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This thesis presents an approximate method for analysis of dense spaceframes. The approach is based on transforming a dense spaceframe into a similar structure with lower density. The reduced structure is analysed in the usual manner and the results are employed to obtain an approximation to the behaviour of the actual structure. To assess the accuracy and limitations of the proposed method, a number of practical examples are analysed. The influence of irregularity of loading and support conditions have also been investigated. A comparison of the results obtained by the method with those obtained by the exact analysis has shown that the accuracy of the method is satisfactory for design purposes. In generating data and organising graphical output for the examples, the concept of formex algebra together with its programming language Formian have been utilised. The application of the method has been extended to composite spaceframes, consisting of skeleton double layer grids combined with concrete slabs. The proposed method is a natural engineering approach. It preserves almost all the particulars of the original structure but allows the analysis to be performed with much smaller systems of simultaneous equations. The method has the potential of being extended in many directions for analysis of other space structures. Also, it would be of interest to extend the idea to the dynamic response calculations and non-linear analysis of spaceframes.

Traveling to space requires a great deal of energy. This then limits the size of spacecraft accessible to transport to space. An optimization of a flexible tube that could be used as a satellite deployable structure was conducted by varying the cross section of the tube and its composite material properties. The material properties manipulated include the selection of a fiber, matrix, filler volume ratio, and orientation. HEEDS, a commercially available software, conducts the optimization process using the SHERPA algorithm. In the optimization, the finite element code, ABAQUS, iteratively performs two simulations. First, ABAQUS determines the stress distribution along the tube when wrapping the tube in its stored configuration. Second, ABAQUS finds the first natural frequency of the deployed structure. The objective function driving the optimization process is minimizing the weight and strain energy of the tube to create a light but highly flexible tube. This provides benefits of avoiding a violent deployment and lowering the dynamic response of the spacecraft during deployment. Three optimizations were performed with 1000 iterations each, using different initial geometries. While all three produce very similar results, one design converges to a clear best result. Using the best design, a series of deployment simulations are performed, using different boundary conditions to represent various scenarios. These boundary conditions include a free body dynamic response to deployment, a restricted response to only allow for rotation about the direction of deployment, and an increased damping deployment. Energy is dissipated differently comparing the results, showing that the most realistic case, being a free body deployment, has the lowest effect on the system. The spacecraft can dissipate energy by oscillating in the other axis. While damping does reduce the settling time for the deployed tube, there is notable oscillation in the middle of the tube seen in the transient state. / Master of Science / The size and weight of a spacecraft is important when considering its feasibility to launch to space. By creating a spacecraft that can be stowed in a small configuration and deploy, new parameters arise, thus new designs can be created. This paper observes using different shapes and materials to create an expandable tube, providing a support structure for a satellite or spacecraft. HEEDS, an optimization software, uses the SHERPA code to select the shape of the cross section and create a composite material. Composite material selection is comprised of a fiber, a matrix, a filler volume ratio, and an angle for the fibers to lay at. After selecting these parameters, HEEDS calls a finite element software, ABAQUS, to perform two simulations. The first simulation wraps the tube around a central hub and observes stress at each timestep. The second simulation finds the first mode of natural frequency of the deployed model. Using user defined constraints that revolve around the safety factor of the stress and minimum frequency, each iteration is marked as feasible or infeasible. An objective function is used to evaluate the best design. This paper focuses on minimizing the weight of the tube and the strain energy inside of the objective function. By minimizing the strain energy, the tube will deploy less violently and cause less rotation due to deployment. HEEDS performs 1000 iterations on three different initial geometry. While there are similar defining factors of each final design, there is one design that is better than the other two. Using the best design, ABAQUS runs three different deployment simulations to observe the deployment behavior. These scenarios encompass different dynamic simulations and show that a realistic deployment where the spacecraft is free to rotate on all axis is safe.

The Canadian Nanosatellite Advanced Propulsion System is the second generation cold-gas propulsion system. Its purpose is to provide the millinewton thrust required for formation control of nanosatellites, in particular the CanX-4/-5 formation flying mission. Additionally, to inject nanosatellites into orbit, a reliable and robust deployer is needed to bridge the gap between the launch vehicle and space. This bridge is the XPOD, the eXoadaptable PyrOless Deployer. Both of these technologies are designed and developed by the Space Flight Lab. This thesis describes the assembly, integration and preliminary testing of the CanX-4/-5 propulsion system. Emphasis is placed on the phases involved with the assembly and integration while highlighting the problems encountered and lessons learned. In addition, the mechanical analysis of the XPOD as well as its assembly and testing is described in detail.

The Canadian Nanosatellite Advanced Propulsion System is the second generation cold-gas propulsion system. Its purpose is to provide the millinewton thrust required for formation control of nanosatellites, in particular the CanX-4/-5 formation flying mission. Additionally, to inject nanosatellites into orbit, a reliable and robust deployer is needed to bridge the gap between the launch vehicle and space. This bridge is the XPOD, the eXoadaptable PyrOless Deployer. Both of these technologies are designed and developed by the Space Flight Lab. This thesis describes the assembly, integration and preliminary testing of the CanX-4/-5 propulsion system. Emphasis is placed on the phases involved with the assembly and integration while highlighting the problems encountered and lessons learned. In addition, the mechanical analysis of the XPOD as well as its assembly and testing is described in detail.

Deployable structures are used for many different spacecraft applications like solar arrays, antennas, and booms. They allow spacecraft with large structural components to comply with the volume restrictions of launch platforms. This research optimizes the shape and size of these structural components with both the stowed and deployed configurations in mind. HEEDS, a commercial optimization software, and ABAQUS, a commercial finite element analysis software, are used to evaluate and alter the structure using a single simulation. This makes the design process more efficient than running many different simulations individually. The optimization objectives, design variables, and constraints are chosen to fit the mission requirements of the structure. The structure analyzed in this research is a composite tube with a compressible cross-section wrapped around a cylinder. The change in cross-section reduces the bending stiffness of the tube and allows it to be wrapped without damaging the material. The dimensions controlling cross-section shape and the thickness of the composite layers are the design variables for the optimization. The maximum strain energy stored in the wrapped tube, the minimum volume of the structure, and the minimum weight of the tube are the objectives for the optimization. The strain energy is maximized to get the stiffest possible structure and satisfy the minimum natural frequency constraint. The weight and volume of the tube are minimized because reducing weight and volume is important for any spacecraft structure. Constraints are placed on the design variables and objectives and the Hashin damage criteria are used to ensure wrapping does not cause material failure. Three optimization runs from different initial designs are completed using SHERPA and genetic algorithm optimization methods. The results are compared to determine which optimization method performs best and how the different starting points affect the final results. After the optimized design is found, the full wrapping and deployment simulation is completed to analyze the behavior of the optimized design. / Master of Science / Spacecraft are launched into space using launch vehicles. There is limited room inside the launch vehicle for the spacecraft, but the spacecraft often needs large components like solar panels, antennas, and booms to complete the mission. These components must be designed in a way that allows them to be stowed in a smaller space. This can be accomplished by designing a system that can change the configuration of the component once the spacecraft is in orbit. This is referred to as a deployable structure, and the objective of this research is to create an optimization method for designing this type of structure. This is challenging because both the stowed and deployed configurations must be considered during the optimization. HEEDS, a commercial optimization software, and ABAQUS, a commercial structural analysis software, are used to evaluate and optimize the structure in a single simulation. The optimization objectives, design variables, and constraints are chosen to fit the mission requirements of the structure. The structure examined in this research is a composite tube with a compressible cross-section wrapped around a cylinder. As the tube is wrapped, it flattens, reducing the bending stiffness so the tube can be wrapped without damaging the material. The variables controlling cross-section shape and the thickness of the composite material layers will be altered during the optimization. The maximum strain energy stored in the wrapped tube, the volume of the tube, and the minimum weight of the tube are the objectives for the optimization. The strain energy is maximized to get the stiffest possible tube when it is unwrapped to ensure there is enough stored energy to facilitate the full deployment and to satisfy the minimum natural frequency constraint. The weight and volume of the tube are minimized because reducing weight and volume is important for any spacecraft structure. Constraints are placed on the design variables and objectives and the Hashin damage criteria are used to ensure wrapping does not cause material failure. The Hashin damage criteria use the strength of the material and the stresses on the material to determine if it is likely to fail. Three optimization runs with different starting points are completed for both the SHERPA and genetic algorithm optimization methods. The results are compared to determine which optimization method performs best and how the different starting points affect the final results. After the optimized design is found, the full wrapping and deployment simulation is completed to analyze the behavior of the optimized design.

Linking the structure of a system with its dynamics is an important problem in the theory of finite dynamical systems. For monomial dynamical systems, that is, a system that can be described by monomials, information about the limit cycles can be obtained from the monomials themselves. In particular, this work contains sufficient and necessary conditions for a monomial dynamical system to have only fixed points as limit cycles. / Ph. D.

This dissertation presents useful nonlinear models for fluid forcing on a moving body in two distinct contexts, and methods for analyzing the geometric structure within those and other mathematical models. This manuscript style dissertation presents three works within the theme of understanding fluid forcing and geometric structure. When a bluff body is free to move in the presence of an incoming bluff body wake, the average forcing on the body is dependent on its position relative to the upstream bluff body. This position-dependent forcing can be conceptualized as a stiffness, much like a spring. This work presents an updated model for the quasi-steady fluid forcing of a wake and extends the notion of wake stiffness to consider a nonlinear spring. These results are compared with kinematic experimental results to provide an example of the application of this framework. Fluid force models also play a role in understanding the behavior of passive aerodynamic gliders, such as gliding animals or plant material. The forces a glider experiences depend on the angle that its body makes with respect to its direction of motion. Modeling the glider as capable of pitch control, this work considers a glider with a fixed angle with respect to the ground. Within this model, all trajectories in velocity space collapse to a 1-dimensional invariant manifold known as the terminal velocity manifold. This work presents methods to identify the terminal velocity manifold, investigates its properties, and extends it to a 2-dimensional invariant manifold in a 3-dimensional space. Finally, in the search for manifolds such as the terminal velocity manifold, this dissertation introduces a new diagnostic for identifying the low dimensional geometric structure of models. The trajectory divergence rate uses instantaneous vector field information to identify regions of large normal stretching and strong normal convergence between nearby invariant manifolds. This work lays out the mathematical basis of the trajectory divergence rate and shows its application to approximate a variety of structures including slow manifolds and Lagrangian coherent structures. This dissertation applies nonlinear theoretical and numerical techniques to analyze models of fluid forcing and their geometric structure. The tools developed in this dissertation lay the groundwork for future research in the fields of flow-induced vibration, plant and animal biomechanics, and dynamical systems. / Ph. D. / When an object moves through a fluid such as air or water, the motion of the surrounding fluid generates forces on the moving object, affecting its motion. The moving object, in turn, affects the motion of the surrounding fluid. This interaction is complicated, nonlinear, and hard to even simulate numerically. This dissertation aims to analyze simplified models for these interactions in a way that gives a deeper understanding of the physics of the interaction between an object and a surrounding fluid. In order to understand these interactions, this dissertation looks at the geometric structure of the models. Very often, there are low-dimensional points, curves, or surfaces which have a very strong effect on the behavior of the system. The search for these geometric structures is another key theme of this dissertation. This dissertation presents three independent studies, with an introduction and conclusion to discuss the overall themes. The first work focuses on the forces acting on a cylinder in the wake of another cylinder. These forces are important to understand, because the vibrations that arise from wake forcing are important to consider when designing bridges, power cables, or pipes to carry oil from the ocean floor to offshore oil platforms. Previous studies have shown that the wake of a circular cylinder acts like a spring, pulling harder on the downstream cylinder the more it is moved from the center of the wake. In this work, I extend this idea of the wake as a spring to consider a nonlinear spring, which keeps the same idea, but provides a more accurate representation of the forces involved. The second work considers a simple model of gliding flight, relevant to understanding the behavior of gliding animals, falling leaves, or passive engineered gliders. Within this model, a key geometric feature exists on which the majority of the motion of the glider occurs, representing a 2-dimensional analogy to terminal velocity. In this work, I study the properties of this influential curve, show several ways to identify it, and extend the idea to a surface in a 3-dimensional model. The third study of this dissertation introduces a new mathematical quantity for studying models of systems, for fluid-body interaction problems, ocean flows, chemical reactions, or any other system that can be modeled as a vector field. This quantity, the trajectory divergence rate, provides an easily computed measurement of highly attracting or repelling regions of the states of a model, which can be used to identify influential geometric structures. This work introduces the quantity, discusses its properties, and shows its application to a variety of systems.

Este trabalho apresenta um estudo sobre o comportamento de treliças espaciais formadas por elementos tubulares de seção circular, com ênfase no desempenho das tipologias de ligação utilizadas no Brasil. Foram ensaiadas experimentalmente 9 treliças espaciais com vãos de 7,5 x 15,0m e uma de 7,5m x 7,5m com altura de 1,5m, variando-se o tipo de ligação entre barras, com o objetivo de caracterizar e comparar o comportamento dos sistemas de ligações mais comuns (nó típico – extremidade estampada, nó de aço e nó com chapa de ponteira).A análise teórica, via elementos finitos, tem como objetivo aferir a validade dos modelos numéricos normalmente utilizados e refiná-los incluindo as características do comportamento estrutural observadas em ensaio. A análise numérica segue duas abordagens: análise global da estrutura incluindo os efeitos não-lineares, excentricidade na ligação e variação de seção nas extremidades das barras; com isso o comportamento das treliças ensaiadas foi representado de forma satisfatória. A análise do comportamento do nó típico, modelado tridimensionalmente com elementos de casca, possibilitou analisar a interação entre as barras na região nodal por meio de elementos de contato. Com esta modelagem, apesar das simplificações, foi possível reproduzir o modo de colapso observado experimentalmente. / This paper presents a study of the behavior of tubular circular section space trusses with the main emphasis placed on the performance of the various truss typologies used in Brazil. Nine space trusses with plan dimensions of 7.5m x 15.0m and one with plan dimensions of 7.5mx7.5m and height of 1.5m were tested. The joint type was varied with the objective to characterize and compare the behavior of the more common types of connection systems (typical node – stamped end, steel node, and end plate node). The theoretical analysis employing finite elements was adopted mainly to ascertain the validity of various numerical models commonly employed and hence refining them by including the some basic characteristics of the observed structural behavior.The numerical analysis employed was based on two methodologies: a global structural analysis that takes into account the effects of non-linearity, eccentricities at connection, and the variation of the end bars cross section. In this manner the actual behavior of the tested trusses was well represented. The analysis of the behavior of a typical node, modeled using tri-dimensional finite shell elements made it possible to analyze the interaction between bars that converge at the nodal region by applying contact elements. Despite it simplicity, predicted results of the collapse mode obtained by using the proposed model, very well reproduce the experimental observation.

In this thesis, two problems are studied. The first problem is to find a technique to generate a particular type of failure information in real time for large flexible space structures (LFSSs). This problem is solved by using structured residuals. The failure information is then incorporated into an existing fault tolerant control scheme. The second problem is a ``spin-off'' from the first. Although the H-infinity sliding mode observer (SMO) cannot be applied to the colocated LFSS , its ability to do robust state and fault estimation of the SMO makes it suitable to be used in an integrated fault tolerant control (IFTC) scheme. We propose to combine the H-infinity SMO with a linear fault accommodation controller. Our IFTC scheme is closed loop stable, suppresses the effects of faults and enjoys enhanced robustness to disturbances. The effectiveness of the IFTC is illustrated through the control of a permanent magnet synchronous motor under actuator fault.