Thesis (Ph. D.)--University of Alabama at Birmingham, 2007. / Additional advisors: Timothy Gawne, Richard Gray, Michael Loop, Michael Sloane, Donald Twieg. Description based on contents viewed Mar. 3, 2008; title from title screen. Includes bibliographical references (p. 88-97).

We first review recent work on stable and multistable random processes and their localisability. Then most of the thesis concerns a new approach to these topics based on characteristic functions. Our aim is to construct processes on R, which are α(x)-multistable, where the stability index α(x) varies with x. To do this we first use characteristic functions to define α(x)-multistable random integrals and measures and examine their properties. We show that an α(x)-multistable random measure may be obtained as the limit of a sequence of measures made up of α-stable random measures restricted to small intervals with α constant on each interval. We then use the multistable random integrals to define multistable random processes on R and study the localisability of these processes. Thus we find conditions that ensure that a process locally ‘looks like’ a given stochastic process under enlargement and appropriate scaling. We give many examples of multistable random processes and examine their local forms. Finally, we examine the dimensions of graphs of α-stable random functions defined by series with α-stable random variables as coefficients.

<p>Architected materials are a class of materials with novel properties that consist of numerous periodic unit cells. <a>In past investigations, researchers have demonstrated how architected materials can achieve these novel properties by </a><a>tailoring the features of the unit cells without changing the bulk materials</a>. <a>Here, a group of architected materials called Phase Transforming Cellular Materials (PXCMs) are investigated with the goal of mimicking the novel properties of shape-memory alloys.</a> <a>A general methodology is developed for creating 1D PXCMs that exhibit temperature-induced reverse phase transformations (i.e., shape memory effect) after undergoing large deformations. During this process, the PXCMs dissipate energy but remain elastic (i.e., superelasticity). </a>Next, inspired by the hydration-induced shape recovery of feathers, a PXCM-spring system is developed that uses the superelasticity of PXCMs to achieve shape recovery. Following these successes, the use of PXCMs to resist simulated seismic demands is evaluated. To study how they behave in a dynamic environment and how well their response can be estimated in such an environment, a single degree of freedom-PXCM system is subjected to a series of simulated ground motions. Lastly, the concept of PXCMs is extended into two dimensions by creating PXCMs that achieve superelasticity in two or more directions. Overall, the findings of this investigation indicate that PXCMs<a>: 1) can achieve shape memory and recovery effects through temperature changes, 2) offer a novel alternative to traditional building materials for resisting seismic demands, and 3) can be expanded into two dimensions while still exhibiting superelasticity. </a></p> <p> </p>

The purpose of this research is to develop the tools necessary to create tristable compliant mechanisms; the work presents the creation of models and concepts for design and a demonstration of the feasibility of the designs through the fabrication of tristable compliant mechanism prototypes on the macro scale. Prior methods to achieve tristable mechanisms rely on detents, friction, or power input; disadvantages to these methods include a high number of parts, the necessity for lubrication, and wear. A compliant tristable mechanism accomplishes tristability through strain energy storage. These mechanisms would be preferable because of increased performance and cost savings due to a reduction in part count and assembly costs. Finite element analysis and the pseudo-rigid-body model are used to design tristable compliant mechanisms. The mechanisms are initially designed by considering symmetrical or nearly symmetrical mechanisms which achieve a stable position if moved in either direction from the initial (fabrication) position, thus resulting in a total of three stable positions. The mechanisms are fabricated and tested in both partially and fully compliant forms, and efforts to miniaturize the mechanism are discussed. The basic mechanism design is used as a starting point for optimization-based design to achieve tailored stable positions or neutrally stable behavior. An alternative to fabrication methods commonly used in compliant mechanisms research is introduced. This method integrates torsion springs made of formed wire into compliant mechanisms, allowing the desired force, stiffness, and motion to be achieved from a single piece of formed wire. Two ways of integrating torsion springs are fabricated and modeled, using either helical coil torsion springs or torsion bars. Because the mechanisms are more complex than ordinary springs, simplified models are presented which represent the wireform mechanisms as four-bar mechanisms using the pseudo-rigid-body model. The method is demonstrated through the design of mechanically tristable mechanisms. The validity of the simplified models is discussed by comparison to finite element models and experimental measurements. Finally, fatigue testing and analysis is presented.

This work evaluates a specific origami device known as the kaleidocycle and the broad classof rigidly foldable origami. Both of these have potential for application in the design of deployableand foldable arrays of spatial mechanisms.Origami is considered a compliant mechanisms because it achieves its motion through thedeflection of paper creases. Compliant mechanisms generally do not allow for continuous rotation;however, the compliant kaleidocycle represents an exception to this generality. Along with theirability to rotate continuously, kaleidocycles may also be designed to exhibit multistable behaviorduring this rotation. These two characteristics make the kaleidocycle an interesting device withpotential for applications in engineering. This work presents the multistable characteristics ofkaleidocycles, showing that devices can be made which exhibit one, two, three, or four distinctstable equilibrium positions. Kaleiocycles may also be designed to exhibit a range over which thedevice is neutrally stable.The second type of origami presented in this work is rigidly foldable origami, a special classof origami in which all deflection occurs at the creases, allowing the panels to remain rigid. Thistype of origami is of particular interest because of its ability to be constructed from materials muchstiffer than paper while retaining its mobility. This property allows rigidly foldable origami to beapplied to fields such as architecture and deployable mechanisms. This work presents a method forevaluating rigid foldability in origami tessellations. This method is used to define seven theoremsfor the rigid foldability of origami twists and to develop new rigidly foldable origami “gadgets”and tessellations.

Many studies have found that fixating or directing spatial attention to different regions can bias the perception of the Necker cube, but whether this effect of spatial attention is due to attended areas perceived as being closer have yet to be examined. This issue was directly investigated in this study. The stimulus used was the diamond stimulus, containing four occluders and four moving lines that can be perceived as coherent or separate motions. The results of Experiment 1 show that coherent motion was perceived more often under the attending-to-occluders condition than under the attending-to-moving-lines condition, indicating that spatial attention can bias multistable perception. The results of Experiment 2 show that the mean probability of reporting lines behind occluders in small binocular disparities was significantly higher under the attending-to-occluders condition than under the attending-to-lines condition, indicating that spatial attention can make attended areas look slightly closer. The results of Experiments 3 and 4 show that the effect of spatial attention on biasing multistable perception was weakened when there were binocular or monocular depth cues to define the depth relationship between the occluders and the lines. These results are all consistent with the notion that spatial attention can bias multistable perception through affecting depth perception, making attended areas look closer.

No description available.

<p>Structures with inherent shape change capabilities enable adaptive, efficient designs without the weight and complexity of external actuators and sensors. Morphing structures are found in nature: plants are able to achieve fast motion without muscular or nervous systems. For example, the Venus flytrap snaps to a closed state with spatially distributed curvatures in less than one second. In contrast, synthetic shape change has been limited by a trade-off between complexity and speed. Shape memory polymers (SMPs) can remember complex shapes, but morphing is slow and one-way. Multistability due to mechanical buckling is fast and reversible, but it has been limited to simple shapes. Furthermore, many examples of biological shape change follow logical patterns with mechanisms that selectively respond to environmental stimuli. This suggests that synthetic morphing structures may also lend themselves to alternative forms of sensing, memory, and logic.</p> <p><br></p> <p>In this research, we introduce a new method of using SMPs in combination with the hierarchical architectures of pre-strained multistable laminates to create switchable multistable structures (SMS). An SMS can remember multiple permanent shapes and reversibly snap between them. We use extrusion-based 3D printing to encode contrasting shape memory-based pre-strain fields in a bilayer. Above the SMP’s glass transition temperature, the SMS becomes compliant and remembers multiple encoded permanent shapes with fast snap-through between them. Below the transition temperature, the SMS regains its stiffness and is fixed in a single state. The geometric freedom of 3D printing enables the design and manufacture of bioinspired structures with complex pre-strain fields and deflections. The developed printing method is applied in multiple subsequent studies, including mechanical pixels, self-folding spring origami structures, and multistable structures printed with thermoset composite inks. </p> <p><br></p> <p>The highly nonlinear behavior of bistable, pre-strained structures makes their design difficult and nonintuitive. Generally, these structures are designed using a slow, iterative process with finite element analysis (FEA). We aim to solve the inverse optimization problem: start with target stable states and solve for the necessary pre-strain distributions. To this end, we develop and implement the switching tunneling method (STM) to design pre-strained,</p> <p>multistable structures. Instead of FEA, we leverage analytical solutions for gradient-based optimization. Tunneling allows for the efficient search of a design space which may contain multiple local and global minima. Switching enables us to take advantage of two different function transformations, depending on if the search is far from or close to a minimum. The STM is validated through FEA and experiments for both conventional and variable</p> <p>pre-strain bistable structures.</p> <p><br></p> <p>Structures designed to react to external conditions or events offer the opportunity to directly integrate sensing, memory, and computation into a structure. This concept is explored using metasheets composed of locally bistable unit cells, which display spatiotemporal mechanical sensing (mechanosensing) and memory. A unit cell consists of a bistable dome with a piezoresistive strip at the base; the resistance indicates the state of the dome. The mechanics of bistability offer inherent filtering and nonlinear signal amplification capabilities, tunable via geometric parameters. Metasheet arrays of these unit cells display distributed sensing capabilities, as well as hierarchical multistability.</p> <p><br></p> <p>We explore the use of time-dependent material properties combined with the mechanics of multistability to encode many unique values within a single mechanosensor unit cell, beyond binary memory. When the piezoresistive material is viscoelastic, cyclic loading causes cumulative changes in both the ground and inverted state resistances. Effectively, the metamaterial is able to count how many times an external force has been applied; this count is stored in the metamaterial’s intrinsic, measurable properties.</p> <p><br></p> <p>This work demonstrates the importance of incorporating memory concepts into structural design, which enables multistability with complex stable shapes, as well as spatiotemporal sensing and memory capabilities. Engineered systems require increasingly adaptive and responsive structures to improve efficiency. The incorporation of inherent memory and sensing enables the complex behaviors needed to interact with unstructured environments</p> <p>and biological features, a pressing issue for aerospace, soft robotics and biomedical devices. The methodology developed here to manufacture, design, and analyze multistable structures advances the state of the art and makes their implementation more practical.</p>

[pt] Nos últimos anos, tem-se observado um interesse crescente em estruturas multiestáveis. Sistemas com múltiplas configurações de equilíbrio estável geralmente são obtidos através de uma cadeia de unidades biestáveis conectadas por elementos rígidos ou flexíveis. Entretanto, pouco se sabe sobre seu comportamento estático e dinâmico não linear. Neste trabalho realiza-se uma análise não linear estática e dinâmica detalhada de sistemas multiestáveis formados por duas unidades biestáveis abatidas, especificamente, duas treliças de von Mises ou dois arcos, conectados em ambos os casos por elementos rígidos ou flexíveis. Para isto, as equações não lineares de equilíbrio e de movimento são obtidas através do princípio da energia potencial estacionária e do princípio de Hamilton, respectivamente, considerando um material elástico linear. Utilizando algoritmos de continuação, os caminhos de equilíbrio são obtidos e a estabilidade analisada utilizando o princípio da energia potencial mínima. Múltiplos caminhos de equilíbrio são identificados, levando a múltiplas soluções coexistentes, estáveis e instáveis, e vales potenciais intimamente ligados às simetrias dos sistemas. O efeito das inevitáveis imperfeições iniciais é também esclarecido. As oscilações não lineares e as bifurcações dos sistemas sob carregamento harmônico são estudadas através de diagramas de bifurcação, mapas de Poincaré e bacias de atração. Estuda-se também o efeito do pré-carregamento estático na dinâmica global. Observam-se, em virtude de sequências de bifurcações emergindo de cada posição de equilíbrio estável, um elevado número de soluções coexistentes, periódicas e aperiódicas, levando a bacias de atração complexas e com amplas regiões fractais. Por um lado, estes cenários podem ser valiosos em diversas aplicações. Por outro, múltiplos atratores e suas bacias fractais podem levar à perda da estabilidade e integridade dinâmica. Desta forma, o conhecimento do comportamento estático e dinâmico não linear de sistemas multiestáveis é imprescindível em qualquer aplicação em engenharia. Como exemplo de aplicação, se utiliza um sistema formado por treliças de von Mises no processo de coleta de energia através de elementos piezoelétricos. O comportamento altamente não linear resulta em movimentos de grande amplitude para largas faixas de excitação, aumentando sua eficiência e aplicabilidade. / [en] In the last years, an increasing interest in multistable structures has been observed. Multistable systems are generally attained by a chain of bistable units connected by rigid or flexible elements. However, little is known about their nonlinear static and dynamic responses. In this work, a detailed nonlinear static and dynamic analysis of multistable systems formed by two shallow bistable units is conducted, specifically, two von Mises trusses or two arches, connected in both cases by rigid or flexible elements. For this, the nonlinear equilibrium equations and equations of motion are obtained through the principle of stationary potential energy and Hamilton s principle, respectively, considering a linear elastic material. Using continuation algorithms, the nonlinear equilibrium paths are obtained, and stability analyzed using the principle of minimum potential energy. Multiple equilibrium paths are identified, leading to several stable and unstable coexisting solutions and potential wells with are closely linked to the systems symmetries. The effect of unavoidable initial imperfections is also clarified. The nonlinear dynamics and bifurcations of systems under harmonic forcing are studied using bifurcation diagrams, Poincaré maps and cross-sections of the basins of attraction. The effect of a static pre-load on global dynamics is also studied. Due to the bifurcation sequences emerging from each stable equilibrium configuration, a high number of coexisting solutions are observed, both periodic and aperiodic, leading to complex basins of attraction with broadening fractal regions. On the one hand, these scenarios can be valuable in several applications. On the other hand, multiple attractors and their fractal basins can lead to the loss of stability and dynamic integrity. Therefore, knowledge on the nonlinear static and dynamic behavior of multistable systems is primordial in any engineering application. As an application example, a system composed by two von Mises trusses is used in the process of energy harvesting through piezoelectric elements. The highly nonlinear behavior results in large amplitude oscillations for a wide range of excitation frequency, increasing its efficiency and applicability.

Un nombre de sujets concernant la microrobotique numérique ont été abordés dans le cadre de cette the` se. Une nouvelle génération du microrobot numérique ”DiMiBot” a e´ te´ proposé ce qui rend le DiMiBot plus précis, plus contrôlable et plus petit. La nouvelle structure est formée de deux modules multistables seulement, ce qui ajoute des fonctionnalités´ s importantes comme l’augmentation du nombre de positions avec une taille plus réduite et la capacité´ de réaliser des trajectoires complexes dans l’espace de travail. Le principe du nouveau module multistable combine les avantages des microactionneurs pas à pas en termes du principe et du concept numérique en termes de la répétabilité et la robustesse en boucle ouverte. Un mécanisme de positionnement précis, capable de compenser les incertitudes de fabrication a e´ te´ développé et utilise´ pour assurer un positionnement précis. En parallèle, des modèles analytiques ont e´ te´ développés pour les principaux composants dans le DiMiBot: poutres flambées préformées et actionneurs e´ électrothermiques en U. Des méthodes de conception ont été développées par la suite qui permettent de choisir les dimensions optimales garantissant les performances requises en respectant les spécifications et limites de design. Des prototypes de modules multistables, fabrique´ s dans la salle Blanche MIMENTO, ont montré´ un bon Fonctionnement dans les expériences. / A number of topics concerning digital microrobotics were addressed in this thesis. A new generation of the digital microrobot ”DiMiBot” was proposed with several advantages making the DiMiBot more accurate, more controllable and smaller. The new structure consists of only two multistable modules which adds some important features such as increasing the number of positions with smaller size and the ability to realize complex trajectories in the workspace. The principle of the new multistable module combines the advantages of the stepping microactuators in terms of the principle and of the digital concept in terms of the repeatability and robustness without feedback. The accuracy is ensured with an accurate positioning mechanism that compensate the fabrication tolerances. In parallel, analytical models was developed for the main components in the DiMiBot: preshaped curved beams and U-shaped electrothermal actuators. Subsequently, design methods were developed that allow choosing the optimal dimensions that ensure the desired outputs and respecting the design specifications and limitations. Multistable module prototypes, fabricated in the clean room MIMENTO, showed a proper functioning in the experiments.