Thin-shell structures are becoming increasingly popular for space missions due to their high stiffness-to-mass ratio, easy folding and coiling, and self-deployment using stored strain energy. Broadly, two deployment strategies exist: 1) controlled or deterministic, and 2) unconstrained. Controlled deployment involves carefully orchestrated events using control or guidance systems, while in unconstrained deployment, the structure is simply allowed to self-deploy with minimal guidance. Unconstrained deployment offers lighter deployment mechanisms and better packaging efficiency but the unpredictability of this process has been a significant obstacle to its adoption.
This study focuses on demonstrating the predictability of unconstrained dynamic deployment of thin-shell structures, using the Caltech Space Solar Power Project (SSPP) structures as a case study. The Caltech SSPP uses composite triangular rollable and coilable longerons as the primary building blocks to create large bending-stiff structures. The specific objective is to improve the predictability and robustness of the unconstrained dynamic deployment of the Caltech SSPP structures. Deployment is influenced by the initial conditions and the interaction between the structure and the mechanism during the deployment. To understand these effects, high-fidelity numerical simulations are developed and validated against experiments. The study also examines the sensitivity of deployment characteristics to various design parameters and external influences to ensure the robustness of deployment.
This research demonstrates that the interaction between the structure and the deployment mechanism must be minimal to ensure the predictability of deployment, as thin-shell structures can self-deploy using stored strain energy. This study’s sensitivity analysis will inform the design of future SSPP deployment mechanisms and structures. Additionally, the numerical simulation techniques developed have broader applicability beyond this specific case study to any deployable thin-shell structure.
Due to the large aspect ratios of thin-shell structures, a very fine finite element mesh is required to model them accurately. A dense finite element mesh is also required to model the contact interactions between the structure and the rigid components of the deployment mechanism. As large spacecraft structures become increasingly complex, full-scale numerical modeling becomes impractical, necessitating the search for more computationally efficient finite element methods. In this study, NURBS-based isogeometric analysis is explored, and it is shown that it is not yet worth switching to NURBS-based elements for the analysis of thin-shell deployable structures. In addition, h-adaptive meshing for quadrilateral shell elements is investigated, and more efficient refinement indicators and solution mapping techniques for nonlinear analyses are proposed and their superior performance is demonstrated using a test case of quasi-static folding of a tape spring.
This thesis fills a gap in the literature on unconstrained dynamic deployment of space structures, providing crucial insights and numerical modeling tools for further research. It establishes a knowledge and resource foundation to advance space structure design and promote more frequent use of unconstrained deployment, marking a pivotal contribution to the field and enabling safe and efficient space structure deployment. Furthermore, the study provides insights into more computationally efficient finite element methods, such as h-adaptive meshing. These insights are broadly applicable and can inform the design of future deployable structures beyond the tested cases.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/gt81-0s18, author = {Canales Escobedo, Fabricio Gianfranco}, title = {Numerical Analysis of Folding and Deployment Dynamics of Thin Shell Structures with Localized Folds}, school = {California Institute of Technology}, year = {2023}, doi = {10.7907/gt81-0s18}, url = {https://resolver.caltech.edu/CaltechTHESIS:06012023-233806562}, abstract = {This thesis focuses on the analysis of tape springs folded in the opposite sense and their dynamic deployment, and aims to use methods to reduce the computational cost of the analysis. The tape spring is a thin shell deployable structure that has features in common with other deployable structures. The deployment process of such structures can be difficult to predict, and the use of numerical models can be a more cost-effective alternative to experimental testing. Approaches to reduce the computational cost of the analysis of tape springs are investigated such as adaptive meshing and reduced order models. The thesis also presents an accurate analysis of tape spring deployment and a detailed study of the energies and the physics of the deployment. This is used to investigate the energy leak observed in previous tape spring deployment work. Overall, this thesis contributes to improving the efficiency and accuracy of the analysis of deployable structures, particularly tape springs, which can have significant applications in spacecraft technology.}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/x286-g488, author = {Ubamanyu, Uba Kanthasamy}, title = {Time-Dependent Failure of Thin-Ply Composite Laminates}, school = {California Institute of Technology}, year = {2023}, doi = {10.7907/x286-g488}, url = {https://resolver.caltech.edu/CaltechTHESIS:05312023-210300139}, abstract = {The demand for larger and lighter structures for next-generation space designs necessitates the use of deployable structures. Among the materials that hold promise for such applications, thin-laminate fiber composites with thicknesses less than 200 μm stand out due to their strength-to-weight ratio, packaging efficiency, and ability to deploy using stored strain energy. However, designing deployable structures with thin-laminate composites is challenging as they need to be stiff enough to withstand loads during deployment while also having a small volume in the packaged configuration. Complicating matters further, stress relaxation of the polymer matrix within the composite during long-term stowage in response to an imposed curvature can drastically impact both the deployment process and the performance of the structure in its deployed state, even leading to catastrophic failure in the stowed configuration.
This thesis presents a comprehensive study of the time-dependent failure behavior of thin-laminate fiber composites under bending, with a focus on a fundamental material-level understanding. The work is divided into three main parts. First, a novel test method called Flattening to Rupture (FTR) test was developed to effectively load composite coupons under long-term bending, enabling the measurement of time-dependent rupture and identification of the underlying failure mechanisms. Second, numerical simulations using the Abaqus/Standard finite element software were developed to understand the sequence of rupture events and the influence of several parameters that affect time-dependent rupture. Finally, a statistical approach was proposed to model the stochastic nature of the failure of thin composite laminates.
The contributions of this thesis extend the understanding of the microscale failure mechanisms involved in the time-dependent failure of fiber composites. These new insights pave the way for the efficient design of tightly and safely packaged deployable structures under long-term loading. The findings of this research can be utilized to optimize the design and performance of deployable space structures made of fiber composites, leading to new technologies that can advance space exploration.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/w6na-w476, author = {Marshall, Michael Aaron}, title = {Dynamics of Ultralight Flexible Spacecraft During Slew Maneuvers}, school = {California Institute of Technology}, year = {2022}, doi = {10.7907/w6na-w476}, url = {https://resolver.caltech.edu/CaltechTHESIS:05262022-221946560}, abstract = {Traditional spacecraft design paradigms rely on stiff structures with comparatively flexible appendages. More recent trends, however, trade deployed stiffness for packaging efficiency to stow increasingly large-area apertures inside existing launch vehicles. By leveraging recent advances in materials and structures, these ultralight, packageable, and deployable spacecraft, hereafter referred to as ultralight flexible spacecraft, are up to several orders of magnitude lighter and more flexible than the current state-of-the-art. They promise to deliver higher performance for a wide range of applications, but this comes at a cost, in this case, due to their very low-frequency structural dynamics. Structural dynamics can negatively interact with spacecraft attitude control systems and degrade pointing performance.
These developments motivate the main objective of this thesis: to demonstrate the feasibility and limitations of maneuvering next-generation ultralight flexible spacecraft. To that end, the thesis proposes a quantitative method for determining structure-based performance limits for flexible spacecraft slew maneuvers using reduced-order modal models. It then develops a geometrically nonlinear flexible multibody dynamics finite element model of a representative ultralight flexible spacecraft based on the Caltech Space Solar Power Project architecture to validate this method. The results demonstrate that contrary to common assumptions, other constraints impose more restrictive limits on slew maneuver performance than the dynamics of the structure. In particular, they show that the available attitude control system momentum and torque are often significantly more limiting than the structure. Consequently, these results suggest that spacecraft structures can either be (i) maneuvered significantly faster, assuming suitable actuators are available, or (ii) built using lighter-weight, less-stiff, and lower-cost construction that moves the structure-based performance limits closer to those of the rest of the system. Thus, there is a significant opportunity to design less-conservative, higher-performance space systems.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/ph2w-9a34, author = {Dorn, Charles Jacob}, title = {Geometry Synthesis and Multi-Configuration Rigidity of Reconfigurable Structures}, school = {California Institute of Technology}, year = {2022}, doi = {10.7907/ph2w-9a34}, url = {https://resolver.caltech.edu/CaltechTHESIS:09182021-045958776}, abstract = {Reconfigurable structures are structures that can change their shapes to change their functionalities. Origami-inspired folding offers a path to achieving shape changes that enables multi-functional structures in electronics, robotics, architecture and beyond. Folding structures with many kinematic degrees of freedom are appealing because they are capable of achieving drastic shape changes, but are consequently highly flexible and therefore challenging to implement as load-bearing engineering structures. This thesis presents two contributions with the aim of enabling folding structures with many degrees of freedom to be load-bearing engineering structures.
The first contribution is the synthesis of kirigami patterns capable of achieving multiple target surfaces. The inverse design problem of generating origami or kirigami patterns to achieve a single target shape has been extensively studied. However, the problem of designing a single fold pattern capable of achieving multiple target surfaces has received little attention. In this work, a constrained optimization framework is presented to generate kirigami fold patterns that can transform between several target surfaces with varying Gaussian curvature. The resulting fold patterns have many kinematic degrees of freedom to achieve these drastic geometric changes, complicating their use in the design of practical load-bearing structures.
To address this challenge, the second part of this thesis introduces the concept of multi-configuration rigidity as a means of achieving load-bearing capabilities in structures with multiple degrees of freedom. By embedding springs and unilateral constraints, multiple configurations are rigidly held due to the prestress between the springs and unilateral constraints. This results in a structure capable of rigidly supporting finite loads in multiple configurations so long as the loads do not exceed some threshold magnitude. A theoretical framework for rigidity due to embedded springs and unilateral constraints is developed, followed by a systematic method for designing springs to maximize the load-bearing capacity in a set of target configurations. An experimental study then validates theoretical predictions for a linkage structure. Together, the application of geometry synthesis and multi-configuration rigidity constitute a path towards engineering reconfigurable load-bearing structures.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/4zbq-g037, author = {Pedivellano, Antonio}, title = {Deployment Dynamics of Thin-Shell Space Structures}, school = {California Institute of Technology}, year = {2021}, doi = {10.7907/4zbq-g037}, url = {https://resolver.caltech.edu/CaltechTHESIS:06012021-002457442}, abstract = {Thin-shell structures provide a lightweight solution for deployable structure applications. Despite being only few tens of microns thick, these structures provide excellent bending stiffness, thanks to their curved cross-section. Their thinness also allows them to be elastically packaged into small volumes to fit into a launch vehicle; once in space, they can be self-deployed by releasing their stored elastic energy.
Most space applications use thin-shell structures to deploy and tension thin membranes, such as solar sails, drag sails, and solar arrays. Recently, a novel space solar power architecture has been developed at Caltech, and it relies on distributed thin-shell components, connected in a space frame, to create large-area deployable structures. Thanks to the unique properties of thin shells, these structure provide superior stiffness-to-mass ratio and self-deployment capabilities. However, to demonstrate their reliability and enable their use on space missions, their deployment dynamics must be understood and predicted.
Ground testing is the established approach to verify a structure throughout its design and qualification process. However, replicating the space environment in a laboratory setting is generally not possible, especially for lightweight structures, which are very sensitive to the effects of gravity and air. Numerical models are therefore the only tool to predict the behavior of a structure in space. However, validation with ground experiments is necessary to build confidence in the models, which must be able to capture the complexity of the interaction with air, gravity, and the suspension system that supports the weight of the structure.
The goal of this thesis is to develop high-fidelity models for large space structures, where multiple thin-shell components are folded together and deploy by releasing their strain energy. This overall objective is achieved in 3 steps. First, a ladder-type rectangular strip is introduced, as a building block for more complex architectures. The strip is composed by two thin-shell longerons, symmetrically folded at two locations. The deployment dynamics of this structure is investigated through experiments on 1 m-scale prototypes, both in air and in vacuum. A detailed analysis of its elastic folds is performed using full-field displacement measurements from Digital Image Correlation. A finite element model of this strip is presented, and it is shown to accurately capture the dynamics of the strip for all tested conditions. Then, the implementation of the packaging and deployment scheme of a space solar power spacecraft, composed of multiple strips, is discussed. A kinematic model of the structure is proposed as a design tool to achieve systematic folding. A novel concept of a deployment mechanism to coil the structure in a robust and reliable way is proposed. Also, a staged deployment scheme is demonstrated, to reduce the uncertainty of strain-energy deployment for large space structures. Finally, the deployment dynamics of a 2 m-scale space structural prototype, based on the space solar power architecture, is investigated. A full-scale finite element model of the structure is implemented to replicate its complex folding scheme and capture the deployment process, including the interaction with the deployment mechanism and the suspension system. The simulations predict well the behavior of the structure observed in experiments through motion capture techniques.
The work presented in this thesis advances previous studies on the deployment dynamics of simple thin-shell components, and demonstrates that even complex thin-shell architectures can be packaged and deployed in a controlled and predictable way. The solutions proposed in this thesis have guided the packaging process and the design of the deployment mechanism for DOLCE, an upcoming flight demonstration of the space solar power architecture described in this work. However, this research has much broader implications, as the experimental and numerical framework presented herein can be generalized to different shell-based architectures, and contributes to enabling a new generation of lightweight deployable structures for future space applications.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/ksn2-t598, author = {Royer, Fabien A.}, title = {Probing the Buckling of Thin-Shell Space Structures}, school = {California Institute of Technology}, year = {2021}, doi = {10.7907/ksn2-t598}, url = {https://resolver.caltech.edu/CaltechTHESIS:05312021-185024653}, abstract = {The overarching goal of the research presented in this dissertation is to apply and extend a newly developed methodology to understand the buckling of complex thin shell structures. This methodology enables the determination of tighter buckling criteria and paves the way to the development of more efficient structures, used closer than ever to their buckling load and even beyond. It would result in dramatically lighter structures to be built and has the potential to enable new applications, such as extremely large aperture satellites.
We first analyze the stability of open section thin shell structures under a pure bending moment, through simulations. These structures are composed of longitudinal thin-shell elements connected transversely by thin rods, and inspired by real spacecraft structures. The present study applies and extends recent work on the stability of cylindrical and spherical shells. The role of localization in the buckling of these structures is investigated and early transitions into the post-buckling regime are unveiled using a probe that locally displaces the structure. The probing method enables the computation of the energy input needed to transition early into a post-buckling state, which is central to determining the critical buckling mechanism for the structure. We show that the structure follows stability landscapes also found in cylindrical and spherical shell buckling problems. This initial computational study is the basis for the first ever probing experiment on a complex structure.
In order to test these new structures under bending, a new bending apparatus is designed and implemented. The boundary conditions are chosen such that the apparatus is statically determinate (isostatic), and no state of self stress can develop in the sample during its mounting and testing. This feature is especially desirable in the study of thin shell structures and their elastic instabilities, for which imperfection sensitivity plays a crucial role in the buckling transition and the post-buckling regime. The accuracy of the isostatic bending machine is first assessed through the testing of rods, and its imperfection insensitive behavior is then highlighted in experiments on tape springs, and through numerical studies of the same structures.
The new bending machine is complemented by a probing apparatus, and the stability of the open section thin-shell structures subjected to a pure bending moment is studied experimentally. The experiment confirms that localization of deformations plays a paramount role in the structure’s nonlinear post-buckling regime and is extremely sensitive to imperfections. This characteristic is investigated through probing experiments. The range of moments for which the early buckling of the structure can be triggered using this probe perturbation is determined, as well as the energy barrier separating the pre-buckling and post-buckling states. The stability of the local buckling mode is then illustrated by an experimental stability landscape of shell buckling, and probing is then extended to the entire structure to reveal alternate buckling modes disconnected from the structure’s fundamental path. These results can be used to elaborate efficient buckling criteria for this type of structures, through the use of transition diagrams determined experimentally.
Finally, the buckling and post-buckling behavior of ultralight ladder-type coilable structures is investigated. These specific structures are used in the Space Solar Power Project at Caltech and are referred to as strips. Similarly to the previous studies, the stability of strip structures loaded by normal pressure is computationally studied by applying controlled perturbations through localized probing. The probing technique is generalized to higher-order bifurcations along the post-buckling path, and low-energy escape paths into buckling that cannot be predicted by a classical eigenvalue formulation are identified. It is shown that the stability landscape for a pressure-loaded strip is similar to the landscape for classical shells, and the open section thin shell structure studied initially in this thesis. While classical shell structures buckle catastrophically, strip structures feature a large stable post-buckling range. Probing enables the full characterization of the structure’s unstable behavior, which paves the way to extend its operation closer than ever to the buckling load, and even in the post-buckling regime. It would enable the design of more efficient structures by dramatically reducing their mass, therefore enabling new large spacecraft to be built.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/X60S-BR30, author = {Leclerc, Christophe}, title = {Mechanics of Ultra-Thin Composite Coilable Structures}, school = {California Institute of Technology}, year = {2020}, doi = {10.7907/X60S-BR30}, url = {https://resolver.caltech.edu/CaltechTHESIS:01232020-134850757}, abstract = {Coilable structures are thin-shell structures that can be coiled around a hub by flattening their cross-section. They are attractive for multiple space applications as they allow efficient packaging and deployment of large planar structures. Reducing the shell thickness enables smaller coiling radius and more efficient packaging.
This thesis investigates TRAC structures, a type of coilable structure, made of ultra-thin composite materials. A design using a laminate made of glass fiber plainweave fabric and carbon fiber unidirectional tape is proposed, leading to a shell thickness of 0.08 mm. An in-autoclave, two-cure manufacturing process is presented, and a shape measurement method is used to mitigate post-cure shape changes due to residual stresses.
A study of the structure behavior in its deployed configuration is performed. First, the behavior when subjected to pure bending is investigated experimentally for structures with a length of 575 mm. Two regimes are observed, with a pre-buckling phase transitioning to a stable post-buckling phase after an initial buckling event. The ultimate buckling moment following the stable post-buckling regime can be as high as four times the initial buckling moment. A finite element model is developed and is able to reproduce all the features observed experimentally, except the ultimate buckling. This simulation model is used to study the effect of varying the structure length from 300 mm to 5000 mm on the initial buckling moment. Results show that nonlinearities in the pre-buckling deformations of the flanges under compression lead to a constant wavelength lateral-torsional buckling mode for which the critical moment is mostly constant across the range of length. The torsional behavior of the TRAC structure is also investigated. Good agreement is obtained between experiments and numerical simulations, and initial twist in the structure is shown to have little effect on the overall behavior due to the small torsional stiffness in the underformed configuration.
An analytical method to predict the buckling load of a TRAC structure under pure bending is presented. It is achieved by considering only one flange of the structure and solving the problem of a cylindrical shell panel with a longitudinal free edge under non-uniform axial compression. Partially uncoupled stability equations for a balanced laminate are derived and are used in conjunction with the Rayleigh-Ritz method to approximate the buckling load. This method overestimates the buckling load by 44% in the case of a 500 mm TRAC structure made with ultra-thin composite materials.
A study of the coiling behavior is also presented. High localized curvature in the transition region between the coiled and deployed regions is observed in experiments, leading to material failure for a structure made only of carbon fiber unidirectional tape. A numerical framework is developed and reproduces the localized curvature observed in experiments, predicting stress concentration at this location. The study shows that changing the laminate to a a single ply of carbon fiber unidirectional tape sandwiched between plies of glass fiber plainweave fabrics reduces significantly the maximum stress in the transition region, to the extent that the highest stress is now in the fully coiled region and can be accurately predicted using simple equations based on the change of curvatures due to the coiling process.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/ZG2D-2K77, author = {Talon, Thibaud}, title = {Surface Reconstruction from Distributed Angle Measurements}, school = {California Institute of Technology}, year = {2020}, doi = {10.7907/ZG2D-2K77}, url = {https://resolver.caltech.edu/CaltechTHESIS:02282020-192725947}, abstract = {This thesis presents an innovative solution to the shape measurement of large structures for space applications. The current state-of-the-art heavily relies on optical solutions such as cameras or lasers to recover the shape of a surface. Because of the impracticality of placing a system in front of a large structure flying in space, new solutions need to be developed. The proposed solution is to embed angular sensors (such as sun sensors) directly on the surface. The sensors provide a collection of distributed measurements that form a discrete map of the angular orientation of the structure. An integration scheme can then estimate the 3D shape of the surface.
A mathematical model to perform the integration from angle measurements to the shape of a 3D surface is presented first. This model is purely geometric and serves as a basis for similar concepts. The surface is known in a reference configuration and is assumed to have deformed inextensibly to its current shape. Inextensibility conditions are enforced through a discretization of the metric tensor generating a finite number of constraints. This model parameterizes the shape of the surface using a small number of unknowns, and thus requires a small number of sensors. We study the singularities of the equations and derive necessary conditions for the problem to be well-posed. The limitations of the algorithm are highlighted. Simulations are performed on developable surfaces to analyze the performance of the method and to show the influence of the parameters used in the algorithm. Optimal schemes which lower the RMS error between the reconstructed shape and the actual one are presented.
An experimental validation of the proposed solution and algorithm is performed on a 1.3 x 0.25 m structure with 14 embedded sun sensors. The sensors measure the two local angles of the surface from a light source placed in front of the surface. A small, lightweight and expandable design of the sensors is shown in this thesis. A calibration procedure accurately correlates the output of the sensor with a 0.5° precision. The procedure also highlights the limitations of the design. The structure was deformed in bending and torsion with amplitudes of a few centimeters, and its shape was reconstructed to an accuracy on the order of a millimeter.
The accuracy of the initial algorithm is found to be limited by local shape deformations caused by the mechanical response of the structure. A new algorithm, replacing the discrete inextensibility conditions with the equilibrium equations derived from a finite-element model, is shown. This new algorithm is tested on the experimental structure and the accuracy of the reconstruction is increased by a factor of 2. The RMS error is under a millimeter on average over the different applied shapes and goes as low as 0.3 mm.
To understand how this solution can apply to large space structures, simulations are performed on a model of a large planar spacecraft. A 25 x 25 m structure representing the current concept for the Caltech Space Solar Power Project satellite is used as an example. Sensors with similar noise properties as the ones built for the experiment are placed on the spacecraft. A finite-element model combining the vibration of the spacecraft with large rigid body rotations is presented. This model is used in a Kalman filter that estimates the shape of the structure by iterative prediction from the dynamic finite-element model and correction from the angle measurements. Simulations are performed around the thruster actuation applied at the corner of the structure to follow a specific guidance scheme that is optimal for space solar power satellites. The actuation creates both vibrations of the structure with amplitudes of few centimeters and large rotations of the spacecraft. The designed Kalman filter can accurately estimate both effects and it is shown that millimeter accuracy is achievable. The relationship between the number of sensors, the reconstructed shape error, as well as potential stiffness deviations in the FE model is studied. The results provide first order estimates of the performance of this measurement system, in order to enable the design of future space missions.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/9VZ4-3E71, author = {Ferraro, Serena}, title = {Topology Optimization and Failure Analysis of Deployable Thin Shells with Cutouts}, school = {California Institute of Technology}, year = {2020}, doi = {10.7907/9VZ4-3E71}, url = {https://resolver.caltech.edu/CaltechTHESIS:02032020-164711057}, abstract = {Shell structures with cutouts are widely used in architectural and engineering applications. For thin, lightweight, and deployable space structures, cutouts are cleverly positioned to fold and store the structure in a small volume. To maintain shape accuracy, these structures must fold without becoming damaged and must be stiff in their deployed configurations. Intuitive designs often fail to satisfy these two requirements. This research proposes solutions to the topology optimization of composite, thin shell structures with cutouts.
A novel optimization algorithm was developed that makes no assumptions on the initial number, shape, and location of cutouts on deployable thin shells. The algorithm uses a density-based approach, which distributes the material within the structure by assigning a density parameter to discretized locations. This parametrization of the design domain allows for the finding of new features and the connectivity of the domain, thus providing a completely general formulation to the optimization problem. The goal is to study the effects of volume and stress constraints imposed in a deformed configuration of thin shell structures. While classical topology optimization studies focus on finding solutions to linear problems, this method is applicable to geometrically nonlinear problems and implements stress constraints in the deformed, and hence most stressed, configuration of these shells. A mathematical formulation of the optimization problem and interpolation schemes for stiffness tensor, volume, and stress are presented. A sensitivity analysis of objective function, volume, and stress constraints is provided. Finally, solutions for a thin plate and a tape spring are proposed.
Density-based methods are computationally expensive when applied to large structures and complex shapes because of the large number of design variables. To address these challenges, two optimization methods that provide more specific solutions to the problem of composite, deployable shells are proposed. The first method uses level sets to parametrize the cutouts, thereby restricting the design space and simultaneously limiting the number of design variables. This greatly reduces the computational cost. Using this approach, successful solutions are found for stiff, composite, thin shells with complex shapes that can fold without becoming damaged. The second method uses a spline representation of the contour of a single cutout on the shell, thus performing fine tuning of the shape of the cutout. Modeling techniques that simulate localized strain and experimental methods for studying the quasi-static folding of these composite shells are developed. A laminate failure criterion suitable for thin, plain-weave composites is used in simulations to predict the onset of failure in folded shells. Numerical results are validated with folding experiments that demonstrated good agreement with numerical solutions.
Lastly, it was discovered that many of the best performing solutions have multiple closely spaced cutouts, as opposed to current designs for deployable space structures that have fewer large cutouts. This leads to the formation of small strips of material between cutouts. Hence, the behavior of thin, plain-weave composite material was characterized and the first study on size-scaling effects at small length scales (≤ 15 mm) in this type of material was performed. Size-scaling effects on stiffness and strength shown in this study were introduced in numerical simulations of deployable thin shells. The study demonstrates that the prediction of the onset of failure in folded shells strongly depends on these size effects. Numerical predictions are corroborated by an experimental investigation of localized damage in thin strips of material forming between cutouts. Deployable shells resulting from the optimization studies are built and tested and localized damage is measured via digital volume correlation techniques.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/4DRX-2X87, author = {Wei, Yuchen}, title = {Deployable Piezoelectric Thin Shell Structures: Concepts, Characterization and Vibration Control}, school = {California Institute of Technology}, year = {2019}, doi = {10.7907/4DRX-2X87}, url = {https://resolver.caltech.edu/CaltechTHESIS:06072019-114129662}, abstract = {The thesis presents three interconnected technology paths to the design and realization of novel deployable active thin shell structures. The baseline concept envisioned is built upon a deployable ultra-thin piezoelectric active thin shell architecture, with segmented tessellations. This vision is motivated by the need to deploy and control large, curved and precise surfaces for a variety of applications including future space telescopes, and is made possible by recent progress in ultra-thin high-performance composites and active material technologies. The thesis uses a combination of heuristic design, theoretical analysis, numerical modeling and novel experimental techniques to construct and validate proposed concepts for deployable piezoelectric thin shells.
Specifically, the thesis answers the following questions: i) How to design and manufacture precise, foldable and curved piezoelectric shells. ii) How to deploy these shells reliably and maintain shape correctability in the deployed state. iii) How to synthesize large, curved deployable surfaces with the aforementioned advantages. iv) How to characterize and predict the nonlinear behavior of piezoelectric materials and thin structures under high electric field actuation and large bending deformations. v) How to improve the shape stability of piezoelectric active thin shells under dynamic disturbances without introducing external sensors.
First, the thesis proposes new methodologies and design criteria to synthesize deployable, modular edge-supported thin shells based on a combination of origami-inspired folding patterns and spatial mechanisms. In contrast to traditional deployable surface designs, which attach rigid shells to deployable trusses, the proposed methodology enables concurrent folding of flat or curved shells along with the support structures. Starting from a basic module, a variety of deployable surface concepts are proposed through tessellations of the module.
A piezoelectric material unimorph architecture is further introduced, providing global curvature and shape correction capabilities. All components of the basic concept are validated through model prototyping and material folding tests, and it is discovered that both the ultra thin carbon fiber composites and piezoelectric ceramic materials can achieve a small folding radius without failure. A composite, doubly-curved foldable shell is also designed and manufactured while still maintaining low shape error. These efforts have led to a new family of deployable piezoelectric thin shell structures that integrate low areal density, high shape accuracy, and structural foldability to an unprecedented degree.
The thesis then tackles the challenge of estimating the actuation response and residual structural deformation of unimorph active thin shells under high electric field and large bending motion. A rate-independent, full field phenomenological constitutive model for a polycrystalline piezoelectric material is characterized experimentally. It successfully captures both the observed ferroelectric and ferroelastic domain switching effects. To overcome the difficulty of testing ultra thin piezoelectric plates, a set of novel characterization techniques is developed and implemented to measure the dielectric and mechanical responses of this material. The characterized material constitutive relation is implemented in an efficient model for estimating the structural response of unimorph thin shells under general electric and mechanical loading. The complete set of governing equations is integrated with a Backward-Euler algorithm, reproducing the measured responses of both the material and the structure under complex loading sequences.
Active vibration damping based on self-sensing piezoelectric thin shells is then analyzed and demonstrated on testbed. The self-sensing architecture removes redundant external sensors by making dual use of the piezoelectric layer of the active shell. An adaptive identification method with the associated hardware to track the evolution of field dependent piezoelectric capacitance is implemented, and a new identification strategy is proposed. Closed loop damping with in-situ capacitance adaptation is conducted in bench tests on self-sensing cantilever beams and achieves -12~dB attenuation at the resonance frequency. A highly efficient modeling technique for general self-sensing piezoelectric thin shell structures is proposed which is able to construct closed loop dynamic models based on the vibration eigenmodes and actuation responses obtained from commercial finite element software. These validated modeling techniques are extended to a multi-electrode doubly curved thin shell, where the improvements of shape stability under closed loop damping are evaluated through simulations. It is discovered that the electrode pattern of the self-sensing piezoelectric layer determines the damping performance under the specific boundary conditions of the shell.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/CNKG-8Y84, author = {Bilgi, Pavaman}, title = {Optimization of CCD Charge Transfer for Ground and Space-Based Astronomy}, school = {California Institute of Technology}, year = {2019}, doi = {10.7907/CNKG-8Y84}, url = {https://resolver.caltech.edu/CaltechTHESIS:05302019-172558320}, abstract = {This thesis will be of particular interest to anyone integrating Charge-Coupled Devices (CCDs) into any precision scientific imaging instrument, especially so in space. The first part of the thesis concerns optimization of a CCD camera as a whole. CCDs for the WaSP imager at the Hale telescope are characterized using a minimal amount of data using just a flat-field illumination source. By measuring performance over the entire parameter space of (clock and bias) inputs and analyzing the multidimensional output (linearity, dynamic range, read noise etc), optimal operating conditions can be selected quickly (and possibly automatically). With ever growing sizes of detector arrays such as the recently launched Gaia mission, the upcoming Euclid mission and ground-based cameras such as the LSST (189 CCDs), the task of streamlining detector optimization will be increasingly important. In the second (larger) part, the optimization of Charge Transfer Efficiency (CTE) is explored in particular. In modern CCDs, CTE is caused by lattice defects in the bulk silicon and is significantly worsened by radiation exposure, which is unavoidable in space. As shown in the literature, just a year of exposure to high energy solar proton radiation at low earth orbit can result in CTE reducing to 0.9999 for a signal level of 10,000e- — problematic for most precision astronomical measurements. Here, CTE degrading traps are fully explored in an undamaged CCD to new levels of accuracy. Several unique species are identified, and their population statistics are analyzed by both wafer and sub-pixel location. Subsequently, easily applied CTE measurement techniques are presented, yielding results with new levels of accuracy, concluding in the presentation of a new trap mitigating readout clocking scheme. This scheme can be readily applied to any CCD employing a parallel transfer gate without readout speed penalty. It is proposed that the results herein may be used to construct a simple model to predict CTE given a temperature, readout timing and signal level. This model could then be used to automatically optimize CTE for any CCD, given only its trap parameter statistics.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Kulkarni, Shrinivas R.}, } @phdthesis{10.7907/CNPY-A883, author = {Sakovsky, Maria}, title = {Design and Characterization of Dual-Matrix Composite Deployable Space Structures}, school = {California Institute of Technology}, year = {2018}, doi = {10.7907/CNPY-A883}, url = {https://resolver.caltech.edu/CaltechTHESIS:05302018-165415595}, abstract = {Dual-matrix composites are a promising approach to deployable high performance antennas for small satellites. Several techniques exist for packaging large antenna apertures. Assemblies of rigid bars and hinges obtain high deployed precision but are heavy and mechanically complex. Thin shell structures deployed using stored strain energy are a lightweight alternative offering efficient packaging but reduced surface precision. Moreover, elastomer composites shells attain even smaller fold radii upon packaging but are limited by the deployed structure’s stiffness. Dual-matrix composites combine the advantages of several of these approaches to enable larger antenna apertures. They consist of a continuous woven fiber reinforcement with an elastomer matrix embedded in localized hinge regions and a stiff epoxy resin elsewhere. Such structures can achieve small fold radii, are strain energy deployable, and promise high deployed stiffness.
This research demonstrates the capabilities of the proposed dual-matrix structures through direct comparison to existing antenna designs. Analytic scaling relations between structural and electromagnetic performance of various deployable antenna designs are developed. These are used to rapidly predict achievable antenna performance as a function of a common set of antenna geometric parameters. Plotting of this data on a coordinated set of 2D design plots enables the direct comparison of antenna concepts and the selection of specific designs meeting all requirements. This methodology was used to design a deployable dual-matrix composite conical log spiral (CLS) antenna for use on CubeSats which outperformed existing off-the-shelf designs through higher gain, higher bandwidth, and more efficient packaging.
Starting from this initial design, the antenna is tuned to maximize performance and an assembly including the CubeSat, dual-matrix antenna, dual-matrix hinge for antenna deployment, and a flexible feeding network is developed. All portions of the assembly are prototyped and tested. The antenna electromagnetic performance is predicted using ANSYS HFSS and verified by testing in an anaechoic chamber with antenna gains predicted within 4% of measured values. Structural stiffness is characterized through the antenna’s fundamental frequency with simulated performance in the Abaqus finite element software within 6% of measured values. Comparison of antenna performance before and after packaging and deployment shows the structural frequency, antenna gain, and antenna bandwidth are unaffected by folding, demonstrating that dual-matrix composites are appropriate for use as deployable structures.
Techniques for the quasi-static deployment of dual-matrix composites are presented. An analytic minimum energy method, which accounts for fiber microbuckling in regions of high curvature, is used to predict the folded shape and deployment moments of a dual-matrix hinge. The model shows excellent agreement with LS-Dyna finite element simulations for a variety of material properties. Comparison with experimental characterization demonstrates the capability of the models to predict folded radii and deployment moment of a prototype hinge withing 5% of measured values. The developed analysis tool-set enables a design of deployment restraints and mechanisms.
The woven elastomer composites forming the fold regions in dual-matrix composites have been the subject of very few studies. Existing methods for predicting the stiffness of woven epoxy composites are applied to elastomer composites here and show poor agreement with measurements. A novel approach is presented for the prediction of tow stiffness in elastomer composites using a semi-empirical approach. The reinforcing efficiency parameter in the well-established Halpin-Tsai model for tow homogenization is estimated using experimental measurements of stiffnesses of several laminates. It is shown that for elastomer composites, the parameter values are orders of magnitude higher than the heuristic values used for epoxy composites. The method is used to predict the stiffness of woven epoxy and elastomer composites making up the dual-matrix structures studied in this work showing agreement withing 15% of experimental measurements for arbitrary layups. The method is extended to the prediction of viscoelastic behavior of dual-matrix structures to enable investigation of deployment reliability after long storage times.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/Z9B27S96, author = {Wilson, Lee L.}, title = {Analysis of Packaging and Deployment of Ultralight Space Structures}, school = {California Institute of Technology}, year = {2017}, doi = {10.7907/Z9B27S96}, url = {https://resolver.caltech.edu/CaltechTHESIS:05242017-230338904}, abstract = {This thesis presents a new approach to modeling in finite element analysis (FEA) creased thin-film sheets such as those used for drag sails, as well as modeling the packaging behavior of coilable deployable booms. This is highly advantageous because these deployable space structures are challenging to test on the ground due to their lightweight nature and the effects of gravity and air resistance. Such structures are utilized in the space industry due to their low mass and ability to be packaged into a small volume during their launch into space.
It is shown that removing the crease bending stiffness in creased sheets still allows the deployment behavior of a benchmark problem to be captured, including deployment forces and equilibrium configurations. In addition, folding creased sheets from a flat state into a packaged configuration can result in crease crumpling and excessive wrinkling. To avoid this the Momentless Crease Force Folding (MCFF) technique is developed.
Further presented is the behavior of tape springs and Tubular Rollable and Coilable (TRAC) booms when coiled to radii greater than their natural bend radius. Under these conditions the booms can form multiple localized folds which may jam during boom deployment. Understanding this behavior is important for extending the use of these booms to large scale space structures such as orbital solar power stations.
A useful analytical model is developed determining when the localized folds in a tape spring will bifurcate and is verified against simulation results. Additionally, a numerical model of the wrapping an isotropic tape spring around a hub with a radius greater than the localized fold radii is validated against physical experiments. This model is used to predict trends in the force required to fully wrap a tape spring around a given hub radii.
Finally, when examining the coiling and uncoiling behavior of TRAC booms it was found that the tension force required to keep a TRAC boom tightly coiled is significantly less than the force required to initially coil the boom.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/Z9HT2MC8, author = {Delapierre, Mélanie}, title = {Dynamics and Stability of Spinning Membranes}, school = {California Institute of Technology}, year = {2017}, doi = {10.7907/Z9HT2MC8}, url = {https://resolver.caltech.edu/CaltechTHESIS:05222017-093718571}, abstract = {Many future space missions require large structures subject to stringent shape accuracy requirements. Spinning membrane-like structures are a cost effective solution for these applications. However, any small deflection of a spinning structure, due to maneuvers or solar radiation pressure, leads to geometrically nonlinear effects on its stability and dynamics. Accurate experiments, simulation tools, and models are required to ensure that buckling and vibrations will not affect mission objectives.
We first focus on the influence of transverse uniform loads on the dynamics and stability of spinning isotropic uniform membranes. A transverse uniform load models the effect of a transverse light beam on flat membranes with small deflections. We present experimental measurements of the angular velocities at which various membranes become wrinkled, and of the wrinkling mode transitions that occur upon spin down. A theoretical formulation to predict the critical angular velocities and critical transverse loads is also presented. The transition between bending dominated and in-plane dominated behavior is identified, and the wrinkling modes are obtained. Next, deflected, non-buckled membranes are further analyzed. Axisymmetric nonlinear oscillations are studied analytically, and a reduced-order model is presented. This model predicts that the deflection of the membrane introduces a hardening behavior at low angular velocities and a softening behavior at high angular velocities. This model is validated through experiments and FEM simulations.
Then, we relax the assumption of uniform membranes loaded by transverse light beams. We present an Abaqus model of foldable membranes and show that for particular types of hinges and at high angular velocities, these structures behave like uniform membranes. Finally, we derive an FEM model for solar radiation pressure for quadrilateral surface elements and 3D problems and present its implementation in Abaqus. We show that this follower load introduces an unsymmetric stiffness matrix and that instabilities known as solarelastic flutter can develop. This new FEM capability enables equilibrium and frequency-based stability analyses for a wide range of spacecraft.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/Z9T151NT, author = {Hogstrom, Kristina}, title = {Robotically Assembled Space Telescopes with Deployable Modules: Concepts and Design Methodologies}, school = {California Institute of Technology}, year = {2017}, doi = {10.7907/Z9T151NT}, url = {https://resolver.caltech.edu/CaltechTHESIS:07182016-100030713}, abstract = {This thesis first presents a novel architecture for robotically assembled optical telescopes with apertures between 20 m and 100 m, that utilizes only currently available technology. In this architecture, the primary mirror consists of two layers: a reflective layer and a truss backplane layer. The reflective layer is divided into mirror modules, or groups of mirror segments and actuators. The truss backplane layer is divided into truss modules that fold compactly for launch and are deployed in space by the robot. In this thesis, the design methodology of the mirror modules and truss modules is detailed. The ability of the designed truss layer to maintain precision requirements in the presence of typical space environment loads is demonstrated.
This architecture requires the deployment of many truss modules, and thus the deployment must be reliable despite errors introduced during manufacturing. In this thesis, a new simulation-based toolkit for estimating deployment reliability is described, including the experimental validation of the deployment simulation and the Monte Carlo-style method for repeating deployment simulations with different distributions of random fabrication errors to statistically estimate reliability. Using the toolkit, a set of reliability trade studies are then presented, revealing how different types of errors and design parameters affect reliability. Finally, the manufacturing tolerances and design modifications required to ensure high reliability are proposed.
Even if all modules deploy successfully, fabrication errors will still be present and may affect the assembly process. In this thesis, a new simulation method is presented that can model the step-by-step assembly of flexible modules with errors. The method is used to reveal that overall shape errors grow with the number of connections, resulting in significantly decreased surface precision and large-scale deformations from the nominal backplane shape as the size of the backplane increases. The misalignment at each individual connection does not increase as the backplane increases, but can still be much larger than the applied manufacturing tolerances simply due to random combinations. A simple design for the interconnects between modules is then tested, with simulation results demonstrating that it is unlikely to fully engage when the expected errors are present. With this information, a requirement on the complexity of the interconnect design is inferred, and potential modifications that may increase its efficacy are suggested.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/Z9Z60M0D, author = {Arya, Manan}, title = {Packaging and Deployment of Large Planar Spacecraft Structures}, school = {California Institute of Technology}, year = {2016}, doi = {10.7907/Z9Z60M0D}, url = {https://resolver.caltech.edu/CaltechTHESIS:05232016-115519723}, abstract = {This thesis presents a set of novel methods to biaxially package planar structures by folding and wrapping. The structure is divided into strips connected by folds that can slip during wrapping to accommodate material thickness. These packaging schemes are highly efficient, with theoretical packaging efficiencies approaching 100%. Packaging tests on meter-scale physical models have demonstrated packaging efficiencies of up to 83%. These methods avoid permanent deformation of the structure, allowing an initially flat structure to be deployed to a flat state.
Also presented are structural architectures and deployment schemes that are compatible with these packaging methods. These structural architectures use either in-plane pretension – suitable for membrane structures – or out-of-plane bending stiffness to resist loading. Physical models are constructed to realize these structural architectures. The deployment of these types of structures is shown to be controllable and repeatable by conducting experiments on lab-scale models.
These packaging methods, structural architectures, and deployment schemes are applicable to a variety of spacecraft structures such as solar power arrays, solar sails, antenna arrays, and drag sails; they have the potential to enable larger variants of these structures while reducing the packaging volume required. In this thesis, these methods are applied to the preliminary structural design of a space solar power satellite. This deployable spacecraft, measuring 60 m x 60 m, can be packaged into a cylinder measuring 1.5 m in height and 1 m in diameter. It can be deployed to a flat configuration, where it acts as a stiff lightweight support framework for multifunctional tiles that collect sunlight, generate electric power, and transmit it to a ground station on Earth.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/Z91J97P9, author = {Ning, Xin}, title = {Imperfection Insensitive Thin Shells}, school = {California Institute of Technology}, year = {2015}, doi = {10.7907/Z91J97P9}, url = {https://resolver.caltech.edu/CaltechTHESIS:05212015-174045815}, abstract = {The buckling of axially compressed cylindrical shells and externally pressurized spherical shells is extremely sensitive to even very small geometric imperfections. In practice this issue is addressed by either using overly conservative knockdown factors, while keeping perfect axial or spherical symmetry, or adding closely and equally spaced stiffeners on shell surface. The influence of imperfection-sensitivity is mitigated, but the shells designed from these approaches are either too heavy or very expensive and are still sensitive to imperfections. Despite their drawbacks, these approaches have been used for more than half a century.
This thesis proposes a novel method to design imperfection-insensitive cylindrical shells subject to axial compression. Instead of following the classical paths, focused on axially symmetric or high-order rotationally symmetric cross-sections, the method in this thesis adopts optimal symmetry-breaking wavy cross-sections (wavy shells). The avoidance of imperfection sensitivity is achieved by searching with an evolutionary algorithm for smooth cross-sectional shapes that maximize the minimum among the buckling loads of geometrically perfect and imperfect wavy shells. It is found that the shells designed through this approach can achieve higher critical stresses and knockdown factors than any previously known monocoque cylindrical shells. It is also found that these shells have superior mass efficiency to almost all previously reported stiffened shells.
Experimental studies on a design of composite wavy shell obtained through the proposed method are presented in this thesis. A method of making composite wavy shells and a photogrametry technique of measuring full-field geometric imperfections have been developed. Numerical predictions based on the measured geometric imperfections match remarkably well with the experiments. Experimental results confirm that the wavy shells are not sensitive to imperfections and can carry axial compression with superior mass efficiency.
An efficient computational method for the buckling analysis of corrugated and stiffened cylindrical shells subject to axial compression has been developed in this thesis. This method modifies the traditional Bloch wave method based on the stiffness matrix method of rotationally periodic structures. A highly efficient algorithm has been developed to implement the modified Bloch wave method. This method is applied in buckling analyses of a series of corrugated composite cylindrical shells and a large-scale orthogonally stiffened aluminum cylindrical shell. Numerical examples show that the modified Bloch wave method can achieve very high accuracy and require much less computational time than linear and nonlinear analyses of detailed full finite element models.
This thesis presents parametric studies on a series of externally pressurized pseudo-spherical shells, i.e., polyhedral shells, including icosahedron, geodesic shells, and triambic icosahedra. Several optimization methods have been developed to further improve the performance of pseudo-spherical shells under external pressure. It has been shown that the buckling pressures of the shell designs obtained from the optimizations are much higher than the spherical shells and not sensitive to imperfections.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/Z99W0CFB, author = {Steeves, John Bradley}, title = {Multilayer Active Shell Mirrors}, school = {California Institute of Technology}, year = {2015}, doi = {10.7907/Z99W0CFB}, url = {https://resolver.caltech.edu/CaltechTHESIS:05282015-145339959}, abstract = {
This thesis presents a novel active mirror technology based on carbon fiber composites and replication manufacturing processes. Multiple additional layers are implemented into the structure in order to provide the reflective layer, actuation capabilities and electrode routing. The mirror is thin, lightweight, and has large actuation capabilities. These features, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Structural redundancy in the form of added material or support structures is replaced by thin, unsupported lightweight substrates with large actuation capabilities.
Several studies motivated by the desire to improve as-manufactured figure quality are performed. Firstly, imperfections in thin CFRP laminates and their effect on post-cure shape errors are studied. Numerical models are developed and compared to experimental measurements on flat laminates. Techniques to mitigate figure errors for thicker laminates are also identified. A method of properly integrating the reflective facesheet onto the front surface of the CFRP substrate is also presented. Finally, the effect of bonding multiple initially flat active plates to the backside of a curved CFRP substrate is studied. Figure deformations along with local surface defects are predicted and characterized experimentally. By understanding the mechanics behind these processes, significant improvements to the overall figure quality have been made.
Studies related to the actuation response of the mirror are also performed. The active properties of two materials are characterized and compared. Optimal active layer thicknesses for thin surface-parallel schemes are determined. Finite element simulations are used to make predictions on shape correction capabilities, demonstrating high correctabiliity and stroke over low-order modes. The effect of actuator saturation is studied and shown to significantly degrade shape correction performance.
The initial figure as well as actuation capabilities of a fully-integrated active mirror prototype are characterized experimentally using a Projected Hartmann test. A description of the test apparatus is presented along with two verification measurements. The apparatus is shown to accurately capture both high-amplitude low spatial-frequency figure errors as well as those at lower amplitudes but higher spatial frequencies. A closed-loop figure correction is performed, reducing figure errors by 94%.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/Z34C-NY82, author = {Maqueda Jiménez, Ignacio}, title = {High Strain Composites and Dual-Matrix Composite Structures}, school = {California Institute of Technology}, year = {2014}, doi = {10.7907/Z34C-NY82}, url = {https://resolver.caltech.edu/CaltechTHESIS:05292014-191924394}, abstract = {Most space applications require deployable structures due to the limiting size of current launch vehicles. Specifically, payloads in nanosatellites such as CubeSats require very high compaction ratios due to the very limited space available in this typo of platform. Strain-energy-storing deployable structures can be suitable for these applications, but the curvature to which these structures can be folded is limited to the elastic range. Thanks to fiber microbuckling, high-strain composite materials can be folded into much higher curvatures without showing significant damage, which makes them suitable for very high compaction deployable structure applications. However, in applications that require carrying loads in compression, fiber microbuckling also dominates the strength of the material. A good understanding of the strength in compression of high-strain composites is then needed to determine how suitable they are for this type of application.
The goal of this thesis is to investigate, experimentally and numerically, the microbuckling in compression of high-strain composites. Particularly, the behavior in compression of unidirectional carbon fiber reinforced silicone rods (CFRS) is studied. Experimental testing of the compression failure of CFRS rods showed a higher strength in compression than the strength estimated by analytical models, which is unusual in standard polymer composites. This effect, first discovered in the present research, was attributed to the variation in random carbon fiber angles respect to the nominal direction. This is an important effect, as it implies that microbuckling strength might be increased by controlling the fiber angles. With a higher microbuckling strength, high-strain materials could carry loads in compression without reaching microbuckling and therefore be suitable for several space applications.
A finite element model was developed to predict the homogenized stiffness of the CFRS, and the homogenization results were used in another finite element model that simulated a homogenized rod under axial compression. A statistical representation of the fiber angles was implemented in the model. The presence of fiber angles increased the longitudinal shear stiffness of the material, resulting in a higher strength in compression. The simulations showed a large increase of the strength in compression for lower values of the standard deviation of the fiber angle, and a slight decrease of strength in compression for lower values of the mean fiber angle. The strength observed in the experiments was achieved with the minimum local angle standard deviation observed in the CFRS rods, whereas the shear stiffness measured in torsion tests was achieved with the overall fiber angle distribution observed in the CFRS rods.
High strain composites exhibit good bending capabilities, but they tend to be soft out-of-plane. To achieve a higher out-of-plane stiffness, the concept of dual-matrix composites is introduced. Dual-matrix composites are foldable composites which are soft in the crease regions and stiff elsewhere. Previous attempts to fabricate continuous dual-matrix fiber composite shells had limited performance due to excessive resin flow and matrix mixing. An alternative method, presented in this thesis uses UV-cure silicone and fiberglass to avoid these problems. Preliminary experiments on the effect of folding on the out-of-plane stiffness are presented. An application to a conical log-periodic antenna for CubeSats is proposed, using origami-inspired stowing schemes, that allow a conical dual-matrix composite shell to reach very high compaction ratios.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/S7JS-A837, author = {Patterson, Keith D.}, title = {Lightweight Deformable Mirrors for Future Space Telescopes}, school = {California Institute of Technology}, year = {2014}, doi = {10.7907/S7JS-A837}, url = {https://resolver.caltech.edu/CaltechTHESIS:12182013-094108778}, abstract = {This thesis presents a concept for ultra-lightweight deformable mirrors based on a thin substrate of optical surface quality coated with continuous active piezopolymer layers that provide modes of actuation and shape correction. This concept eliminates any kind of stiff backing structure for the mirror surface and exploits micro-fabrication technologies to provide a tight integration of the active materials into the mirror structure, to avoid actuator print-through effects. Proof-of-concept, 10-cm-diameter mirrors with a low areal density of about 0.5 kg/m² have been designed, built and tested to measure their shape-correction performance and verify the models used for design. The low cost manufacturing scheme uses replication techniques, and strives for minimizing residual stresses that deviate the optical figure from the master mandrel. It does not require precision tolerancing, is lightweight, and is therefore potentially scalable to larger diameters for use in large, modular space telescopes. Other potential applications for such a laminate could include ground-based mirrors for solar energy collection, adaptive optics for atmospheric turbulence, laser communications, and other shape control applications.
The immediate application for these mirrors is for the Autonomous Assembly and Reconfiguration of a Space Telescope (AAReST) mission, which is a university mission under development by Caltech, the University of Surrey, and JPL. The design concept, fabrication methodology, material behaviors and measurements, mirror modeling, mounting and control electronics design, shape control experiments, predictive performance analysis, and remaining challenges are presented herein. The experiments have validated numerical models of the mirror, and the mirror models have been used within a model of the telescope in order to predict the optical performance. A demonstration of this mirror concept, along with other new telescope technologies, is planned to take place during the AAReST mission.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/RSSF-1C35, author = {Kwok, Kawai}, title = {Mechanics of Viscoelastic Thin-Walled Structures}, school = {California Institute of Technology}, year = {2013}, doi = {10.7907/RSSF-1C35}, url = {https://resolver.caltech.edu/CaltechTHESIS:06122012-184825377}, abstract = {
Thin-walled structures made of polymers and reinforced polymer composites are prominent candidates for constructing large lightweight structures. A major challenge in designing polymer-based thin-walled structures is their time and temperature dependent behavior originating from material viscoelasticity and its interaction with the highly geometrically nonlinear response due to thinness of the walls. Although polymer viscoelasticity and geometric nonlinearity have been extensively studied, the mechanics of structures exhibiting both phenomena are not well understood.
This thesis presents a combination of experimental, numerical, and analytical investigations of the behavior of viscoelastic thin-walled structures. The first goal of this research is to establish general methods of analysis for two types of structural components, namely composite shells and polymer membranes, that will serve as the basis for full-scale structural analysis. The second goal is to demonstrate the capability of the developed methods by analyzing time and temperature dependent behavior of deployable structures and balloon structures.
In the study of deployable structures, the deployment and shape recovery processes after stowage are investigated. Fundamental features of viscoelastic deployable structures are studied first with homogeneous polymer beams and shells. A simple closed-form solution describing the shape evolution of a beam after stowage is proposed. The effects of rate and temperature on the bending instability of shells are revealed. Building on the understanding gained from the analysis of homogeneous structures, modeling techniques are developed for polymer composite structures. A micromechanical viscoelastic model for carbon fiber reinforced polymer thin shells is established through finite element homogenization and applied to evaluate the effects of long-term stowage in a representative composite deployable structure.
In the study of balloon structures, a membrane model is developed to study polymer balloon films with stress concentrations due to thickness variation. A nonlinear viscoelastic constitutive model is first formulated for the film material. The wrinkling instability behavior is incorporated into the model through correction of stress and strain states in the presence of wrinkling. Stress concentration factors in balloon films are predicted and measured with the membrane model and full-field displacement measurement techniques, respectively.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/YYTP-2005, author = {Deng, Xiaowei}, title = {Clefted Equilibrium Shapes of Superpressure Balloon Structures}, school = {California Institute of Technology}, year = {2012}, doi = {10.7907/YYTP-2005}, url = {https://resolver.caltech.edu/CaltechTHESIS:06062012-202646378}, abstract = {This thesis presents a numerical and analytical study of the clefted equilibrium shape of superpressure balloon structures. Lobed superpressure balloons have shown a tendency to deploy into unexpected asymmetric shapes, hence their design has to strike a balance between the lower stresses achieved by increasing lobing and the risk of incomplete deployment. Extensive clefting is a regular feature of balloons that are incompletely inflated, and is regularly seen during launch and ascent. Our particular interest in the research is in clefts that remain once a balloon has reached its float altitude and is fully pressurized.
A simplified simulation technique for orthotropic viscoelastic membranes is presented in the thesis. Wrinkling is detected by a combined stress-strain criterion and an iterative scheme searches for the wrinkle angle using a pseudoelastic material stiffness matrix based on a nonlinear viscoelastic constitutive model. This simplified model has been implemented in ABAQUS/Explicit and is able to compute the behavior of a membrane structure by superposition of a small number of response increments. The model has been tested against a published solution for a time-independent isotropic membrane under simple shear and also against experimental results on StratoFilm 420 under simple shear.
A fully three-dimensional finite element model of balloon structures incorporating wrinkling and frictionless contact, able to simulate the shapes taken up by lobed superpressure balloons during the final stages of their ascent has been established. Two different methods have been considered to predict the clefts: (i) deflation and inflation method and (ii) constraint shift method. In method (i), the starting configuration is obtained by deflating an initially symmetric balloon subject to uniform pressure. The deflation simulation is continued until the differential pressure at the bottom of the balloon has become negative, at which point the balloon is extensively clefted. The balloon is then inflated by increasing the bottom pressure while maintaining a uniform vertical ressure gradient, and the evolution of the shape and stress distribution of the balloon is studied. Two different designs of uperpressure balloons are investigated: a flat facet balloon and a ighly lobed balloon. It is found that the flat facet balloon follows essentially the same path during deflation and inflation, and hence will deploy into a unique, symmetric shape. For the lobed balloon it is found that it follows different paths during deflation and inflation, and deploys into an alternate, clefted equilibrium shape.
Compared to method (i), method (ii) is computationally a more efficient clefting test. The test consists in setting up the balloon in its symmetrically inflated configuration, then breaking the symmetry of this shape by artificially introducing a clefting imperfection, and finally determining the equilibrium shape of the balloon. The clefting imperfection is computed by shifting the constraint at the bottom of the balloon and removing the pressure in the bottom region, below the shifted constraint. The clefting test is applied successfully to three 27~m diameter superpressure balloons that have been tested indoors by NASA, of which one had remained clefted when it was inflated and the other two had deployed completely.
In addition to numerical simulations, formulation of a new cleft factor, employed as an indicator of tendency to S-cleft for superpressure balloons based on constant-stress design has been established through dimensional analysis. The cleft factor, defined as the ratio of clefted volume to cyclically symmetrical volume, is expressed in the form of power law relation of the dimensionless groups. An example illustrates how to calculate the coefficients of the analytical formula and analyze sensitivity of design parameters to clefting.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, } @phdthesis{10.7907/A773-KF92, author = {Lopez Jimenez, Francisco}, title = {Mechanics of Thin Carbon Fiber Composites with a Silicone Matrix}, school = {California Institute of Technology}, year = {2011}, doi = {10.7907/A773-KF92}, url = {https://resolver.caltech.edu/CaltechTHESIS:03152011-154253229}, abstract = {This thesis presents an experimental, numerical and analytical study of the behavior of thin fiber composites with a silicone matrix. The main difference with respect to traditional composites with epoxy matrix is the fact that the soft matrix allows the fibers to microbuckle without breaking. This process acts as a stress relief mechanism during folding, and allows the material to reach very high curvatures, which makes them particularly interesting as components of space deployable structures. The goal of this study is to characterize the behavior and understand the mechanics of this type of composite.
Experimental testing of the bending behavior of unidirectional composites with a silicone matrix shows a highly non-linear moment vs. curvature relationship, as well as strain softening under cyclic loading. These effects are not usually observed in composites with an epoxy matrix. In the case of tension in the direction transverse to the fibers, the behavior shows again non-linearity and strain softening, as well as an initial stiffness much higher than what would be expected based on the traditional estimates for fiber composites.
The micro mechanics of the material have been studied with a finite element model. It uses solid elements and a random fiber arrangement produced with a reconstruction process based on micrographs of the material cross section. The simulations capture the macroscopic non-linear response, as well as the fiber microbuckling, and show how microbuckling reduces the strain in the fibers. The model shows good agreement for the bending stiffness of specimens with low fiber volume fraction, but it overestimates the effect of the matrix for more densely packed fibers. This is due to the high matrix strain that derives from the assumption of perfect bonding between fiber and matrix. In the case of tension transverse to the fibers, the model shows a much better agreement with experiments than traditional composite theory, and shows that the reason for the observed high stiffness is the incompressibility of the matrix. In order to capture the strain softening due to fiber debonding, cohesive elements have been introduced between the fibers and the matrix. This allows the model to capture quantitatively the non-linear behavior in the case of loading transverse to the fibers, and the damage due to cyclic loading. A single set of parameters for the cohesive elements produce good agreement with the experimental results for very different values of the fiber volume fraction, and could also be used in the analysis of more complicated loading cases, such as bending or biaxial tension.
In addition to the simulations, a homogenized analytical model has also been created. It extends previous analysis of composites with a soft matrix to the case of very thin composites. It provides a good qualitative description of the material behavior, and it helps understand the mechanics that take place within the material, such as the equilibrium of energy terms leading to a finite wave length, as opposed to microbuckling under compression.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, } @phdthesis{10.7907/D3AR-G573, author = {Stohlman, Olive Remington}, title = {Repeatability of Joint-Dominated Deployable Masts}, school = {California Institute of Technology}, year = {2011}, doi = {10.7907/D3AR-G573}, url = {https://resolver.caltech.edu/CaltechTHESIS:05242011-022845109}, abstract = {Deployable masts are a class of structure that can be stowed in a small volume and expanded into long, slender, and stable booms. Their greatest benefit as space structures is their packing ratio: masts can typically be packed to a fraction of their deployed length at a diameter only modestly wider than their deployed width. This thesis is concerned with precision deployable masts, which can be stowed and deployed with repeatability of the tip position of better than 1 mm over 60 m. The methods of investigation are experimental measurements of a sample mast and numerical modeling of the mast with specially attention to hysteretic joints.
A test article of an ADAM mast was used for the experimental work. Two categories of experi- ment were pursued: measurements of mast components as inputs to the model, and measurements of full bays as validation cases for the model. Measurements of the longeron ball end joint friction, cable preload, and latch behavior are of particular note, and were evaluated for their variability. Further measurements were made of a bay in torsion and a short two-bay mast in shear, showing that there is residual displacement in this mast after shear loading is applied and released.
The modeling approach is described in detail, with attention to the treatment of the mast latches, which lock the structure in its deployed configuration. A user element subroutine was used within the framework of the Abaqus finite element analysis solver to model the behavior of the latches with high fidelity.
Validation cases for the model are presented in comparison with experimental observations of a two-bay mast. These cases show that the model captures a number of important and complex nonlinear effects of the hysteretic mast components. Parametric studies of the impacts of component behaviors and modeling practices are explored, emphasizing the impacts of part variability and the idealization of the mast latching mechanisms.
}, address = {1200 East California Boulevard, Pasadena, California 91125}, advisor = {Pellegrino, Sergio}, }