraft skin so as to fit seamlessly into the designs. Multiple issues can arise when attempting to do this, which this thesis tackles. To develop optimized, multifunctional designs the thesis balances the structural needs to integrate the designs into existing aircraft against the electromagnetic needs of the antenna systems it replaces. Gaps in the existing literature are addressed through the development of a curve fit to properly account for issues caused by the slots cut into the upper surface of the waveguides. New methods are also employed to simplify the optimization procedure. The first is reducing the load on the metallic waveguide through an initial gap by deriving a simplified model and eliminating the need for the complex models previously required. The next step is the creation of a new curve fit to relate the buckling of a single, less complex single waveguide model, to the buckling of the larger, more complex panel models. Throughout all of this, constraints and model validations are used to ensure that the designs meet their requirements, both as an antenna as well as a load bearing part of the aircraft's skin, specifically that of the X-47B.

Artificial intelligence (AI) has progressed significantly during the last several decades, along with the rapid advancements in computational power. This advanced technology is currently being employed in various engineering fields, not just in computer science. In aerospace engineering, AI and machine learning (ML), a major branch of AI, are now playing an important role in various applications, such as automated systems, unmanned aerial vehicles, aerospace optimum design structure, etc. This dissertation mainly focuses on structural engineering to employ AI to develop lighter and safer aircraft structures as well as challenges involving structural optimization and analysis. Therefore, various ML applications are studied in this research to provide novel frameworks for structural optimization, analysis, and design. First, the application of a deep-learning-based (DL) convolutional neural network (CNN) was studied to develop a surrogate model for providing optimum structural topology. Typically, conventional structural topology optimization requires a large number of computations due to the iterative finite element analyses (FEAs) needed to obtain optimal structural layouts under given load and boundary conditions. A proposed surrogate model in this study predicts the material density layout inputting the static analysis results using the initial geometry but without performing iterative FEAs. The developed surrogate models were validated with various example cases. Using the proposed method, the total calculation time was reduced by 98 % as compared to conventional topology optimization once the CNN had been trained. The predicted results have equal structural performance levels compared to the optimum structures derived by conventional topology optimization considered ``ground truths". Secondly, reinforcement learning (RL) is studied to create a stand-alone AI system that can design the structure from trial-and-error experiences. RL application is one of the major ML branches that mimic human behavior, specifically how human beings solve problems based on their experience. The main RL algorithm assumes that the human problem-solving process can be improved by earning positive and negative rewards from good and bad experiences, respectively. Therefore, this algorithm can be applied to solve structural design problems whereby engineers can improve the structural design by finding the weaknesses and enhancing them using a trial and error approach. To prove this concept, an AI system with the RL algorithm was implemented to drive the optimum truss structure using continuous and discrete cross-section choices under a set of given constraints. This study also proposed a unique reward function system to examine the constraints in structural design problems. As a result, the independent AI system can be developed from the experience-based training process, and this system can design the structure by itself without significant human intervention. Finally, this dissertation proposes an ML-based classification tool to categorize the vibrational mode shapes of tires. In general, tire vibration significantly affects driving quality, such as stability, ride comfort, noise performance, etc. Therefore, a comprehensive study for identifying the vibrational features is necessary to design the high-performance tire by considering the geometry, material, and operation conditions. Typically, the vibrational characteristics can be obtained from the modal test or numerical analysis. These identified modal characteristics can be used to categorize the tire mode shapes to determine the specific mode cause poorer driving performances. This study suggests a method to develop an ML-based classification tool that can efficiently categorize the mode shape using advanced feature recognition and classification algorithms. The best-performed classification tool can accurately predict the tire category without manual effort. Therefore, the proposed classification tool can be used to categorize the tire mode shapes for subsequent tire performance and improve the design process by reducing the time and resources for expensive calculations or experiments. Doctor of Philosophy Artificial intelligence (AI) has significantly progressed during the last several decades with the rapid advancement of computational capabilities. This advanced technology is currently employed to problems in various engineering fields, not just problems in computer science. Machine learning (ML), a major branch of AI, is actively applied to mechanical/structural problems since an ML model can replace a physical system with a surrogate model, which can be used to predict, control, and optimize its behavior. This dissertation provides a new framework to design and analyze structures using ML-based techniques. In particular, the latest ML technologies, such as convolutional neural networks, widely used for image processing and feature recognition, are applied to replace numerical calculations in structural optimization and analysis with the ML-based system. Also, this dissertation suggests how to develop a smart system that can design the structure by itself using reinforcement learning, which is utilized for autonomous driving systems and robot walking algorithms. Finally, this dissertation suggests an ML-based classification approach to categorize complex vibration modes of a structure.

The discovery of carbon nanotubes in 1990s popularized a new area of research in materials science called Nanoscience. In the following decades, several carbon based nanoparticles were discovered or engineered and with the discovery of Graphene nanoplatelets (GNP) in 2010, carbon based nanoparticles were propelled as the most promising class of nanoparticles. High mechanical strength and stiffness, excellent electrical and thermal conductivity, and high strength to weight ratios are some of the unique abilities of CNTs and GNPs which allow their use in a wide array of applications from aerospace materials to electronic devices. In the current work presented herein, CNTs and GNPs are added to polymeric materials to create a nanocomposite material. The effects of this nanoparticle addition (a.k.a reinforcement) on the mechanical properties of the nanocomposite polymer materials are studied. Specifically, efforts are focused on studying fracture toughness, a material property that describes the material's ability to resist crack growth. Relative to the conventional metals used in structures, epoxy-based composites have poor fracture toughness. This has long been a weak link when using epoxy composites for structural applications and therefore several efforts are being made to improve their fracture toughness. In the first, second and third chapters, the enhancement of fracture toughness brought about by the addition of carbon nanotubes (CNTs) and graphene nanoplatelets (GNPs) was investigated. CNT-Epoxy and GNP-Epoxy Compact Tension (CT) samples were fabricated with 0.1% and 0.5% nanofiller weight concentrations. The potential synergistic effects of dual nanofiller reinforcements were also explored using CNT/GNP-Epoxy CT samples at a 1:3, 3:1 and 1:1 ratio of CNT:GNP. Displacement controlled CT tests were conducted according to ASTM D5045 test procedure and the critical stress intensity factor, $K_{IC}$, and the critical fracture energy, $G_{IC}$, were calculated for all the material systems. Significant enhancements relative to neat epoxy were observed in reinforced epoxies. Fracture surfaces were analyzed via scanning electron microscopy. Instances of CNT pullouts on the fracture surface were observed, indicating the occurrence of crack bridging. Furthermore, increased surface roughness, an indicator of crack deflection, was observed along with some crack bifurcations in the GNP-Epoxy samples. In the fourth chapter of Part I, the influence of pre-crack characteristics on the Mode-I fracture toughness of epoxy is investigated. Pre-crack characteristics such as pre-crack length, crack front shape, crack thickness and crack plane profile are evaluated and their influence on the peak load, fracture displacement, and the critical stress intensity factor, $K_{IC}$ is studied. A new method of razor blade tapping was used, which utilized a guillotine-style razor tapping device to initiate the pre-crack and through-thickness compression to arrest it. A new approach of quantitatively characterizing the crack front shape using a two-parameter function is introduced. Surface features present on the pre-crack surface are classified and their effects on the post crack initiation behavior of the sample are analyzed. This study aims to identify and increase the understanding of the various factors that cause variation in the fracture toughness data of polymeric materials, thus leading to more informed engineering design decisions and evaluations. Chapters six and seven of Part II investigate the SHM capabilities of dispersed MWCNTs in mock, inert, and active energetics. In these experimental investigations, the strain and damage sensing abilities of multi-walled carbon nanotube (MWCNT) networks embedded in the binder phase of polymer bonded energetics (PBEs) are evaluated. PBEs are a special class of particulate composite materials that consist of energetic crystals bound by a polymer matrix, wherein the polymer matrix serves to diminish the sensitivity of the energetic phase to accidental mechanical stimuli. The structural health monitoring (SHM) approach presented in this work exploits the piezoresistive properties of the distributed MWCNT networks. Major challenges faced during such implementation include the low binder concentrations of PBEs, presence of conductive/non-conductive particulate phases, high degree of heterogeneity in the PBE microstructure, and achieving the optimal MWCNT dispersion. In chapter seven, Ammonium Perchlorate (AP) crystals as the oxidizer, Aluminum grains as the metallic fuel, and Polydimethylsiloxane (PDMS) as the binder are used as the constituents for fabricating PBEs. To study the effect of each constituent on the MWCNT network's SHM abilities, various materials systems are comprehensively studied: MWCNT/PDMS (nBinder) materials are first evaluated to study the binder's electromechanical response, followed by AP/MWCNT/PDMS (inert nPBE) to assess the impact of AP addition, and finally, AP/AL/MWCNT/PDMS (active nPBE-AL) to evaluate the impact of adding conductive aluminum grains. Compression samples (ASTM D695) were fabricated and subjected to monotonic compression. Electrical resistance is recorded in conjunction with the mechanical test via an LCR meter. Gauge factors relating the change in normalized resistance to applied strain are calculated to quantify the electromechanical response. MWCNT dispersions, and mechanical failure modes are analyzed via scanning electron microscopy (SEM) imaging of the fracture surfaces. Correlations between the electrical behavior in response to the mechanical behavior are presented, and possible mechanisms that influence the electromechanical behavior are discussed. The results presented herein demonstrate the successful ability of MWCNT networks as structural health monitoring sensors capable of real-time strain and damage assessment of polymer bonded energetics. Doctor of Philosophy The discovery of carbon nanotubes in 1990s popularized a new area of research in materials science called Nanoscience. Carbon nanotubes (CNTs) are one of several forms of Carbon, meaning a differently structured carbon molecule in the same physical state similar to diamonds, graphite, and coal. In the following decades, several carbon based nanoparticles were discovered or engineered and with the discovery of Graphene (GNP) in 2010, carbon based nanoparticles were propelled as the most promising class of nanoparticles. High mechanical strength and stiffness, excellent electrical and thermal conductivity, and high strength to weight ratios are some of the unique abilities of CNTs and GNPs which allow their use in a wide array of applications from aerospace materials to electronic devices. In the current work presented herein, CNTs and GNPs are added to polymeric materials to create a nanocomposite material, where the term "composite" refers to a material prepared with two or more constituent materials. The effects of this nanoparticle addition (a.k.a reinforcement) on the mechanical properties of the nanocomposite polymer materials are studied. Specifically, efforts are focused on studying fracture toughness, a material property that describes the material's ability to resist crack growth. Fracture toughness is a critical material property often associated with material and structural failures, and as such it is very important for safe and reliable engineering design of structures, components, and materials. Moving from a single function (i.e. mechanical enhancement) to a more multi-functional role, taking advantage of the excellent electrical and mechanical abilities of CNTs, a structural health monitoring system is developed for use in polymer bonded energetics (eg. solid rocket propellants). When a material undergoes mechanical deformation or damage, the measured electrical properties of the material undergo some change as well. Using sensor networks built with multiple CNTs dispersed within a polymeric material, a whole structure can be made into an effective sensor where by simply monitoring the electrical properties, the extent of material deformation and damage can be known. Such a system is geared towards providing early warning of impending catastrophic material failures thus directly improving the safety during material handling and operations.

With the proliferation of unmanned aircraft designed for national security and commercial purposes, opportunities exist to create high-fidelity aerodynamic models with flight test techniques developed specifically for remotely piloted aircraft. Then, highly maneuverable unmanned aircraft can be employed to their greatest potential in a safe manner using advanced control laws. In this dissertation, novel techniques are used to identify nonlinear, coupled, aerodynamic models for fixed-wing, unmanned aircraft from flight test data alone. Included are quasi-steady and unsteady nominal flight models, aero-propulsive models, and spinning flight models. A novel flight test technique for unmanned aircraft, excitation with remote uncorrelated pilot inputs, is developed for use in nominal and nonlinear flight regimes. Orthogonal phase-optimized multisine excitation signals are also used as inputs while collecting gliding, aero-propulsive, and spinning flight data. A novel vector decomposition of explanatory variables leads to an elegant model structure for stall spin flight data analysis and spin aerodynamic modeling. Results for each model developed show good agreement between model predictions and validation flight data. Two novel applications of aerodynamic modeling are discussed including energy-based nonlinear directional control and a spin flight path control law for use as a flight termination system. Experimental and simulation results from these applications demonstrate the utility of high-fidelity models developed from flight data. Doctor of Philosophy This dissertation presents flight test experiments conducted using a small remotely controlled airplane to determine mathematical equations and parameter values, called models, to describe the airplane's motion. Then, the models are applied to control the path of the airplane. The process to develop the models and predict an airplane's motion using flight data is described. New techniques are presented for data collection and analysis for unusual flight conditions, including a spinning descent. Results show the techniques can predict the airplane's motion very well. Two experiments are presented demonstrating new applications and the usefulness of the mathematical models.

Flight testing has been the historical standard for determining aircraft airworthiness - however, increases in the cost of flight testing and the accuracy of inexpensive CFD promote certification by analysis to reduce or replace flight testing. A framework is introduced to predict the performance in the special case of a modification to an existing, previously certified aircraft. This framework uses a combination of existing flight test or high fidelity data of the original aircraft as well as lower fidelity data of the original and modified configurations. Two methods are presented which estimate the model form uncertainty of the modified configuration, which is then used to conduct non-deterministic simulations. The framework is applied to an example aircraft system with simulated flight test data to demonstrate the ability to predict the performance and associated uncertainty of modified aircraft configurations. However, it is important that the models and methods used are applicable and accurate throughout the intended use domain. The factors and limitations of the framework are explored to determine the range of applicability of the framework. The effects of these factors on the performance and uncertainty results are demonstrated using the example aircraft system. The framework is then applied to NASA's X-57 Maxwell and each of its modifications. The estimated performance and associated uncertainties are then compared to the airworthiness criteria to evaluate the potential of the framework as a component to the certification by analysis process. Doctor of Philosophy Aircraft are required to undergo an airworthiness certification process to demonstrate the capability for safe and controlled flight. This has historically been satisfied by flight testing, but there is a desire to use computational analysis and simulations to reduce the cost and time required. For aircraft which are based on an aircraft which has already been certified, but contain minor changes, computational tools have the potential to provide a large benefit. This research proposes a framework to estimate the flight performance of these modified aircraft using inexpensive computational or ground based methods and without requiring expensive flight testing. The framework is then evaluated to ensure that it provides accurate results and is suitable for use as a supplement to the airworthiness certification process.

Finite Element (FE) analysis is a powerful numerical technique widely utilized to simulate the real-world response of complex engineering structures. With the advancements in adaptive optimization frameworks, multi-fidelity (coupled shell-solid) FE models are increasingly sought during the early design stages where a large design space is being explored. This is because multi-fidelity models have the potential to provide accurate solutions at a much lower computational cost. However, the time and effort required to create accurate and optimal multi-fidelity models with acceptable meshes for highly complex structures is still significant and is a major bottleneck in the FE modeling process. Additionally, there is a significant level of subjectivity involved in the decision-making about the multi-fidelity element topology due to a high dependence on the analyst's experience and expertise, which often leads to disagreements between analysts regarding the optimal modeling approach and heavy losses due to schedule delays. Moreover, this analyst-to-analyst variability can also result in significantly different final engineering designs. Thus, there is a greater need to accelerate the FE modeling process by automating the development of robust and adaptable multi-fidelity models as well as eliminating the subjectivity and art involved in the development of multi-fidelity models. This dissertation presents techniques and frameworks for accelerating the finite element modeling process of multi-fidelity models. A framework for the automated development of multi-fidelity models with adaptable 2-D/3-D topology using the parameterized full-fidelity and structural fidelity models is presented. Additionally, issues related to the automated meshing of highly complex assemblies is discussed and a strategic volume decomposition technique blueprint is proposed for achieving robust hexahedral meshes in complicated assembly models. A comparison of the full-solid, full-shell, and different multi-fidelity models of a highly complex stiffened thin-walled pressure vessel under external and internal tank pressure is presented. Results reveal that automation of multi-fidelity model generation in an integrated fashion including the geometry creation, meshing and post-processing can result in considerable reduction in cost and efforts. Secondly, the issue of analyst-to-analyst variability is addressed using a Decision Tree (DT) based Fuzzy Inference System (FIS) for recommending optimal 2D-3D element topology for a multi-fidelity model. Specifically, the FIS takes the structural geometry and desired accuracy as inputs (for a range of load cases) and infers the optimal 2D-3D topology distribution. Once developed, the FIS can provide real-time optimal choices along with interpretability that provides confidence to the analyst regarding the modeling choices. The proposed techniques and frameworks can be generalized to more complex problems including non-linear finite element models and as well as adaptable mesh generation schemes. Doctor of Philosophy Structural analysis is the process of determining the response (mainly, deformation and stresses) of a structure under specified loads and external conditions. This is often performed using computational modeling of the structure to approximate its response in real-life conditions. The Finite Element Method (FEM) is a powerful and widely used numerical technique utilized in engineering applications to evaluate the physical performance of structures in several engineering disciplines, including aerospace and ocean engineering. As optimum designs are increasing sought in industries, the need to develop computationally efficient models becomes necessary to explore a large design space. As such, optimal multi-fidelity models are preferred that utilize higher fidelity computational domain in the critical areas and a lower fidelity domain in less critical areas to provide an optimal trade-off between accuracy and efficiency. However, the development of such optimal models involves a high level of expertise in making a-priori and a-posteriori optimal modeling decisions. Such experience based variability between analysts is often a major cause of schedule delays and considerable differences in final engineering designs. A combination of automated model development and optimization along with an expert system that relieves the analyst of the need for experience and expertise in making software and theoretical assumptions for the model can result in a powerful and cost-effective computational modeling process that accelerates technological advancements. This dissertation proposes techniques for automating robust development of complex multi-fidelity models. Along with these techniques, a data-driven expert system framework is proposed that makes optimal multi-fidelity modeling choices based on the structural configuration and desired accuracy level.

Significant research is ongoing in the world to meet the needs of social and environmental crisis by harnessing wind and solar energy at high altitudes. One such approach is the use of an inflatable High Altitude Aerial Platform (HAAP). In the presented work, such periodically supported beam-like structures are analyzed using various mathematical models primarily modeling them as an equivalent beam using one-dimensional theories. The Euler-Bernoulli Theory (EBT) has been widely used for high aspect ratio beams, whereas the First Order Shear Deformation Theory (FSDT), or the Timoshenko beam theory, considers transverse shear effects and hence is superior in modeling low aspect ratio beams. First, an Isogeometric Analysis (IGA) is conducted using both FSDT and EBT to predict thermal buckling of periodically supported composite beams. Isogeometric analysis overcomes the limitations of the Gibbs phenomenon at discontinuities for a periodically supported beam using a higher order textit{k}-refinement. Next, an Integral Equation Approach (IEA) is implemented using EBT to obtain natural frequencies and buckling loads of periodically supported non-prismatic beams. Ill-conditioning errors were alleviated using admissible orthogonal Chebychev polynomials to obtain higher modes. We also present the prediction of the onset of flutter instability for metal plate and inflatable wing shaped foam test articles analyzed using finite element analysis (FEA). FEA updating based on modal testing and by conducting a geometrically nonlinear analysis resulted in a good agreement against the experiment tests. Furthermore, a nonlinear co-rotational large displacement/rotation FEA including the effects of the pressure as a follower forces was implemented to predict deformations of an inflatable structures. The developed FEA based tool namely Structural Analysis of Inflatables using FEA (SAIF) was compared with the experiments and available literature. It is concluded that the validity of the developed tool depends on the flexibility of the beam, which further depends upon the length of the beam and the bending rigidity of the beam. Inflatable structures analyzed with materials with high value of the Young's modulus and low to medium slenderness ratio tend to perform better against the experimental data. This is attributed to the presence of wrinkling and/or the Brazier effect (ovalling of the cross section) for flexible beams. The presented work has applications in programmable buckling, uncertainty quantification, and design of futuristic HAAP models to help face the upcoming environmental crises and meet the societal needs. Doctor of Philosophy In the future, developed countries are projected to face an increase in renewable energy demands due to environmental crises and increasing societal needs for energy due to urbanization. Wind energy, a renewable source, has received increasing attention. Wind farms require large land space and offshore wind energy harvesting is prone to unstable environments. Crosswind kite power is one of the promising and emerging fields where one can harvest energy from the wind farm inaccessible and apparently endless winds at high altitudes. In this dissertation, we present analysis and experiments on investigating complex structures, such as inflatable high altitude aerial platforms (HAAP) by using various mathematical models, primarily modeling them as an equivalent beam using one-dimensional theories. We investigate the effects of internal pressure on such structures, which unlike many other types of applied loads, follow the direction of the deflections. When supported on multiple supports, these structures are more efficient in terms of increased payload capacity due to a better distribution of loads, despite the increased weight penalty. To name a few, there are direct applications of periodic supports in design of bridges and railway sleepers. To avoid violent vibrations or failure, we also investigate the effect of multiple supports on the so-called natural frequency, vibration frequency under absence of applied loads, and buckling loads, instabilities under compression, of such beam-like structures. The presented work will aid in the design of futuristic HAAP models to help face the upcoming environmental crises and meet the energy demands of society due to urbanization.

Modeling and simulation have played an essential role in understanding the effects of blast waves. However, a broad area of engineering problems, such as vehicle structures, buildings, bridges, or even the human body, can benefit by accurately predicting the response to blasts with little need for test or event data. This thesis reviews fundamental concepts of blast waves and explosives and discusses research in blast scaling. Blast scaling is a method that reduces the computational costs associated with modeling blasts by using empirical data and numerically calculating blast field parameters over time for various types and sizes of explosives. This computational efficiency is critical in studying blast waves' near and far-field effects. This thesis also reviews research to differentiate between free-air blasts and gun muzzle blasts and the progress of modeling the muzzle blast-structure interaction. The main focus of this thesis covers an investigation of different numerical and analytical solutions to a simple aerospace structure subjected to blast pressure. The thesis finally presents a tool that creates finite element loads utilizing muzzle blast scaling methods. This tool reduces modeling complexity and the need for multiple domains such as coupled computational fluid dynamics and finite element models by coupling blast scaling methods to a finite element model. Master of Science {Numerical integration methods have helped solve many complex problems in engineering and science due to their ability to solve non-linear equations that describe many phenomena. These methods are beneficial because of how well they lend to programming into a computer, and their impact has grown with the increases in computing power. In this thesis, ``modeling and simulation" refers to the characterization and prediction of an event's outcome through the use of computers and numerical techniques. Modeling and simulation play important roles in studying the effects of blast waves in many areas of engineering research such as aerospace, biomedical, naval, and civil. Their capability to predict the outcome of the interaction of a blast wave to vehicle structures, buildings, bridges, or even the human body while requiring limited experimental data has the chance to benefit a wide area of engineering problems. This thesis reviews fundamental concepts of blast waves, explosives, and research that has applied blast loading in modeling and simulation. This thesis describes the complexity of modeling an axially symmetric blast wave interaction by comparing the numerical and theoretical response blast loaded structure.

With the aim to understand the synergistic roles played by kinematics, aerodynamics, and inertia in flapping wing maneuvers, this thesis first investigates the plunging motion of a simple flat plate as it is a fundamental motion in the kinematics of many flying animals. A wide range of frequency (k) and amplitude (h) is investigated to account for a robust kinematic characterization in the form of plunge velocity (kh). Leading Edge Vortices (LEVs) are found to be responsible for producing thrust while Trailing Edge Vortices (TEVs) produce drag. The vortex dynamics becomes nonlinear for higher kh and three main vortex-vortex interactions (VVI) are identified in the flow-field. To estimate the sole effect of LEVs on thrust coefficient, TEVs are eliminated by introducing a splitter plate. This resulted in reduced non-linearity in VVI and facilitated a parametrization of aerodynamic thrust coefficient with key kinematic features, frequency (k) and amplitude (h) [C_T= A.k^1.4 h-B where A and B are constants]. This is followed by investigating the more direct problem of bio-inspired MAV research – the interplay of kinematics, aerodynamics, and inertia on maneuvering bat flights. At first, an ascending right turn of a H. pratti bat is investigated to elucidate on the kinematic features and aerodynamic mechanisms used to effectuate the maneuver. Deceleration in flight speed, an increase in flapping frequency, shortening of the upstroke, and thrust generation at the end of the upstroke is observed during this maneuver. The turn is initiated by the synergisytic implementation of roll and yaw rotation where the turning moments are generated by drawing the inside wing closer to the body, by introducing phase lags in force generation between the two wings and by redirecting force production to the outer part of the wing outside of the turn. Upon comparison with a similar maneuver by a H. armiger bat, some commonalities as well as differences were observed. This analysis was followed by a comparative study among different maneuvering flights (a straight flight, two ascending right turns, and a U-turn) in order to establish the complete motion dynamics of a maneuver in action. The individual effects of aerodynamics and wing inertia for maneuvering flights of a H. armiger and H. pratti are investigated. It is found that for both, translation and rotation the overall trajectory trend is mostly driven by the aerodynamic forces and moments, whereas inertial effects drive the intricate intra-cycle fluctuations as well as the vertical velocity and altitude gain during ascent. Additionally, inertial moments play a dominant role for effecting yaw rotations where the importance of the Coriolis and centrifugal moments increase with increasing acuteness of the maneuver, with the largest effect of centrifugal moments being evidenced in the U-turn. Doctor of Philosophy The study of flapping wing is of paramount interest in the field of small aerial and aquatic vehicle propulsion. The intricate mechanisms acting behind a flapping wing maneuver can be explained by the synergistic roles played by 3 main components; details of the wing motion or the kinematics, how the air reacts to the wing motion or the aerodynamics, and the effort or force required to move the wings or wing inertia. This dissertation systematically reports the contribution of these components to a flapping flight maneuver. At first, the plunging motion of a simple flat plate is investigated as it is a fundamental motion in the flapping flight of many flying animals. A wide range of frequency and amplitude is investigated and their effect is characterized by a single parameter called "plunge velocity". It is found that, the resultant flow field becomes disorderly for higher plunge velocities which can be characterized by three different types of vortex interactions. The observed results facilitated a robust parametrization of aerodynamic thrust production with key kinematic features, frequency and amplitude. After this, the dissertation focuses on the bio-inspiration aspect of flapping flight by investigating the interplay of kinematics, aerodynamics, and inertia of maneuvering bat flights. At first, an ascending right turn of one species (H. pratti) is investigated to elucidate on the kinematic features and aerodynamic mechanisms used to effectuate the maneuver. Some characteristic features observed are – lowering of flight speed, increase in flapping rate, shortening of upstrokes, and generation of a forward force at the end of the upstroke. It is observed, that the bat turns by using synergistic body rotations in multiple directions which are effected by various techniques such as - drawing the wing inside the turn closer to the body, and changing the timing and location of the forces produced between the two wings. Upon comparison with a similar maneuver by a H. armiger bat, some commonalities as well as differences were observed in the maneuver mechanisms. This analysis was followed by a comparative study among different maneuvering flights (a straight flight, two ascending right turns, and a U-turn) to establish the complete motion dynamics of a maneuver. The individual contributions of aerodynamics and wing inertia for maneuvering flights of a H. armiger and H. pratti are investigated. It is found that for both, translation and rotation the overall trajectory is mostly influenced by the aerodynamic forces and moments, whereas inertial effects are responsible for trajectory fluctuations during a flapping cycle as well contributing to altitude gain during ascent for the H. armiger bat.

Aircraft engines are one of the most heavily instrumented parts of an aircraft, and the data from various types of instrumentation across these engines are continuously monitored both offline and online for potential anomalies. Vibration monitoring in aircraft engines is traditionally performed using an order tracking methodology. Currently, there are no representative and efficient physics-based models with the adequate fidelity to perform vibration predictions in aircraft engines, given various parametric dependencies existing among different attributes such as temperature, pressure, and external conditions. This gap in research is primarily attributed to the limited understanding of mutual interactions of different variables and the nonlinear nature of engine vibrations. The objective of the current study is three-fold: (i) to present a preliminary investigation of tracked order vibrations in aircraft engines and statistically analyze them in the context of their operating environment, (ii) to develop data-driven modeling methodology to approximate a dynamical system from input-output data, and (iii) to leverage these data-driven modeling methodologies to develop highly accurate models for tracked order vibration in a turbo-fan engine valid over a wide range of operating conditions. Off-the-shelf data-driven modeling techniques, such as machine learning methods (eg., regression, neural networks), have several drawbacks including lack of interpretability and limited scope, when applying them to a complex multiscale multi-physical dynamical system. Moreover, for dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function, but should also generally approximate the input-output behavior of the data source. The author proposes a novel methodology known as Wavelet-based Dynamic Mode Decomposition (WDMD). The methodology entails using wavelets in conjunction with input-output dynamic mode decomposition (ioDMD). Similar to time-delay embedded DMD (Delay-DMD), WDMD builds on the ioDMD framework without the restrictive assumption of full state measurements. The author demonstrates the present methodology's applicability by modeling the input-output response of an Euler-Bernoulli finite element beam model, followed by an experimental investigation. As a first step towards modeling the tracked order vibration amplitudes of turbofan engines, the interdependencies and cross-correlation structure between various thermo-mechanical variables and tracked order vibration are analyzed. The order amplitudes are further contextualized in terms of their operating regime, and exploratory data analyses are performed to quantify the variability within each operating condition (OC). The understanding of complex correlation structures is leveraged and subsequently utilized to model tracked order vibrations. Switching linear dynamical system (SLDS) models are developed using individual data-driven models constructed using WDMD, and its performance in approximating the dynamics of the $1^{st}$ order amplitudes are compared with the state-of-the-art time-delay embedded dynamic mode decomposition (Delay-DMD) and Lasso regression. A parametric approach is proposed to improve the model further by leveraging previously developed WDMD and Delay-DMD methods and a parametric interpolation scheme. In particular, a recently developed pole-residue interpolation scheme is adopted to interpolate between several linear, data-driven reduced-order models (ROMs), constructed using WDMD and Delay-DMD surrogates, at known parameter samples. The parametric modeling approach is demonstrated by modeling the transverse vibration of an axially loaded finite element (FE) beam, where the axial loading is the parameter. Finally, a parametric modeling strategy for tracked order amplitudes is presented by constructing locally valid ROMs at different parametric samples corresponding to each pass-off test. The performance of the parametric-ROM is quantified and compared with the previous frameworks. This work was supported by the Rolls-Royce Fellowship, sponsored by the College of Engineering, Virginia Tech. Doctor of Philosophy Vibrations in commercial aircraft engines are of utmost importance as they directly translate to aviation health and safety, and hence are continuously monitored both online and offline for potential abnormalities. Notably, this is of increased interest with the abundance of air transportation in today's world. However, there is limited understanding of the complex higher vibration in aircraft engines. Vibration engineers often face ambiguity when interpreting higher vibrations. This can often lead to a lengthy investigative process resulting in longer downtime and increased testbed occupancy, ultimately leading to revenue loss. It is often hypothesized that prior engine running conditions such as shutdown/cooling time between one engine run to another engine run affect the vibration profile. Nonetheless, there exists a gap in understanding tying together various historical operational conditions, temperature, pressures, and current operational conditions with the expected vibration in the engine. This study aims to fill some of these gaps in our understanding by proposing a data-driven strategy to model the vibrations in commercial aircraft engines. Subsequently, this data-driven model can serve as a baseline model to compare the observed vibrations with the model predicted vibration and supplement physics-based models. The data for the present study is generated by operating a commercial turbofan engine in a testbed. With the advent of machine learning and data fusion, various data-driven techniques exist to model dynamical systems. However, the complexity of the turbofan engine vibrations calls for developing new techniques applicable towards modeling the vibration characteristics of a turbofan engine. Specifically, this dissertation details the development of a novel methodology called Wavelet-based Dynamic Mode Decomposition (WDMD) and applies the technique to model input-output characteristics of various dynamical systems ranging from a numerical finite element (FE) beam to an experimental free-free beam to shaft vibrations in a turbofan engine. The study finally presents an improved modeling framework by incorporating the existing techniques with parametric dependencies. This enables the existing method to consider slight differences existing from one engine run to another, such as the history of the engine, the shutdown time, and the outside environmental parameters.

Flaps used in modern aircraft are known to produce high-intensity noise. Their blunt side edges of the wing's flap produce vorticial wakes which are the main contributors to the noise generated. A concept called continuous mold-line (CML) link flap has been studied rigorously for its impact on the acoustic behavior of the wing. These studies found that eliminating the blunt side tips with a continuous mold-line reduces the noise generated by the wing, drastically. However, very few studies have discussed the effects of mold-line shape on its aerodynamic characteristics. Therefore, the objective of this research is to investigate the effect of shape and geometry on the aerodynamics of CML wings. First, the shape of the continuous mold-line is parametrized using a hyperbolic tangent curve. Then, using ANSYS FLUENT a computational model is developed to calculate the lift and drag generated by different CML configurations. Both, inviscid and viscous studies are performed using FLUENT's pressure-based solver. The effect of span and slope at the mid-point of the transition zone are discussed. The study found that the slope at the mid-point of the transition zone does not affect the overall lift generated by the wing. Also, increasing the span of the transition zone initially increases the drag and begins to decrease at higher span lengths. Overall, it was found that the aerodynamic characteristics (such as lift, drag, and efficiency) of the CML wing are better than the conventional blunt tip hinged flap. Master of Science Flaps used in modern aircraft are known to produce high-intensity noise. One of the main contributors to the high-intensity noise is the blunt side edges of the wing's flap. To eliminate the noise produced by the flaps, researchers have come up with a concept called continuous mold-line (CML) link flap. In this concept, we join the flap side edge with the main wing and thus remove the side edges. Studies undertaken till now have mainly focused on the acoustic aspects of the CML wing. Hence, this study focuses on the effect the mold-line shape has on the wing's aerodynamic behavior. The study first discusses a parametric curve that will be used to define the shape of the CML region of the wing. Then, the study calculates the aerodynamic characteristics, such as lift and drag generated by the wing, using the commercial software ANSYS FLUENT. The results obtained by changing the slope at the mid-point and length of the CML region are discussed. Finally, the study presented also compares the aerodynamic characteristics (such as lift, drag, and efficiency) of the CML wing are better than the conventional blunt tip hinged flap.

Ultra-high temperature ceramics (UHTCs) are a class of materials that maintain their structural integrity at high temperatures, e.g. 2000 °C. They have been limited in their aerospace applications because of their relatively high density and the difficulty involved in forming them into complex shapes, like leading edges and inlets. Recent advanced processing techniques have made significant headway in addressing these challenges, where the introduction of multiscale porosity has resulted in lightweight UHTCs dubbed multiscale porous UHTCs. The effect of multiscale porosity on material properties must be characterized to enable design, but doing so experimentally can be costly, especially when attempting to replicate hypersonic flight conditions for relevant testing of selected candidate samples. As such, this dissertation seeks to computationally characterize the thermomechanical properties of multiscale porous UHTCs, specifically titanium diboride, and validate those results against experimental results so as to build confidence in the model. An implicit quasi-static variant of the Material Point Method (MPM) is developed, whose capabilities include intrinsic treatment of large deformations and contact which are needed to capture the complex material behavior of the as-simulated porous UHTC microstructures. It is found that the MPM can successfully obtain the elastic thermomechanical properties of multiscale porous UHTCs over a wide range of temperatures. Furthermore, characterizations of post-elastic behavior are found to be qualitatively consistent with data obtained from uniaxial compression experiments and Brazilian disk experiments. Doctor of Philosophy This dissertation explores a class of materials called ultra-high temperature ceramics (UHTCs). These materials can sustain very high temperatures without degrading, and thus have the potential to be used on hypersonic aircraft which routinely experience high temperatures during flight. In lieu of performing experiments on physical UHTC specimens, one can perform a series of computer simulations to figure out how UHTCs behave under various conditions. This is done here, with a particular focus what happens when pores are introduced into UHTCs, thus rendering them more like a sponge than a solid block of material. Doing computer simulations instead of physical experiments is attractive because of the flexibility one has in a computational environment, as well as the significantly decreased cost associated with running a simulation vs. setting up and performing an experiment. This is especially true when considering challenging operating environments like those experienced by high-speed aircraft. The ultimate goal with this research is to develop a computational tool than can be used to design the ideal distribution of pores in UHTCs so that they can best perform their intended functions.

Due to high specific strength and stiffness as well as outstanding energy-absorption characteristics, sandwich structures are extensively used in aircraft, aerospace, automobile, and marine industries. With the objective of finding lightweight blast-resistant sandwich structures for protecting infrastructure, we have found, for a fixed areal mass density, one- or two-core doubly-curved sandwich shell's (plate's) geometries and materials and fiber angles of unidirectional fiber-reinforced face sheets for it to have the maximum first failure load under quasistatic (blast) loads. The analyses employ a third-order shear and normal deformable plate/shell theory (TSNDT), the finite element method (FEM), a stress recovery scheme (SRS), the Tsai-Wu failure criterion and the Nest-Site selection (NeSS) optimization algorithm, and assume the materials to be linearly elastic. For a sandwich shell under the spatially varying static pressure on the top surface, the optimal non-symmetric one-core (two-core) design improves the first failure load by approximately 33% (27%) and 50% (36%) from the corresponding optimal symmetric design with clamped and simply-supported edges, respectively. For a sandwich plate under blast loads, it is found that the optimal one-core design is symmetric about the mid-surface with thick face sheets, and the optimal two-core design has a thin middle face sheet and thick top and bottom face sheets. Furthermore, the transverse shear stresses (in-plane transverse axial stresses) primarily cause the first failure in a core (face sheet). For the computed optimal design under a blast load, we also determined the collapse load by using the progressive failure analysis that degrades all elasticities of the failed material point to very small values. The collapse load of the clamped (simply-supported) sandwich structure is approximately 15%–30% (0%–17%) higher than its first failure load. Incompressible materials such as rubbers, polymers, and soft tissues that can only undergo volume preserving deformations have numerous applications in engineering and biomedical fields. Their vibration characteristics are important for using them as wave reflectors at interfaces with a fiber-reinforced sheet. In this work we have numerically analyzed free vibrations of plates made of a linearly elastic incompressible rubber-like material (Poison's ratio = 0.5) by using a TSNDT for incompressible materials and the mixed FEM. The displacements at nodes of a 9-noded quadrilateral element and the hydrostatic pressure at four interior nodes are taken as unknowns. Computed results are found to match well with the corresponding either analytical or numerical ones obtained with the commercial FE software Abaqus and the 3-dimensional linear elasticity theory. The analysis discerns plate's in-plane vibration modes. It is found that a simply supported plate admits more in-plane modes than the corresponding clamped and clamped-free plates. Doctor of Philosophy A simple example of a sandwich structure is a chocolate ice cream bar with the chocolate layer replaced by a stiff plate. Another example is the packaging material used to protect electronics during shipping and handling. The intent is to find the composition and the thickness of the "chocolate layer" so that the ice cream bar will not shatter when dropped on the floor. The objective is met by enforcing the chocolate layer with carbon fibers and then finding fiber materials, their alignment, ice cream or core material, and its thickness to resist anticipated loads with a prescribed level of certainty. Thus, a sandwich structure is usually composed of a soft thick core (e.g., foam) bonded to two relatively stiff thin skins (e.g., made of steel, fiber-reinforced composite) called face sheets. They are lightweight, stiff, and effective in absorbing mechanical energy. Consequently, they are often used in aircraft, aerospace, automobile, and marine industries. The load that causes a point in a structure to fail is called its first failure load, and the load that causes it to either crush or crumble is called the ultimate load. Here, for a fixed areal mass density (mass per unit surface area), we maximize the first failure load of a sandwich shell (plate) under static (dynamic) loads by determining its geometric dimensions, materials and fiber angles in the face sheets, and the number (one or two) of cores. It is found that, for a non-uniformly distributed static pressure applied on the central region of a sandwich shell's top surface, an optimal design that has different materials for the top and the bottom face sheets improves the first failure load by nearly 30%-50% from that of the optimally designed structure with identical face sheets. For the structure optimally designed for the first failure blast load, the ultimate failure load with all of its edges clamped (simply supported) is about 15%-30% (0%-17%) higher than its first failure load. This work should help engineers reduce weight of sandwich structures without sacrificing their integrity and save on materials and cost. Rubberlike materials, polymers, and soft tissues are incompressible since their volume remains constant when they are deformed. Plates made of incompressible materials have a wide range of applications in everyday life, e.g., we hear because of vibrations of the ear drum. Thus, accurately predicting their dynamic behavior is important. A first step usually is determining natural frequencies, i.e., the number of cycles of oscillations per second (e.g., a human heart beats at about 1 cycle/sec) completed by the structure in the absence of any externally applied force. Here, we numerically find natural frequencies and mode shapes of rubber-like material rectangular plates with different supporting conditions at the edges. We employ a plate theory that reduces a 3-dimensional (3-D) problem to a 2-D one and the finite element method. The problem is challenging because the incompressibility constraint requires finding the hydrostatic pressure as a part of the problem solution. We show that the methodology developed here provides results that match well with the corresponding either analytical or numerical solutions of the 3-D linear elasticity equations. The methodology is applicable to analyzing the dynamic response of composite structures with layers of incompressible materials embedded in it.

Atmospheric planetary waves play a role in introducing variability to the low-latitude ionosphere. To better understand this coupling, this study investigates times when oscillations seen in both atmospheric planetary waves and ionospheric data-sets have similar periodicity. The planetary wave data-set used are temperature observations made by Sounding of the Atmosphere using Broadband Emission Radiometry (SABER). These highlight periods during which 2-Day westward propagating wave-number 3 waves are evident in the mesosphere and lower thermosphere. The ionospheric data-set is Total Electron Content (TEC), which is used to identify periods during which the ionosphere appears to respond to the planetary waves. Data from KP and F10.7 indices are used to determine events that may be of external origin. A 17-year time-span from 2002 to 2018 is used for this analysis so that both times of solar minimum and maximum can be studied. To extract the periods of this collection of data a Morlet Wavelet analysis is used, along with thresholding to indicate events when similar periods are seen in each data-set. Trends are then determined, which can lead to verification of previous assumptions and new discoveries. Master of Science The thermosphere and ionosphere are impacted by many sources. The sun and the magnetosphere externally impact this system. Planetary waves, which originate in the lower atmosphere, internally impact this system. This interaction leads to periodic signatures in the ionosphere that reflect periodic signatures seen in the lower atmosphere, the sun and the magnetosphere. This study identifies these times of similar oscillations in the neutral atmosphere, the ionosphere, and the sun, in order to characterize these interactions. Events are cataloged through wavelet analysis and thresholding techniques. Using a time-span of 17 years, trends are identified using histograms and percentages. From these trends, the characteristics of this coupling can be concluded. This study is meant to confirm the theory and provide new insights that will hopefully lead to further investigation through modeling. The goal of this study is to gain a better understanding of the role that planetary waves have on the interaction of the atmosphere and the ionosphere.

In this thesis, a continuum sensitivity analysis method is presented for calculation of shape sensitivities of an elastic bar. The governing differential equations and boundary conditions for the elastic bar are differentiated with respect to the shape design parameter to derive the continuum sensitivity equations. The continuum sensitivity equations are linear ordinary differential equations in terms of local or material shape design derivatives, otherwise known as shape sensitivities. One of the novelties of this work is the derivation of three variational formulations for obtaining shape sensitivities, one in terms of the local sensitivity and two in terms of the material sensitivity. These derivations involve evaluating (a) the variational form of the continuum sensitivity equations, or (b) the sensitivity of the variational form of the analysis equations. We demonstrate their implementation for various combinations of design velocity and global basis functions. These variational formulations are further solved using finite element analysis. The order of convergence of each variational formulation is determined by comparing the sensitivity solutions with the exact solutions for analytical test cases. This research focusses on 1-D structural equations. In future work, the three variational formulations can be derived for 2-D and 3-D structural and fluid domains. Master of Science When solving an optimization problem, the extreme value of the performance metric of interest is calculated by tuning the values of the design variables. Some optimization problems involve shape change as one of the design variables. Change in shape leads to change in the boundary locations. This leads to a change in the domain definition and the boundary conditions. We consider a 1-D structural element, an elastic bar, for this study. Subsequently, we demonstrate a method for calculating the sensitivity of solution (e.g. displacement at a point) to change in the shape (length for 1-D case) of the elastic bar. These sensitivities, known as shape sensitivities, are critical for design optimization problems. We make use of continuum analytical shape sensitivity analysis to derive three variational formulations to compute these shape sensitivities. The accuracy and convergence of solutions is verified using a finite element analysis code. In future, the approach can be extended to multi-dimensional structural and fluid domain problems.

In this study, Ritz method has been employed to analyze the following problems: free vibrations of plates with curvilinear stiffeners, the lowest 100 frequencies of thick isotropic plates, free vibrations of thick quadrilateral laminates and free vibrations and static deformations of rectangular laminates, and sandwich structures. Admissible functions in the Ritz method are chosen as a product of the classical Jacobi orthogonal polynomials and weight functions that exactly satisfy the prescribed essential boundary conditions while maintaining orthogonality of the admissible functions. For free vibrations of plates with curvilinear stiffeners, made possible by additive manufacturing, both plate and stiffeners are modeled using a first-order shear deformation theory. For the thick isotropic plates and laminates, a third-order shear and normal deformation theory is used. The accuracy and computational efficiency of formulations are shown through a range of numerical examples involving different boundary conditions and plate thicknesses. The above formulations assume the whole plate as an equivalent single layer. When the material properties of individual layers are close to each other or thickness of the plate is small compared to other dimensions, the equivalent single layer plate (ESL) theories provide accurate solutions for vibrations and static deformations of multilayered structures. If, however, sufficiently large differences in material properties of individual layers such as those in sandwich structure that consists of stiff outer face sheets (e.g., carbon fiber-reinforced epoxy composite) and soft core (e.g., foam) exist, multilayered structures may exhibit complex kinematic behaviors. Hence, in such case, Cz⁰ conditions, namely, piecewise continuity of displacements and the interlaminar continuity of transverse stresses must be taken into account. Here, Ritz formulations are extended for ESL and layerwise (LW) Nth-order shear and normal deformation theories to model sandwich structures with various face-to-core stiffness ratios. In the LW theory, the C⁰ continuity of displacements is satisfied. However, the continuity of transverse stresses is not satisfied in both ESL and LW theories leading to inaccurate transverse stresses. This shortcoming is remedied by using a one-step well-known stress recovery scheme (SRS). Furthermore, analytical solutions of three-dimensional linear elasticity theory for vibrations and static deformations of simply supported sandwich plates are developed and used to investigate the limitations and applicability of ESL and LW plate theories for various face-to-core stiffness ratios. In addition to natural frequency results obtained from ESL and LW theories, the solutions of the corresponding 3-dimensional linearly elastic problems obtained with the commercial finite element method (FEM) software, ABAQUS, are provided. It is found that LW and ESL (even though its higher-order) theories can produce accurate natural frequency results compared to FEM with a considerably lesser number of degrees of freedom. Doctor of Philosophy In everyday life, plate-like structures find applications such as boards displaying advertisements, signs on shops and panels on automobiles. These structures are typically nailed, welded, or glued to supports at one or more edges. When subjected to disturbances such as wind gusts, plate-like structures vibrate. The frequency (number of cycles per second) of a structure in the absence of an applied external load is called its natural frequency that depends upon plate's geometric dimensions, its material and how it is supported at the edges. If the frequency of an applied disturbance matches one of the natural frequencies of the plate, then it will vibrate violently. To avoid such situations in structural designs, it is important to know the natural frequencies of a plate under different support conditions. One would also expect the plate to be able to support the designed structural load without breaking; hence knowledge of plate's deformations and stresses developed in it is equally important. These require mathematical models that adequately characterize their static and dynamic behavior. Most mathematical models are based on plate theories. Although plates are three-dimensional (3D) objects, their thickness is small as compared to the in-plane dimensions. Thus, they are analyzed as 2D objects using assumptions on the displacement fields and using quantities averaged over the plate thickness. These provide many plate theories, each with its own computational efficiency and fidelity (the degree to which it reproduces behavior of the 3-D object). Hence, a plate theory can be developed to provide accurately a quantity of interest. Some issues are more challenging for low-fidelity plate theories than others. For example, the greater the plate thickness, the higher the fidelity of plate theories required for obtaining accurate natural frequencies and deformations. Another challenging issue arises when a sandwich structure consists of strong face-sheets (e.g., made of carbon fiber-reinforced epoxy composite) and a soft core (e.g., made of foam) embedded between them. Sandwich structures exhibit more complex behavior than monolithic plates. Thus, many widely used plate theories may not provide accurate results for them. Here, we have used different plate theories to solve problems including those for sandwich structures. The governing equations of the plate theories are solved numerically (i.e., they are approximately satisfied) using the Ritz method named after Walter Ritz and weighted Jacobi polynomials. It is shown that these provide accurate solutions and the corresponding numerical algorithms are computationally more economical than the commonly used finite element method. To evaluate the accuracy of a plate theory, we have analytically solved (i.e., the governing equations are satisfied at every point in the problem domain) equations of the 3D theory of linear elasticity. The results presented in this research should help structural designers.

This dissertation develops a variety of structure-preserving algorithms for mechanical systems with external forcing and also extends those methods to systems that evolve on non-Euclidean manifolds. The dissertation is focused on numerical schemes derived from variational principles – schemes that are general enough to apply to a large class of engineering problems. A theoretical framework that encapsulates variational integration for mechanical systems with external forcing and time-dependence and which supports the extension of these methods to systems that evolve on non-Euclidean manifolds is developed. An adaptive time step, energy-preserving variational integrator is developed for mechanical systems with external forcing. It is shown that these methods track the change in energy more accurately than their fixed time step counterparts. This approach is also extended to rigid body systems evolving on Lie groups where the resulting algorithms preserve the geometry of the configuration space in addition to being symplectic as well as energy and momentum-preserving. The advantages of structure-preservation in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching. Doctor of Philosophy Accurate numerical simulation of dynamical systems over long time horizons is essential in applications ranging from particle physics to geophysical fluid flow to space hazard analysis. In many of these applications, the governing physical equations derive from a variational principle and their solutions exhibit physically meaningful invariants such as momentum, energy, or vorticity. Unfortunately, most traditional numerical methods do not account for the underlying geometric structure of the physical system, leading to simulation results that may suggest nonphysical behavior. In this dissertation, tools from geometric mechanics and computational methods are used to develop numerical integrators that respect the qualitative features of the physical system. The research presented here focuses on numerical schemes derived from variational principles– schemes that are general enough to apply to a large class of engineering problems. Energy-preserving algorithms are developed for mechanical systems by exploiting the underlying geometric properties. Numerical performance comparisons demonstrate that these algorithms provide almost exact energy preservation and lead to more accurate prediction. The advantages of these methods in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching.

High-speed planing craft operating in waves are subject to frequent water impact, or slamming, as a portion or whole of the craft exits the water and re-enters at high velocity. The global load induced by slamming can cause fatigue-related damages to structures. The local slamming can cause local damage to structures and its induced acceleration can cause damage to equipment and personnel aboard. Therefore the slamming loads in high-speed craft are critical design loads. Nowadays, due to the increasing use of composite materials in high-speed craft, the interaction between the hydrodynamic loading and structural response, or hydroelasticity, must be considered. In this work, a flexible V-shaped wedge, which vertically enters the calm water with an impact velocity, was examined experimentally and numerically to characterize the slamming of a representative cross-section of high-speed craft. Physical quantities of interest include rigid-body kinematic motions, spray root propagation, hydrodynamic loading, and structural response. In the experimental work, with varied impact velocity and flexural rigidity of the wedge bottom plate, a wide range of hydroelasticity factors were investigated. The intersection between the bottom plate and side plate is called chine. The phases before and after the spray root reached the chine are called chine-unwetted and chine-wetted phase, respectively. It was found that the maximum deflection and strain occur in the chine-unwetted phase while a structural vibration with rapidly decaying magnitude is observed in the chine-wetted phase. Furthermore, the kinematic effect of hydroelasticity changes the spray root propagation and hence the pressure, while the inertial effect elongates the natural period of the plate. Inspired by the experimental work, a computational framework was proposed to focus on the chine-unwetted phase. Several hydroelastic models can be obtained from this framework. The hydroelastic models were validated to show reasonable agreement with experiments. Various parameters were studied through the computational framework. The hydroelasticity factor was modified to account for the mass and boundary conditions. It was found that the nondimensional rigid-body kinematic motions and maximum deflection showed little dependence on the hydroelasticity factor. Hydroelastic effects increased the time it takes for the peak maximum deflection to be reached for small values of the hydroelasticity factor. Hydroelastic effects also have little influence on the magnitude of the maximum deflection. These discoveries further the understanding of hydroelastic slamming and show the potential to guide the structural optimization and design of high-speed craft. Doctor of Philosophy High-speed planing craft operating in waves are prone to frequent water impact, or slamming, as a portion or whole of the craft exits the water and re-enters at high velocity. The slamming loads in high-speed craft are critical design loads as the slamming can cause damage to the structures and equipment as well as injure personnel aboard. Nowadays, due to the increasing use of composite materials in high-speed craft, the interaction between the hydrodynamic loading and structural response, or hydroelasticity, must be considered. In this work, a flexible V-shaped wedge entering water is studied experimentally and computationally to characterize the slamming of a representative cross-section of high-speed craft. The contact point between the water surface and the wedge bottom is called the spray root. It was found that the hydrodynamic loading and structural response interact with each other through the spray root. The maximum deflection and strain occur when the wedge bottom is partially submerged while a structural vibration with rapidly decaying magnitude is observed when the wedge bottom is fully submerged. Using the hydroelasticity factor proposed by other researchers, the extent of fluid-structure interaction was quantified. Hydroelastic effects manifest themselves when the hydroelasticity factor is small These discoveries further the understanding of hydroelastic slamming and show the potential to guide the structural optimization and design of high-speed craft.

When designing aircraft wings shapes, it is important to ensure that the flight envelope does not overlap with regions of flutter or Limit Cycle Oscillation (LCO). A quick assessment of these dynamic aeroelastic for various design candidates is key to successful design. Flutter based design requires the sensitivity of flutter parameters to be known with the respect of design parameters. Traditionally, frequency domain based methods have been used to predict flutter characteristics and its sensitivity. However, this approach is only applicable for linear or linearized models and cannot be applied to systems undergoing LCO or other nonlinear effects. Though the time accurate approach can be implemented to overcome this problem, it is computationally expensive. Also, the unsteady adjoint formulation for sensitivity analysis, requires the state and adjoint variables to be stored at every time step, which prohibitively increases the memory requirement. In this work, these problems have been overcome by implementing a time spectral method based approach to compute flutter onset, LCOs and their design sensitivities in a computationally efficient manner. The time spectral based formulation approximates the solution as a discrete Fourier series and directly solves for the periodic steady state, leading to a steady formulation. This can lead to the time spectral approach to be faster than the time accurate approach. More importantly, the steady formulation of the time spectral method also eliminates the memory issues faced by the unsteady adjoint formulation. The time spectral based flutter/LCO prediction method was used to predict flutter and LCO characteristics of the AGARD 445.6 wing and pitch/plunge airfoil section with NACA 64A010 airfoil. Furthermore, the adjoint based sensitivity analysis was used to carry out aerodynamic shape optimization, with an objective of maximizing the flutter velocity with and without constraints on the drag coefficient. The resulting designs show significant increase in the flutter velocity and the corresponding LCO velocity profile. The resulting airfoils display a greater sensitivity to the transonic shock which in turn leads to greater aerodynamic damping and hence leading to an increase in flutter velocity. Doctor of Philosophy When designing aircrafts, dynamic aeroelastic effects such as flutter onset and Limit Cycle Oscillations need to considered. At low enough flight speeds, any vibrations arising in the aircraft structure are damped out by the airflow. However, beyond a certain flight speed, instead of damping out the vibrations, the airflow accentuates these vibrations. This is known as flutter and it can lead to catastrophic structural failure. Hence, during the aircraft design phase, it must be ensured that the aircraft would not experience flutter during the flight conditions. One of the contribution of this work has been to come up with a fast and accurate method to predict flutter using computational modelling. Depending on the scenario, it is also possible that during flutter, the vibrations in the structure increase to a certain amplitude before leveling off due to interaction of non-linear physics. This condition is known as limit cycle oscillation. While they can arise due to different kinds of non-linearities, in this work the focus has been on aerodynamic non-linearities arising from shocks in transonic flight conditions. While limit cycle oscillations are undesirable as they can cause structural fatigue, they can also save the aircraft from imminent structural fracture and hence it is important to accurately predict them as well. The main advantage of the method developed in this work is that the same method can be used to predict both the flutter onset condition and limit cycle oscillations. This is a novel development as most of the traditional approaches in dynamic aeroelasticity cannot predict both the effects. The developed flutter/LCO prediction method has then been used in design with the goal of achieving superior flutter characteristics. In this study, the shape of the baseline airfoil is changed with the goal of increasing the flutter velocity. This enables the designed system to fly faster without addition of weight. Since the design has been carried out using gradient based optimization approach, an efficient way to compute the gradient needs to be used. Traditional approaches to compute the gradient, such as Finite Difference Method, have computational cost proportional to the number of design variables. This becomes a problem for shape design optimization, where a large number of design variables are required. This has been overcome by developing an adjoint based sensitivity analysis method. The main advantage of the adjoint based sensitivity analysis is that it its computational cost is independent of the number of design variables, and hence a large number of design variables can be accommodated. The developed flutter/LCO prediction and adjoint based sensitivity analysis framework was used to carry out shape design for a pitch/plunge airfoil section. The objective of the design process was to maximize the flutter onset velocity with and without constraints on drag. The resulting optimized airfoils showed significant increase in the flutter velocity.

The impressive kinematic capabilities and structural adaptations presented by bio-locomotion continue to inspire some of the advancements in today's small-scaled flying and swimming vehicles. These vehicles operate in a low Reynolds number flow regime where viscous effects dominate flow interactions, which makes it challenging to generate lift and thrust. Overcoming these challenges means utilizing non-conventional lifting and flow control mechanisms generated by unsteady flapping body motion. Understanding and characterizing the aerodynamic phenomena associated with the unsteady motion is vital to predict the unsteady fluid loads generated, to implement control methodologies, and to assess the dynamic stability and control authority of airborne and underwater vehicles. This dissertation presents experimental results for forced oscillations on multi-element airfoils and hydrofoils for Reynolds numbers between Re=104 and Re=106. The document divides the work into four main sections: The first topic presents wind tunnel measurements of lift forces generated by an oscillating trailing edge flap on a NACA-0012 airfoil to illustrate the effects that frequency and pitching amplitude have on lift enhancement. The results suggest that this dynamic trailing edge flap enhances the mean lift by up to 20% in the stalled flow regime. Using frequency response approach, it is determined that the maximum enhancement in circulatory lift amplitude occurs at stalled angles of attack for lower pitching amplitudes. The second topic presents wind tunnel measurements for lift and drag generated by a sinusoidal and non-sinusoidal oscillations of a NACA-0012 airfoil. The results show that 'trapezoidal' pitching enhances the mean lift and the RMS lift by up to 50% and 35% in the pre-stall flow regime, respectively, whereas the 'reverse sawtooth' and sinusoidal pitching generate the most substantial increase of the lift-to-drag ratio in stall and post-stall flow regimes, respectively. The third topic involves a study on the role of fish-tail flexibility on thrust and propulsive efficiency. Flexible tails enhance thrust production in comparison to a rigid ones of the same size and under the same operating conditions. Further analysis indicates that varying the tail's aspect ratio has a more significant effect on propulsive efficiency and the thrust-to-power ratio at zero freestream flow. On the other hand, changing the material's property has the strongest impact on propulsive efficiency at non-zero freestream flow. The results also show that the maximum thrust peaks correspond to the maximum passive tail amplitudes only for the most flexible case. The final topic aims to assess the unsteady hydrodynamic forces and moments generated by a three-link swimming prototype performing different swimming gaits, swimming speeds, and oscillatory frequencies. We conclude that the active actuation of the tail's first mode bending produces the most significant thrust force in the presence of freestream flow. In contrast, the second mode bending kinematics provides the most significant thrust force in a zero-freestream flow. Doctor of Philosophy It is by no surprise that animal locomotion continues to inspire the design of flying and swimming vehicles. Although nature produces complex kinematics and highly unsteady flow characteristics, simplified approximations to model bio-inspired locomotion in fluid flows are experimentally achievable using low degrees of freedom motion, such as pitching airfoils and trailing edge flaps. The contributions of this dissertation are divided into four primary foci: (a) wind tunnel force measurements on a flapped NACA-0012 airfoil undergoing forced pitching, (b) wind tunnel measurements of aerodynamic forces generated by sinusoidal and non-sinusoidal pitching of a NACA-0012 airfoil, (c) towing tank measurements of thrust forces and torques generated by a one-link swimming prototype with varying tail flexibilities, and (d) towing tank measurements of hydrodynamic forces and moments generated by active tail actuation of a multi-link swimming prototype. From our wind tunnel measurements, we determine that lift enhancement by a trailing edge flap is achieved under certain flow regimes and oscillating conditions. Additionally, we assess the aerodynamic forces for a sinusoidal and non-sinusoidal pitching of an airfoil and show that 'trapezoidal' pitching produces the largest lift coefficient amplitude whereas the sinusoidal and 'reverse sawtooth' pitching achieve the best lift to drag ratios. From our towing tank experiments, we note that the role of tail flexibility enhances thrust generation on a swimming device. Finally, we conclude that different kinematics on an articulating body strongly affect the hydrodynamic forces and moments. The results of the towing tank measurements are accessible from an online public database to encourage research and contribution in underwater vehicle design through physics-based low-order models that can accommodate hydrodynamic principles and geometric control concepts.

The NASA Performance Adaptive Aeroelastic Wing (PAAW) project goals include significant reductions in fuel burn, emissions, and noise via efficient aeroelastic design and improvements in propulsion systems. As modern transport airplane designs become increasingly lightweight and incorporate high aspect-ratio wings, aeroservoelastic effects gain prominence in modeling and design considerations. As a result, the influence of the flight dynamics and controls on the optimal structural and aerodynamic design needs to be captured in the design process. There is an increasing interest in more integrated aircraft multidisciplinary design optimization (MDAO) processes that can bring flight control design into the early stage of an aircraft design cycle. So, in this thesis different flight dynamics modeling methodologies are presented that can be integrated within the MDAO framework. MDAO studies are conducted to maximize the controllability and observability of a UAV type aircraft using curvilinear SpaRibs and straight spars and ribs as the internal structural layout. The impulse residues and controllability Gramians are used as surrogates for the control objectives in the MDAO to maximize the controllability and observability of the aircraft. The optimal control designs are compared with those obtained using weight minimization as the design objective. It is found that using the aforementioned control objectives, the resulting aircraft design is more controllable and can be used to expand the flight envelope by up to 50% as compared to the weight minimized design. Doctor of Philosophy Over the last two decades, several attempts have been made towards multidisciplinary design analysis and optimization (MDAO) of flexible wings by integrating flight control laws in the wing design so that the aircraft will have sufficient control authority across different flying conditions. However, most of the studies have been restricted to the wing design only using a predefined control architecture approach, which would be very difficult to implement at the conceptual design stage. There is a need for an approach that would be faster and more practical. Including control surface and control law designs at the conceptual design stage is becoming increasingly important, due to the complexity of both the aircraft control laws and that of the actuation and sensing, and the enhanced wing flexibility of future transport aircraft. A key question that arises is, can one design an aircraft that is more controllable and observable? So, in this thesis, a more fundamental approach, in which the internal structural layout of the aircraft is optimized to design an aircraft that is more controllable, is presented and implemented. The approach uses the fundamentals of linear systems theory for maximizing the controllability and observability of the aircraft using an MDAO framework.

This dissertation focuses on implementing and analyzing advanced methods of model predictive control to control helicopters into stable flight near a ship and perform a soft touchdown from that state. A shrinking horizon model predictive control method is presented which can target specific states at specific times and take into account several important factors during landing. This controller is then used in simulation to perform a touchdown maneuver on a ship for a helicopter by targeting a landed state at a specific time. Increasing levels of fidelity are considered in the simulations. Computational power required reduces the closer the helicopter starts to the landing pad. An infinite horizon model predictive controller which allows simultaneous cost on state tracking, control energy, and control rates and allows tracking of an arbitrary equilibrium to infinity is then presented. It is applied in simulation to control a helicopter initially in a random flight condition far from a ship to slowly transition to stable flight near the ship, holding an arbitrary rough position relative to the ship indefinitely at the end. Three different target positions are simulated. This infinite horizon control method can be used to prepare for landing procedures that desire starting with the helicopter in some specific position in close proximity to the landing pad, such as the finite horizon method of landing control described previously which should start with the helicopter close to the ship to reduce computation power required. A method of constructing a landing envelope is then presented and used to construct a landing envelope for the finite horizon landing controller. A pre-existing method of combining linear controllers to account for nonlinearity is then slightly modified and used on implementations of the finite horizon landing controller to make a control that takes into account some of the nonlinearity of the problem. This control is tested in simulation. Doctor of Philosophy This dissertation proposes and, using simulation, analyzes control algorithms and their use on helicopter shipboard operations. Various benefits and advances for controls in this area are suggested, tested, and discussed. The control methods presented and implemented, while not limited to these use cases, are particularly well suited for them. One control algorithm is used for controlling flight near the landing point on a ship and performing a soft touchdown on the ship. The algorithm is tested in simulation. Another algorithm is used to control a helicopter initially in flight far away from the ship to slowly transition to stable flight near the ship, holding a rough position relative to the ship indefinitely at the end. This control could be used to set up the helicopter for later use of the touchdown control. This control is also tested in simulation. A method of quantifying what conditions the touchdown controller has a relatively good chance of successfully landing in is then suggested. The range of conditions for which successful touchdown has a relatively high chance of being achieved along with an analysis of that likelihood is called the landing envelope. Using the landing envelope construction method with numerous simulations, a landing envelope for the touchdown controller is obtained. The touchdown controller assumes that the helicopter’s dynamics are linear. Helicopter dynamics (like most dynamics of real systems) are nonlinear. However, under conditions near the point that dynamics are linearized about, a linear approximation is sufficiently accurate. To improve on the above landing algorithm, a method of combining multiple specific implementations of the touchdown controller to help account for nonlinearity to improve the approximation of the dynamics that the controller assumes is then suggested and performed in simulation.

This dissertation advances tools for the certification of unmanned aircraft system (UAS) flight controllers. We develop two thrusts to this goal: (1) the validation and improvement of an uncertain UAS framework based on integral quadratic constraint (IQC) theory and (2) the development of novel IQC theorems which allow the analysis of uncertain systems having time-varying characteristics. Pertaining to the first thrust, this work improves and implements an IQC-based robustness analysis framework for UAS. The approach models the UAS using a linear fractional transformation on uncertainties and conducts robustness analysis on the uncertain system via IQC theory. By expressing the set of desired UAS flight paths with an uncertainty, the framework enables analysis of the uncertain UAS flying about any level path whose radius of curvature is bounded. To demonstrate the versatility of this technique, we use IQC analysis to tune trajectory-tracking and path-following controllers designed via H2 or H-infinity synthesis methods. IQC analysis is also used to tune path-following PID controllers. By employing a non-deterministic simulation environment and conducting numerous flight tests, we demonstrate the capability of the framework in predicting loss of control, comparing the robustness of different controllers, and tuning controllers. Finally, this work demonstrates that signal IQCs have an important role in obtaining IQC analysis results which are less conservative and more consistent with observations from flight test data. With regards to the second thrust, we prove a novel theorem which enables robustness analysis of uncertain systems where the nominal plant and the IQC multiplier are linear time-varying systems and the nominal plant may have a non-zero initial condition. When the nominal plant and the IQC multiplier are eventually periodic, robustness analysis can be accomplished by solving a finite-dimensional semidefinite program. Time-varying IQC multipliers are beneficial in analysis because they provide the possibility of reducing conservatism and are capable of expressing uncertainties that have unique time-domain characteristics. A number of time-varying IQC multipliers are introduced to better describe such uncertainties. The utility of this theorem is demonstrated with various examples, including one which produces bounds on the UAS position after an aggressive Split-S maneuver. Doctor of Philosophy This work develops tools to aid in the certification of unmanned aircraft system (UAS) flight controllers. The forthcoming results are founded on robust control theory, which allows the incorporation of a variety of uncertainties in the UAS mathematical model and provides tools to determine how robust the system is to these uncertainties. Such a foundation provides a complementary perspective to that obtained with simulations. Whereas simulation environments provide a probabilistic-type analysis and are oftentimes costly, the following results provide worst-case guarantees—for the allowable disturbances and uncertainties—and require far less computational resources. Here we take two approaches in our development of certification tools for UAS. First we validate and improve on an uncertain UAS framework that relies on integral quadratic constraint (IQC) theory to analyze the robustness of the UAS in the presence of uncertainties and disturbances. Our second approach develops novel IQC theorems that can aid in providing bounds on the UAS state during its flight trajectory. Though the applications in this dissertation are focused on UAS, the theory can be applied to a wide variety of physical and nonphysical problems wherein uncertainties in the mathematical model cannot be avoided.

This thesis presents the design of multifunctional structures through the optimal placement of nanomaterial additives. Varying the concentration of Carbon Nanotubes (CNTs) in a polymer matrix affects its local effective properties, including mechanical stiffness, electrical conductivity, and piezoresistivity. These local properties in turn drive global multifunctional performance objectives. A topology optimization algorithm determines the optimal distribution of CNTs within an epoxy matrix in an effort to design a set of structures that are capable of performing some combination of mechanical, electrical, or peizoresistive functions. A Pareto-Based Restart Method is introduced and may be used within a multi-start gradient based optimization to obtain well defined multiobjective Pareto Fronts. A linear design variable filter is used to limit the influence of checkerboarding. The algorithm is presented and applied to the design of beam cross-sections and 2D plane stress structures. It is shown that tailoring the location of even a small amount of CNT (as low as 2 percent and as high as 10 percent, by volume) can have significant impact on stiffness, electrical conductivity, and strain-sensing performance. Stiffness is maximized by placing high concentrations of CNT in locations that either maximize the bending rigidity or minimize stress concentrations. Electrical conductivity is maximized by the formation of highly conductive paths between electrodes. Strain-sensing is maximized via location of percolation volume fractions of CNTs in high strain areas, manipulation of the strain field to increase the strain magnitude in these areas, and by avoiding negative contributions of piezoresistivity from areas with differing net signed strains. It is shown that the location of the electrodes can affect sensing performance. A surrogate model for simultaneous optimization of electrode and topology is introduced and used to optimize a 2D plane stress structure. This results in a significant increase in sensing performance when compared to the fixed-electrode topology optimization. Ph. D. This dissertation presents a method that allows for the best placement of a limited amount of filler material within a base matrix material to form an optimal composite structure. Adding filler material, in this case Carbon Nanotubes, can change the effective behavior of the composite structure, enhancing the capabilities of the base matrix material by adding structural stiffness, electrical conductivity, and even the ability for the structure to measure its own strains. The degree to which these changes occur is dependent on the amount of filler material present in any given subsection of the structure. The method then is focused on determining how much of the filler to place in different subsections of the structure to maximize several measures of performance. These measures pertain to structural performance, electrical conductivity, and the structure’s ability to sense strains. Steps are taken within the method to remove non-physical designs and also to find the overall best design, called the global minima. The method is applied to several test structures of varying complexity, and it is shown that the optimization method can heavily influence performance by tailoring the filler material distribution. Further electrical and sensing performance gains can be obtained by properly selecting where the electrodes are located on the structure. This is demonstrated by including electrode placement in the design method along with the filler distribution.

This paper presents a framework for tuning, validating, and quantifying uncertainties for flight loads. The flight loads are computed using a Nastran doublet lattice model and are validated using measured data from a flight loads survey for a Cessna Model 525B business jet equipped with Tamarack® Aerospace Group’s active winglet modification, ATLAS® (Active Technology Load Alleviation System). ATLAS® allows for significant aerodynamic improvements to be realized by reducing loads to below the values of the original, unmodified airplane. Flight loads are measured using calibrated strain gages and are used to tune and validate a Nastran doublet-lattice flight loads model. Methods used to tune and validate the model include uncertainty quantification of the Nastran model form and lead to an uncertainty quantified model which can be used to estimate flight loads at any given flight condition within the operating envelope of the airplane. The methods presented herein improve the efficiency of the loads process and reduce conservatism in design loads through improved prediction techniques. Regression techniques and uncertainty quantification methods are presented to more accurately assess the complexities in comparing models to flight test results. Master of Science

This thesis compares three variations of the Bayesian network as an aid for decision-making using uncertain information. After reviewing the basic theory underlying probabilistic graphical models and Bayesian estimation, the thesis presents a user-defined static Bayesian network, a static Bayesian network in which the parameter values are learned from data, and a dynamic Bayesian network with learning. As a basis for the comparison, these models are used to provide a prior assessment of the safety of flight of a small unmanned aircraft, taking into consideration the state of the aircraft and weather. The results of the analysis indicate that the dynamic Bayesian network is more effective than the static networks at predicting safety of flight. Master of Science

This thesis describes the development of a nonlinear flight dynamics model for a small, fixed-wing unmanned aerial vehicle (UAV). Models developed for UAVs can be used for many applications including risk analysis, controls system design and flight simulators. Several challenges exist for system identification of small, low-cost aircraft including an increased sensitivity to atmospheric disturbances and decreased data quality from a cost-appropriate instrumentation system. These challenges result in difficulties in development of the model structure and parameter estimation. The small size may also limit the scope of flight test experiments and the consequent information content of the data from which the model is developed. Methods are presented to improve the accuracy of system identification which include data selection, data conditioning, incorporation of information from computational aerodynamics and synthesis of information from different flight test maneuvers. The final parameter estimation and uncertainty analysis was developed from the time domain formulation of the output-error method using the fully nonlinear aircraft equations of motion and a nonlinear aerodynamic model structure. The methods discussed increased the accuracy of parameter estimates and lowered the uncertainty in estimates compared to standard procedures for parameter estimation from flight test data. The significant contributions of this thesis are a detailed explanation of the entire system identification process tailored to the needs of a small UAV and incorporation of unique procedures to enhance identification results. This work may be used as a guide and list of recommendations for future system identification efforts of small, low-cost, minimally instrumented, fixed-wing UAVs. MS

This dissertation addresses the ultimate strength analysis of nonlinear beam-columns under axial compression, the sensitivity of the ultimate strength, structural optimization and reliability analysis using ultimate strength analysis, and Reliability-Based Design Optimization (RBDO) of the nonlinear beam-columns. The ultimate strength analysis is based on nonlinear beam theory with material and geometric nonlinearities. Nonlinear constitutive law is developed for elastic-perfectly-plastic beam cross-section consisting of base plate and T-bar stiffener. The analysis method is validated using commercial nonlinear finite element analysis. A new direct solving method is developed, which combines the original governing equations with their derivatives with respect to deformation matric and solves for the ultimate strength directly. Structural optimization and reliability analysis use a gradient-based algorithm and need accurate sensitivities of the ultimate strength to design variables. Semi-analytic sensitivity of the ultimate strength is calculated from a linear set of analytical sensitivity equations which use the Jacobian matrix of the direct solving method. The derivatives of the structural residual equations in the sensitivity equation set are calculated using complex step method. The semi-analytic sensitivity is more robust and efficient as compared to finite difference sensitivity. The design variables are the cross-sectional geometric parameters. Random variables include material properties, geometric parameters, initial deflection and nondeterministic load. Failure probabilities calculated by ultimate strength reliability analysis are validated by Monte Carlo Simulation. Double-loop RBDO minimizes structural weight with reliability index constraint. The sensitivity of reliability index with respect to design variables is calculated from the gradient of limit state function at the solution of reliability analysis. By using the ultimate strength direct solving method, semi-analytic sensitivity and gradient-based optimization algorithm, the RBDO method is found to be robust and efficient for nonlinear beam-columns. The ultimate strength direct solving method, semi-analytic sensitivity, structural optimization, reliability analysis, and RBDO method can be applied to more complicated engineering structures including stiffened panels and aerospace/ocean structures. Ph. D.

The goal of this work is to investigate the piezoelectricity of composite laminates embedded with layers of zinc oxide (ZnO) nanowires. ZnO nanowire embedded composites have the potential to sense and actuate giving the potential for these smart composites to serve the function of being load bearing structures and monitoring the integrity of the structure. This work examines the piezoelectric characteristics of composite beams by investigating their electromechanical coupling in the form of vibration under the presence of electrical excitation. With the help of a mathematical model, piezoelectric constants are estimated for these samples. A layer of ZnO nanowires were grown on plane woven fiberglass fabric that was incorporated into a carbon fiber epoxy composite. The beam deflection velocity was measured as a varying voltage was applied to the composite. Using Hamilton's Principle and Galerkin's method of weighted residuals, a mathematical model was derived to estimate piezoelectric constants for the composites from the experimental data. Piezoelectric properties were determined using vibrational testing and a mathematical model. Piezoelectric constants h31, g31, and d31 were estimated to be 9.138 E7 V/m, 6.092 E-4 Vm/N, and 2.46 E-14 respectively. To demonstrate the electromechanical coupling, ZnO nanowire composites were bonded to Al beams that were progressively damaged to determine if a change in electrical impedance could be observed to correspond to the change in structural impedance of the host beam. Changes in impedance were detected by a change in root mean squared deviation damage metric M. A significant correlation was shown between increasing damage in the host beam and an increase in damage metric M. Master of Science

The morphing of aircraft wings for flight control started as a necessity for the Wright Brothers but quickly fell out of favor as aircraft increased speed. Currently morphing aircraft control is one of many ideas being explored as we seek to improve aircraft efficiency, reduce noise, and other alternative aircraft solutions. The conventional hinged control surface took over as the predominant method for control due to its simplicity and allowing stiffer wings to be built. With modern technologies in variable stiffness materials, actuators, and design methods, a morphing control surface, which considers deforming a significant portion of the wing's surface continuously, can be considered. While many have considered morphing designs on the scale of small and medium size UAVs, few look at it for full-size commercial transport aircraft. One promising technology in this field is the flexible matrix composite (FMC) actuator. This muscle-like actuator can be embedded with the deformable structure and unlike many other actuators continue to actuate with the morphing of the structure. This was demonstrated in the FMC active spoiler prototype, which was a full-scale benchtop prototype, demonstrated to perform under closed-loop control for both the required deflection and load cases. Based on this FMC active spoiler concept a morphing aileron design was examined. To do this an analysis coupling the structure, fluid, and FMC actuator models was created. This allows for optimization of the design with the objectives of minimizing the hydraulic energy required and mass of the system by varying the layout of the FMC aileron, the material properties used, and the actuator's design and placement with the morphing section. Based on a commercial transport aircraft a design case was developed to investigate the optimal design of a morphing aileron using the developed analysis tool. The optimization looked at minimizing the mass and energy requirements of the morphing aileron and was subject to a series of constraints developed from the design case and the physical limitations of the system. A Pareto front was developed for these two objectives and the resulting designs along the Pareto front explored. From this optimization, a series of design guidelines were developed. Ph. D.

The rolling of an aircraft about its fuselage produces centrifugal forces which affect the stiffness of the wings. A number of previous studies explain the effect of centrifugal stiffening in rotating beams and consequently on the frequencies of the beam. Multiple cases of the rotating beam are explored in this thesis to investigate effects of mass distribution and boundary conditions on the frequencies of centrifugally stiffened beams. It is found that for a uniform beam with all degrees of freedom free on both ends, the rigid modes of the beam are affected and are no longer zero when it is stiffened from centrifugal forces. This thesis aims to set up a model to investigate the stiffening effects using the mAEWing2 aircraft. A preliminary analysis is done for the mAEWing2 aircraft and the roll rate, control surface deflection and angle of attack are identified as the parameters to be studied. For a given angle of attack and control surface deflection, the centrifugal forces in the aircraft in steady roll are determined using trim analysis. These are used to pre-stress the model for modal analysis. It is found that in mAEWing2 aircraft in steady roll maneuvers, the centrifugal stiffening effect on the natural frequencies is not significant. It emphasizes the need to conduct a sensitivity analysis to include centrifugal stiffening in the dynamic analysis while designing an aircraft. This, along with some de-stiffening due to gravity loads might be important for the future N+3 aircraft with their high aspect ratio large wingspans. MS

Use of Slotted Waveguide Antenna Stiffened Structures (SWASS) in future commercial and military aircraft calls for the development of an airworthiness certification procedure. The first step of this procedure is to provide a computationally low-cost method for modeling waveguide antenna arrays on the scale of an aircraft skin panel using a multi-fidelity model. Weather detection radar for the Northrop Grumman X-47 unmanned air system is considered as a case study. COMSOL Multiphysics is used for creating high-fidelity waveguide models that are imported into the MATLAB Phased Array Toolbox for large-scale array calculations using a superposition method. Verification test cases show that this method is viable for relatively accurate modeling of large SWASS arrays with low computational effort. Additionally, realistic material properties for carbon fiber reinforced plastic (CFRP) are used to create a more accurate model. Optimization is performed on a 12-slot CFRP waveguide to determine the waveguide dimensions for the maximum far-field gain and separately for the maximum critical buckling load. Using the two separate optima as utopia points, a multi-objective optimization for the peak far-field gain and critical buckling load is performed, to obtain a balance between EM performance and structural strength. This optimized waveguide is then used to create a SWASS array of approximately the same size as an aircraft wing panel using the multi-fidelity modeling method that is proposed. This model is compared to a typical conventional weather radar system, and found to be well above the minimum mission requirements. Master of Science

Sandwich Panels with cellular cores are widely used in the aerospace industry for their higher stiffness to mass, strength to mass ratio, and excellent energy absorption capability. Even though, sandwich panels are considered state of the art for lightweight aerospace structures, the requirement to further reduce the mass exists due to the direct impact of mass on mission costs. Traditional manufacturing techniques have limited the shape of the cores to be either hexagonal or rectangular, but, with rapid advancements in additive manufacturing, other core shapes can now be explored. This research aims to identify and evaluate the mechanical performance of two-dimensional cores having standard wall geometry, which provide higher specific stiffness than honeycomb cores. Triangular cores were identified to have higher specific in-plane moduli and equivalent specific out-of-plane and transverse shear moduli. To consider practical use of the triangular cores, elastic and elastic-plastic structural analysis was performed to evaluate the stiffness, strength, failure, and energy absorption characteristics of both the core and sandwich panels. The comparison made between triangular cores and hexagonal cores having the same cell size and relative density showed that triangular cores outperform hexagonal cores in elastic range and for applications where in-plane loading is dominant. Triangular cores also have excellent in-plane energy absorption capabilities at higher densities. Master of Science

Stiffeners attached to composite panels and shells may significantly increase the overall buckling load of the resultant stiffened structure. Initially, an extensive literature review was conducted over the past ten years of published work wherein research was conducted on grid stiffened composite structures and stiffened panels, due to their applications in weight sensitive structures. Failure modes identified in the literature had been addressed and divided into a few categories including: buckling of the skin between stiffeners, stiffener crippling and overall buckling. Different methods have been used to predict those failures. These different methods can be divided into two main categories, the smeared stiffener method and the discrete stiffener method. Both of these methods were used and compared in this thesis. First, a buckling analysis was conducted for the case of a grid stiffened composite pressure vessel. Second, a buckling analysis was conducted under the compressive load on the composite stiffened panels for the case of one, two and three longitudinal stiffeners and then, using different parameters, stiffened panels under combined compressive and shear load for the case of one longitudinal centric stiffener and one longitudinal eccentric stiffener, two stiffeners and three stiffeners. Master of Science

The aviation industry is growing at a steady rate but presently, the industry is highly dependent on fossil fuel. As the world is running out of fossil fuels and the wide-spread acceptance of climate change due to carbon emissions, both the governments and industry are spending a significant amount of resources on research to reduce the weight and hence the fuel consumption of commercial aircraft. A commercial fixed-wing aircraft wing consists of spars which are beams running in span-wise direction, carrying the flight loads and ribs which are panels with holes attached to the spars to preserve the outer airfoil shape of the wing. Kapania et al. at Virginia Tech proposed the concept of reducing the weight of aircraft wing using unconventional design of the internal structure consisting of curvilinear spars and ribs (known as SpaRibs) for enhanced performance. A research code, EBF3GLWingOpt, was developed by the Kapania Group. at Virginia Tech to find the best configuration of SpaRibs in terms of weight saving for given flight conditions. However, this software had a number of limitations and it can only create and analyze limited number of SpaRibs configurations. In this work, the limitations of the EBF3GLWingOpt code has been identified and new algorithms have been developed to make is robust and analyze larger number of SpaRibs configurations. The code also has the capability to create cut-outs in the SpaRibs for passage of fuel pipes and wirings. This new version of the code can be used to find best SpaRibs configuration for multiple objectives such as reduction of weight and increase flutter velocity. The code is developed in Python language and it has parallel computational capabilities. The wing is modeled using commercial FEA software, MSC.PATRAN and analyzed using MSC.NASTRAN which are from within EBF3GLWingOpt. Using this code a significant weight reduction for a transport aircraft wing has been achieved. PHD

Large-aspect-ratio wings and composite structures both have been considered for the next-generation civil transport aircraft to achieve improved aerodynamic efficiency and to save aircraft structural weight. The use of the large-aspect-ratio and the light-weight composite wing can lead to an enhanced flexibility of the aircraft wing, which may cause many aeroelastic problems such as large deflections, increased drag, onset of flutter, loss of control authority, etc. Aeroelastic tailoring, internal structural layout design and aerodynamic wing shape morphing are all considered to address these aeroelastic problems through multidisciplinary design, analysis and optimization (MDAO) studies in this work. Performance Adaptive Aeroelastic Wing (PAAW) program was initiated by NASA to leverage the flexibility associated with the use of the large-aspect-ratio wings and light-weight composite structures in a beneficial way for civil transport aircraft wing design. The biologically inspired SpaRibs concept is used for aircraft wing box internal structural layout design to achieve the optimal stiffness distribution to improve the aircraft performance. Along with the use of the active aeroelastic wing concept through morphing wing shape including the wing jig-shape, the control surface rotations and the aeroelastic tailoring scheme using composite laminates with ply-drop for wing skin design, a MDAO framework, which has the capabilities in total structural weight minimization, total drag minimization during cruise, ground roll distance minimization in takeoff and load alleviation in various maneuver loads by morphing its shape, is developed for designing models used in the PAAW program. A bilevel programming (BLP) multidisciplinary design optimization (MDO) architecture is developed for the MDAO framework. The upper-level optimization problem entails minimization of weight, drag and ground roll distance, all subjected to both static constraints and the global dynamic requirements including flutter mode and free vibration modes due to the specified control law design for body freedom flutter suppression and static margin constraint. The lower-level optimization is conducted to minimize the total drag by morphing wing shape, to minimize wing root bending moment by scheduling flap rotations (a surrogate for weight reduction), and to minimize the takeoff ground roll distance. Particle swarm optimization and gradient-based optimization are used, respectively, in the upper-level and the lower-level optimization problems. Optimization results show that the wing box with SpaRibs can further improve the aircraft performances, especially in a large weight saving, as compared to the wing with traditional spars and ribs. Additionally, the nonuniform chord control surface associated with the wing with SpaRibs achieve further reductions in structural weight, total drag and takeoff ground roll distance for an improved aircraft performance. For a further improvement of the global wing skin panel design, an efficient finite element approach is developed in designing stiffened composite panels with arbitrarily shaped stiffeners for buckling and vibration analyses. The developed approach allows the finite element nodes for the stiffeners and panels not to coincide at the panel-stiffeners interfaces. The stiffness, mass and geometric stiffness matrices for the stiffeners can be transformed to those for the panel through the displacement compatibility at their interfaces. The method improves the feasible model used in shape optimizing by avoiding repeated meshing for stiffened plate. Also, it reduces the order of the finite element model, a fine mesh typically associated with the skin panel stiffened by many stiffeners, for an efficient structural analysis. Several benchmark cases have been studied to verify the accuracy of the developed approach for stiffened composite panel structural analyses. Several parametric studies are conducted to show the influence of stiffener shape/placement/depth-ratio on panel's buckling and vibration responses. The developed approach shows a potential benefit of using gradient-based optimization for stiffener shape design. Ph. D.

With increasing applications of composite materials, their health monitoring is of growing importance in engineering practice. Damage development in composite materials is more complex than for metallic materials, because in composite materials (a) multiple damage modes are simultaneously in play, and (b) individual 'damage events' that occur throughout a component's service life may neither noticeably affect its performance, nor suggest future failure. Therefore, informed health monitoring of composite components must include monitoring and analysis of their health state throughout their service life. A crucial aspect of the health monitoring process of composites is the development of tools to help with this goal of understanding the health state of composites throughout their life. This knowledge can lead to timely anticipation of future failure in composite components, and advance the state of current technology. One, timely maintenance can be planned in advance. Two, each component's service life can be determined based on its individual health information, rather than empirical statistics of previously failed components. This dissertation develops such tools and methods. Composite specimens of multiple ply-layups are subjected to tensile loading schemes until failure. Pencil Lead Breaks (PLBs) are used to simulate Acoustic Emission sources and generate acoustic waves that are acquired by installed piezoelectric sensors. A numerical method to estimate the arrival of wave modes from ultrasonic signals is presented. Methods are also presented that utilize PLB signals to indicate approaching failure of specimens under monotonic as well as cyclic loading. These processes have been developed prioritizing simplicity and ease-of-execution, to be adapted for practical deployment. Ph. D.

It is a common practice when designing a system to apply safety factors to the critical failure load or event. These safety factors provide a buffer against failure due to the random or un-modeled behavior, which may lead the system to exceed these limits. However these safety factors are not directly related to the likelihood of a failure event occurring. If the safety factors are poorly chosen, the system may fail unexpectedly or it may have a design which is too conservative. Reliability-Based Design Optimization (RBDO) is an alternative approach which directly considers the likelihood of failure by incorporating a reliability analysis step such as the First-Order Reliability Method (FORM). The FORM analysis requires the solution of an optimization problem however, so implementing this approach into an RBDO routine creates a double-loop optimization structure. For large problems such as Reliability-Based Topology Optimization (RBTO), numeric sensitivity analysis becomes computationally intractable. In this thesis, a general approach to the sensitivity analysis of nested functions is developed from the Lagrange Multiplier Theorem and then applied to several Reliability-Based Design Optimization problems, including topology optimization. The proposed approach is computationally efficient, requiring only a single solution of the FORM problem each iteration. Master of Science

An important part of an aerodynamic design process is optimizing designs to maximize quantities such as lift and the lift-to-drag ratio, in a process known as shape optimization. It is the goal of this thesis to develop and apply understanding of mixed finite element method and sensitivity analysis in a way that sets the foundation for shape optimization. The open-source Incompressible Flow Iterative Solution Software (IFISS) mixed finite element method toolbox for MATLAB developed by Silvester, Elman, and Ramage is used. Meshes are produced for a backward-facing step problem, using built-in tools from IFISS as well as the mesh generation software Gmsh, and grid convergence studies are performed for both sets of meshes along a sampled data line to ensure that the simulations converge asymptotically with increasing mesh resolution. As a preliminary study of sensitivity analysis, analytic sensitivities of velocity components along the backward-facing step data line to inflow velocity parameters are determined and verified using finite difference and complex step sensitivity values. The method is then applied to pressure drag calculated by integrating the pressure over the surface of a circular cylinder in a freestream flow, and verified and validated using published simulation data and experimental data. The sensitivity analysis study is extended to shape optimization, wherein the shape of a circular cylinder is altered and the sensitivities of the pressure drag coefficient to the changes in the cylinder shape are determined and verified. Master of Science

Spacecraft structures rely on honeycomb panels to provide a light weight means to support the vehicle. Honeycomb panels can carry significant load but are most vulnerable to structural failure at their joints where panels connect. This research shows that predicting sandwich panel joint capability using finite element analysis (FEA) is possible. This allows for the potential elimination of coupon testing early in a spacecraft design program to determine joint capability. Linear finite element analysis (FEA) in NX Nastran was used to show that adhesive failure can be predicted with reasonable accuracy by including a fillet model on the edge of the fitting. Predicting the ultimate failure of a joint using linear FEA requires that engineering judgment be used to determine whether failure of certain bonds in a fitting will lead to ultimate joint failure or if other bonds will continue to carry the joint's load. The linear FEA model is also able to predict when the initiation of core failure will begin. This has the limitation that the joint will still be able to continue to carry significantly more load prior to joint ultimate failure even after the core has begun to buckle. A nonlinear analysis is performed using modified Riks' method in Abaqus FEA to show that this failure mode is predictable. The modified Riks' analysis showed that nonlinear post-buckling analysis of a honeycomb coupon can predict ultimate core failure with good accuracy. This solution requires a very high quality mesh in order to continue to run after buckling has begun and requires imperfections based on linear buckling mode shapes and thickness tolerance on the honeycomb core to be applied. Master of Science

Many futuristic aircraft such as the Hybrid Wing Body have numerous control surfaces that can result in large hinge moments, high actuation power demands, and large actuator forces/moments. Also, there is no unique relationship between control inputs and the aircraft response. Distinct sets of control surface deflections may result in the same aircraft response, but with large differences in actuation power. An Artificial Neural Network and a Genetic Algorithm were used here for the control allocation optimization problem of a Hybrid Wing Body to minimize the Sum of Absolute Values of Hinge Moments for a 2.5-G pull-up maneuver. To test the versatility of the same optimization process for different aircraft configurations, the present work also investigates its application on the Forward Swept Wing aircraft. A method to improve the robustness of the process is also presented. Constraints on the load factor and longitudinal pitch rate were added to the optimization to preserve the trim constraints on the control deflections. Another method was developed using stability derivatives. This new method provided better results, and the computational time was reduced by two orders of magnitude. A hybrid scheme combining both methods was also developed to provide a real-time estimate of the optimum control deflection schedules to trim the airplane and minimize the actuation power for changing flight conditions (Mach number, altitude and load factor) in a pull-up maneuver. Finally, the stability derivatives method and the hybrid scheme were applied for an antisymmetric, steady roll maneuver. Master of Science

The excellent in-plane strength and stiffness to-weight ratios, as well as the ease of manufacturing have made the carbon fiber reinforced polymer composites (CFRPs) suitable structural materials for variety of applications such as aerospace, automotive, civil, sporting goods, etc. Despite the outstanding performance of the CFRPs along their fibers direction (on-axis), they lack sufficient strength and performance in the out-of-plane and off-axis directions. Various chemical and mechanical methods were reported to enhance the CFRPs' out-of-plane performance. However, there are two major drawbacks for utilizing these approaches: first, most of these methods induce damage to the carbon fibers and, therefore, deteriorate the in-plane mechanical properties of the entire CFRP, and second, the methods with minimal deteriorating effects on the in-plane mechanical performance have their own limitations resulting in very confined mechanical performance improvements. These methods include integrating nano-sized reinforcements into the CFRPs' structure to form a hybrid or hierarchical CFRPs. In lieu to all the aforementioned approaches, a relatively novel method, referred to as graphitic structures by design (GSD), has been proposed. The GSD is capable of grafting carbon nanotubes (CNTs) onto the carbon fibers surfaces, providing high concentration of CNTs where they are most needed, i.e. the immediate fiber/matrix interface, and in-between the different laminae of a CFRP. This method shows promising improvements in the in-plane and out-of-plane performance of CFRPs. Zinc oxide (ZnO) nanorods are other nano-sized reinforcing structures which can hybridize the CFRPs via their radially growth on the surface of carbon fibers. Among all the reported methods for synthesizing ZnO nanorods, hydrothermal technique is the most straightforward and least destructive route to grow ZnO nanorods over carbon fibers. In this dissertation, the GSD-CNTs growth method and the hydrothermal growth of ZnO nanorods have been utilized to fabricate hybrid CFRPs. The effect of different ZnO nanorods growth morphologies, e.g. size distribution and alignment, on the in-plane tensile performance and vibration attenuation capabilities of the hybrid CFRPs are investigated via quasi-static tension and dynamical mechanical analysis (DMA) tests, respectively. As a result, the in-plane tensile strength of the hybrid CFRPs were improved by 18% for the composite based on randomly oriented ZnO nanorods over the carbon fibers. The loss tangent of the CFRPs, which indicates the damping capability, increased by 28% and 19% via radially and randomly grown ZnO nanorods, respectively. While there are several studies detailing the effects of dispersed nanofillers on the fracture toughness of FRPs, currently, there are no literature detailing the effect of surface GSD grown CNTs and ZnO nanowire -on carbon fiber- on the fracture toughness of these hybrid composites. This dissertation probes the effects of surface grown nano-sized reinforcements on the fracture toughness via double cantilever beam (DCB) tests on hybrid ZnO nanorod or CNT grafted CFRPs. Results show that the surface grown CNTs enhanced the Mode I interlaminar fracture toughness (GIc) of the CFRPs by 22% and 32%, via uniform and patterned growth morphologies, respectively, over the reference composite based on untreated carbon fiber fabrics. The dissertation also explains the basis of the improvements of the fracture toughness via finite element method (FEM). In particular, FEM was employed to simulate the interlaminar crack growth behavior of the hybrid CFRPs under Mode I crack opening loading conditions embodied by the DCB tests. These simulations revealed that the hybrid CFRP based on fibers with uniform surface grown MWCNTs exhibited 55% higher interlaminar strength compared to the reference CFRPs. Moreover, via patterned growth of MWCNTs, the ultimate crack opening resistance of the CFRPs improved by 20%. To mimic the experimental behavior of the various CFRPs, a new methodology has been utilized to accurately simulate the unstable crack growth nature of CFRPs. Several investigations reported the effects of adding nanomaterials-including CNTs- as a filler phase inside the matrix material, on the impact energy absorption of the hybrid FRPs. However, the impact mitigation performance of CFRPs based on ZnO nanorod grafted carbon fibers has not been reported. The dynamic out-of-plane energy dissipation capabilities of different hybrid composites were investigated utilizing high velocity (~90 m/s) impact tests. Comparing the results of the hybrid MWCNT/ZnO nanorod/CFRP with those of reference CFRP, 21% and 4% improvements were observed in impact energy absorption and tensile strain to failure of the CFRPs, respectively. In addition to elevated stiffness and strength, CFRPs should possess enough tolerance not only to monotonic loadings, but also to cyclic loadings to be qualified as alternatives to traditional structural metal alloys. Therefore, the fatigue life of CFRPs is of much interest. Despite the promising potential of incorporating nano-sized reinforcements into the CFRPs structure, not many studies reported on the fatigue behavior of hybrid CFRPs so far. In particular, there are no reported investigations to the effect of surface grown CNTs on the fatigue behavior of the hybrid CFRPs, due to fact that almost all the CNT growth techniques (except for the GSD method) deteriorated the in-plane performance of the hybrid CFRPs. The hybrid ZnO nanorod grafted CFRPs have not been investigated under fatigue loading as well. In this dissertation, different hybrid CFRPs were tested under tension-tension fatigue to reveal the effects of the different nano-reinforcements growth on the fatigue behavior of the CFRPs. A remarkable fatigue damage tolerance was observed for the CFRPs based on uniform and patterned grown CNT fibers. Almost two decades of fatigue life extension was achieved for CFRPs based on surface grown MWCNTs. Ph. D.

This dissertation addresses model form uncertainty quantification, non-deterministic simulations, and sensitivity analysis of the results of these simulations, with a focus on application to analysis of unmanned aircraft systems. The model form uncertainty quantification utilizes equation error to estimate the error between an identified model and flight test results. The errors are then related to aircraft states, and prediction intervals are calculated. This method for model form uncertainty quantification results in uncertainty bounds that vary with the aircraft state, narrower where consistent information has been collected and wider where data are not available. Non-deterministic simulations can then be performed to provide uncertainty quantified estimates of the system performance. The model form uncertainties could be time varying, so multiple sampling methods were considered. The two methods utilized were a fixed uncertainty level and a rate bounded variation in the uncertainty level. For analysis using fixed uncertainty level, the corner points of the model form uncertainty were sampled, providing reduced computational time. The second model better represents the uncertainty but requires significantly more simulations to sample the uncertainty. The uncertainty quantified performance estimates are compared to estimates based on flight tests to check the accuracy of the results. Sensitivity analysis is performed on the uncertainty quantified performance estimates to provide information on which of the model form uncertainties contribute most to the uncertainty in the performance estimates. The proposed method uses the results from the fixed uncertainty level analysis that utilizes the corner points of the model form uncertainties. The sensitivity of each parameter is estimated based on corner values of all the other uncertain parameters. This results in a range of possible sensitivities for each parameter dependent on the true value of the other parameters. Ph. D.

The main purpose of this thesis is to develop a beam element in order to model the wing of a drone, made of composite materials. The proposed model consists of the framework for the structural design and analysis of long slender beam like structures, e.g., wings, wind turbine blades, and helicopter rotor blades, etc. The main feature consists of the addition of the coupling between axial and bending with torsional effects that may arise when using composite materials and the coupling stemming from the inhomogeneity in cross-sections of any arbitrary geometry. This type of modeling approach allows for an accurate yet computationally inexpensive representation of a general class of beam-like structures. The framework for beam analysis consists of main two parts, cross-sectional analysis of the beam sections and then using this section analysis to build up the finite element model. The cross-sectional analysis is performed in order to predict the structural properties for composite sections, which are used for the beam model. The thesis consists of the model to validate the convergence of the element size required for the cross-sectional analysis. This follows by the validation of the shell models of constant cross-section to assess the performance of the beam elements, including coupling terms. This framework also has the capability of calculating the strains and displacements at various points of the cross-section. Natural frequencies and mode shapes are compared for different cases of increasing complexity with those available in the papers. Then, the framework is used to analyze the wing of a drone and compare the results to a model developed in NASTRAN. Master of Science

A high-order hybrid discontinuous Galerkin finite element method (DG-FEM) is developed for multi-layered curved panels having large deformation and finite strain. The kinematics of the multi-layered shells is presented at first. The Jacobian matrix and its determinant are also calculated. The weak form of the DG-FEM is next presented. In this case, the discontinuous basis functions can be employed for the displacement basis functions. The implementation details of the nonlinear FEM are next presented. Then, the Consistent Orthogonal Basis Function Space is developed. Given the boundary conditions and structure configurations, there will be a unique basis function space, such that the mass matrix is an accurate diagonal matrix. Moreover, the Consistent Orthogonal Basis Functions are very similar to mode shape functions. Based on the DG-FEM, three dedicated finite elements are developed for the multi-layered pipes, curved stiffeners and multi-layered stiffened hydrofoils. The kinematics of these three structures are presented. The smooth configuration is also obtained, which is very important for the buckling analysis with large deformation and finite strain. Finally, five problems are solved, including sandwich plates, 2-D multi-layered pipes, 3-D multi-layered pipes, stiffened plates and stiffened multi-layered hydrofoils. Material and geometric nonlinearities are both considered. The results are verified by other papers' results or ANSYS. Master of Science

The aerodynamic behavior of wind tunnels with porous, flexible walls formed from tensioned Kevlar has been characterized and new measurement techniques in such wind tunnels explored. The objective is to bring the aerodynamic capabilities of so-called Kevlar-wall test sections in-line with those of traditional solid-wall test sections. The primary facility used for this purpose is the 1.85-m by 1.85-m Stability Wind Tunnel at Virginia Tech, and supporting data is provided by the 2-m by 2-m Low Speed Wind Tunnel at the Japanese Aerospace Exploration Agency, both of which employ Kevlar-wall test sections that can be replaced by solid-wall test sections. The behavior of Kevlar fabric, both aerodynamically and mechanically, is first investigated to provide a foundation for calculations involving wall interference correction and determination of the boundary conditions at the Kevlar wall. Building upon previous advancements in wall interference corrections for Kevlar-wall test sections, panel method codes are then employed to simulate the wind tunnel flow in the presence of porous, flexible Kevlar walls. An existing two-dimensional panel method is refined by examining the dependency of correction performance on key test section modeling assumptions, and a novel three-dimensional method is presented. Validation of the interference corrections, and thus validation of the Kevlar-wall aerodynamic performance, is accomplished by comparing aerodynamic coefficients between back-to-back tests of models carried out in the solid- and Kevlar-wall test sections. Analysis of the test results identified the existence of three new mechanisms by which Kevlar walls cause wall-interference. Additionally, novel measurements of the boundary conditions are made during the Kevlar-wall tests to characterize the flow at the boundary. Specifically, digital image correlation is used to measure the global deformation of the Kevlar walls under wind loading. Such data, when used in conjunction with knowledge of the pre-tension in the Kevlar wall and the material properties of the Kevlar, yields the pressure loading experienced by the wall. The pressure loading problem constitutes an inverse problem, and significant effort is made towards overcoming the ill-posedness of the problem to yield accurate wall pressure distributions, as well as lift measurements from the walls. Taken as a whole, this document offers a comprehensive view of the aerodynamic performance of Kevlar-wall test sections. Ph. D.

The method of Continuum Sensitivity Analysis (CSA) with Spatial Gradient Reconstruction (SGR) is presented for calculating the sensitivity of fluid, structural, and coupled fluid-structure (aeroelastic) response with respect to shape design parameters. One of the novelties of this work is the derivation of local CSA with SGR for obtaining flow derivatives using finite volume formulation and its nonintrusive implementation (i.e. without accessing the analysis source code). Examples of a NACA0012 airfoil and a lid-driven cavity highlight the effect of the accuracy of the sensitivity boundary conditions on the flow derivatives. It is shown that the spatial gradients of flow velocities, calculated using SGR, contribute significantly to the sensitivity transpiration boundary condition and affect the accuracy of flow derivatives. The effect of using an inconsistent flow solution and Jacobian matrix during the nonintrusive sensitivity analysis is also studied. Another novel contribution is derivation of a hybrid adjoint formulation of CSA, which enables efficient calculation of design derivatives of a few performance functions with respect to many design variables. This method is demonstrated with applications to 1-D, 2-D and 3-D structural problems. The hybrid adjoint CSA method computes the same values for shape derivatives as direct CSA. Therefore accuracy and convergence properties are the same as for the direct local CSA. Finally, we demonstrate implementation of CSA for computing aeroelastic response shape derivatives. We derive the sensitivity equations for the structural and fluid systems, identify the sources of the coupling between the structural and fluid derivatives, and implement CSA nonintrusively to obtain the aeroelastic response derivatives. Particularly for the example of a flexible airfoil, the interface that separates the fluid and structural domains is chosen to be flexible. This leads to coupling terms in the sensitivity analysis which are highlighted. The integration of the geometric sensitivity with the aeroelastic response for obtaining shape derivatives using CSA is demonstrated. Ph. D.

The thermal efficiency of a gas turbine directly depends on the rotor inlet temperature. The ever increasing demand for more power and advances in the field of engineering enabled this temperature to be pushed higher. But the material strength of the blades and vanes can often impose restrictions on the thermal load it can bear. This is where gas turbine cooling becomes very critical and a better cooling design has the potential to extend the blade life span, enables higher rotor inlet temperatures, conserves compressor bleed air. Among various kinds of cooling involved in gas turbines, film cooling will be the subject of this study. A novel concept for film cooling holes referred to as anti-vortex design proposed in 2007 is explored in this study. Coolant exits through two bifurcated cylindrical holes that branched out on either side of the central hole resulting in a tripod-like arrangement. Coolant from the side holes interacted with the mainstream and produced vortices that countered the main central rotating vortex pairs, weakening it and pushing the coolant jet towards the surface. In order to understand the performance of this anti-vortex tripod film cooling, a flat plate test setup and a low speed subsonic wind tunnel linear cascade were built. Transient heat transfer experiments were carried out in the flat plate test setup using Infrared thermography. Film cooling performance was quantified by measuring adiabatic effectiveness and heat transfer coefficient ratio. In order to gauge the performance, other standard hole geometries were also tested and compared with. Following the results from the flat plate test rig, film cooling performance was also evaluated on the surface of an airfoil. Adiabatic effectiveness was measured at different coolant mass flow rates. The tripod hole consistently provided better cooling compared to the standard cylindrical hole in both the flat plate and cascade experiments. In order to understand the anti-vortex concept which is one of the primary reason behind better performance of the tripod film cooling hole geometry, numerical simulations (CFD) were carried out at steady state using RANS turbulence models. The interaction of the coolant from the side holes with the mainstream forms vortices that tries to suppress the vortex formed by the central hole. This causes the coolant jet from the central to stay close to the surface and increases its coverage. Additionally, the coolant getting distributed into three individual units reduces the exit momentum ratio. Tripod holes were found to be capable of providing better effectiveness even while consuming almost half the coolant used by the standard cylindrical holes. Ph. D.