Linear theory is useful in determining small static and dynamic deflections. However, to characterize large static and dynamic deflections, it is no longer useful or accurate, and more sophisticated analysis methods are necessary. In the case of beam deflections, linear beam theory makes use of an approximate curvature expression. Here, the exact curvature expression is used to derive the governing partial differential equations that describe the in-plane equilibrium and dynamics of a long, thin, inextensible beam, where the self-weight of the beam is included in the analysis. These beam equations are expressed in terms of arclength, and the resulting equilibrium shape is called the elastica. The analysis gives solutions that are accurate for any deflection size, and the method can be used to characterize the behavior of many structural systems. Numerical and analytical methods are used to solve or to approximate solutions to the governing equations. Both a shooting method and a finite difference, time-stepping algorithm are developed and implemented to find numerical solutions and these solutions are compared with some analytical approximation method results. The elastica equations are first used to determine both linear and nonlinear equilibrium configurations for a number of boundary conditions and loading types. In the case of a beam with a significant self-weight, the system can exhibit nonlinear static behavior even in the absence of external loading, and the elastica equations are used to determine the weight corresponding to the onset of instability (or self-weight buckling). The equations are also used to characterize linear and nonlinear vibrations of some structural systems, and experimental tests are conducted to verify the numerical results. The linear vibration analysis is applied to a vibration isolator system, where a postbuckled clamped-clamped beam or otherwise highly-deformed structure is used (in place of a conventional spring) to reduce system motion. The method is also used to characterize nonlinear dynamic behavior, and the resulting frequency-response curves are compared with those in the literature. Finally, the method is used to investigate the dynamics of subsea risers, where the effects of gravity, buoyancy, and the current velocity are considered. / Dissertation

The understanding of topics such as friction, wear, lubrication, and adhesive bonds is dependent on the ability to measure surface and interfacial energies. The surface energies of liquids may be measured accurately using a variety of techniques; however, surface energies of solids are much more difficult to accurately measure. In an attempt to develop a method that can be used to measure surface and interfacial energies of solids, this thesis proposes the use of a elastica. The elastica acts as an extremely flexible beam and provides a structure that will permit measurable deformation of the solid by relatively small surface attractions. The ends of the elastica are lifted, bent, and clamped vertically at an equal height and specified distance apart. They are then moved downward, allowing the strip to make contact with a flat, rigid, horizontal surface. Two adhesion models are investigated. First, a JKR-type analysis, which examines the effect of adhesion forces that exist within the area of contact between the elastica and the rigid surface, is considered. Various values for the work of adhesion are examined. A DMT-type analysis, which assumes that the adhesion forces act in the region just outside of the contact area, is also considered. Results are obtained for linear and constant forces. Various values for the maximum DMT force and the vertical separation between the elastica and the rigid substrate at which the adhesion forces terminate are examined. Results from the two types of analyses are compared. / Master of Science

The loop tack test measures the tack (instant grip) of an adhesive. An analytical model of this test seems to be lacking and is the subject of this research. The strip is investigated using several mathematical formulations, and the solutions are obtained numerically. The loop is created from a flexible elastic strip that is bent into a teardrop shape, with its ends clamped together. The strip is tested in a cycle, in which the loop is first pushed onto the surface, compressing the adhesive. Then the loop is pulled up, and gradually debonds from the substrate. The loop is assumed to be nonlinearly elastic and inextensible. The mechanics of the loop tack test are studied in order to determine the impact of various factors on adhesive performance. These factors include the stiffness of the backing, the stiffness and thickness of the adhesive, the elongation of the adhesive before debonding, and the contact time. The relationship between the applied force and the vertical deflection of the loop's ends is determined, as well as that between the applied force and the contact length. Also, the maximum "pull - off" force needed to remove the substrate from the loop is obtained from the results. Shapes of the loop during the cycle are found. This research will increase understanding of the behavior of the adhesive and backing during the loop tack test. With the computer model that has been developed, any set of parameters and conditions can be analyzed, and improvements can be made in the test procedure. / Master of Science

[pt] Apesar do conhecimento do comportamento de estruturas sobre base elástica ser importante para a engenharia de forma geral, a motivação deste trabalho está focada na Biomecânica, nos nossos trabalhos envolvendo o grupo de pesquisa da Clínica do Dr.Ivo Pitanguy e da Santa Casa de Misericórdia. Em tese recente de Doutorado, foi realizada uma modelagem da técnica cirúrgica de expansão da pele. A expansão da pele é um processo fisiológico, definido como a capacidade que a pele tem de aumentar sua área superficial em resposta a uma deformação imposta. Durante as expansões acompanhadas pode- se observar que dependendo da região em que o expansor é implantado seu comportamento pode ser bastante distinto. Expansores que são implantados no couro cabeludo iniciam a expansão da pele assim que é introduzida a solução salina no expansor. Quando o expansor é implantado em regiões com mais gordura, como por exemplo na coxa, a expansão da pele não se inicia imediatamente tendo em vista que o expansor se deforma para dentro, pressionando a gordura (que oferece menos resistência) e não a pele. Este comportamento ocasiona abertura dos pontos na cicatriz e pode chegar a inviabilizar todo o processo de expansão naquela região. Para a simulação do processo de expansão da pele, foi feita a expansão com lençol de borracha e para a base elástica foi usado um conjunto que consistia em uma bexiga elástica preenchida com um material viscoso no seu interior. Este trabalho é pioneiro em investigar tanto numérica quanto experimentalmente o comportamento da expansão de lençóis de borracha sobre base rígida e base elástica, comparando o seu comportamento. Os resultados numéricos e experimentais da expansão do lençol de borracha tiveram uma boa concordância e a análise paramétrica da espessura do lençol de borracha comprovou a importância da obtenção mais precisa da espessura da pele pelos médicos, já que as pressões verificadas são bem diferentes para cada espessura. Foram estudadas diversas equações constitutivas, procurando a que melhor descrevesse o processo da expansão da pele. A formulação do material Neo-Hookeano obteve os melhores resultados para o lençol de borracha. Também foi feito um estudo com a formulação de energia de Delfino para estudar a expansão da pele humana. / [en] Despite the knowledge of the behavior of structures on elastic base being important for the engineering of general form, the motivation of this work is focused in the Biomechanics, in our works involving the group of research of the Clinic of the Dr.Ivo Pitanguy and the Saint Casa de Misericórdia. In recent thesis of Dsc., a modeling of the surgical technique of expansion of the skin was carried through. The expansion of the skin is a physiological process, defined as the capacity that the skin has to increase its superficial area in reply to an imposed deformation. During the expansions it could be observed that depending on the region where the expander is implanted its behavior could be sufficiently distinct. Expanders who are implanted on the head initiate the expansion of the skin immediately when the saline solution is introduced in the expander. When the expander is implanted in regions with more fat, as for example in the thigh, the expansion of the skin does not initiate immediately in view of that the expander is deformed to the inner part, pressuring the fat (that offers little resistance) and not the skin. This behavior causes opening of the points in the scar and can make impracticable the process of expansion in that region. For the simulation the process of skin expansion, it was made an expansion with rubber sheet and a set was used for the elastic base that consisted of a filled elastic bladder with a viscous material in its interior. This work is pioneer in investigating numerical and experimentally the behavior of the rubber sheet expansion on rigid base and elastic base, comparing its behavior. The numerical and experimental results of the expansion of the rubber sheet had a good agreement and the parametric analysis of the thickness of the rubber sheet proved the importance of a precise measure of the skin thickness by the doctors, since the verified pressures are different for each thickness. Diverse constituent equations had been studied, looking the one that better described the process of the expansion of the skin. The formularization of the Neo-Hook material got the best results for the rubber sheet. Also a study with the formularization of energy of Delfino was made to study the expansion of the human skin.

The primary visual cortex (V1) has long been considered the main low level visual analysis area of the brain. The classical view is of a feedfoward system functioning as an edge detector, in which each cell has a receptive field (RF) and a preferred orientation. Whilst intuitive, this view is not the whole story. Although stimuli outside a neuron’s RF do not result in an increased response by themselves, they do modulate a neuron’s response to what’s inside its RF. We will refer to such extra-RF effects as contextual modulation. Contextual modulation is thought to underlie several perceptual phenomena, such as various orientation illusions and saliency of specific features (such as a contour or differing element). This gives a view of V1 as more than a collection of edge detectors, with neurons collectively extracting information beyond their RFs. However, many of the accounts linking psychophysics and physiology explain only a small subset of the illusions and saliency effects: we would like to find a common principle. So first, we assume the contextual modulations experienced by V1 neurons is determined by the elastica model, which describes the shape of the smoothest curve between two points. This single assumption gives rise to a wide range of known contextual modulation and psychophysical effects. Next, we consider the more general problem of encoding and decoding multi-variate stimuli (such as center surround gratings) in neurons, and how well the stimuli can be decoded under substantial noise levels with a maximum likelihood decoder. Although the maximum likelihood decoder is widely considered optimal and unbiased in the limit of no noise, under higher noise levels it is poorly understood. We show how higher noise levels lead to highly complex decoding distributions even for simple encoding models, which provides several psychophysical predictions. We next incorporate more updated experimental knowledge of contextual modulations. Perhaps the most common form of contextual modulations is center surround modulation. Here, the response to a center grating in the RF is modulated by the presence of a surrounding grating (the surround). Classically this modulation is considered strongest when the surround is aligned with the preferred orientation, but several studies have shown how many neurons instead experience strongest modulation whenever center and surround are aligned. We show how the latter type of modulation gives rise to stronger saliency effects and unbiased encoding of the center. Finally, we take an experimental perspective. Recently, both the presence and the underlying mechanisms of contextual modulations has been increasingly studied in mice using calcium imaging. However, cell signals extracted with calcium imaging are often highly contaminated by other sources. As contextual effects beyond center surround modulation can be subtle, a method is needed to remove the contamination. We present an analysis toolbox to de-contaminate calcium signals with blind source separation. This thesis thus expands our understanding of contextual modulation, predicts several new experimental results, and presents a toolbox to extract signals from calcium imaging data which should allow for more in depth studies of contextual modulation.

[pt] O estudo de estacas semi-enterradas tem grande importância na construção civil devido principalmente à sua ampla aplicação em diversas áreas da engenharia. O presente trabalho tem como objetivo obter uma solução exata para as freqüências naturais e modos de vibração dessas estacas e, com base nestes resultados, analisar o comportamento do sistema não-linear. A análise das vibrações lineares parte da obtenção de um funcional de energia e dedução das equações diferenciais parciais de movimento para o trecho enterrado e desenterrado e a determinação das diversas famílias de soluções para cada equação de movimento em função dos parâmetros adimensionais característicos do problema. Essa solução exata possibilita mostrar a influência dos parâmetros de carregamento, de rigidez da fundação, da altura da fundação e das condições de apoio nas freqüências naturais e modos de vibração. A não- linearidade do problema é originária da geometria da estrutura e a sua consideração implica na obtenção de equações diferenciais não-lineares. A resolução destas equações é feita de forma aproximada, empregando-se o método de Ritz para discretizar a coluna no espaço e os métodos de Galerkin-Urabe e do Balanço Harmônico para resolver as equações de movimento resultantes do processo de discretização. Com base nestes resultados, analisa-se a influência dos parâmetros físicos e geométricos do sistema coluna-fundação nas vibrações livres e forçadas da estaca. / [en] The study of partially embedded piles is an important topic in civil engineering due to its use in several engineering fields. The aim of the present work is to derive an exact solution for the natural frequencies and vibration modes of these piles and, based on these results, to analyze the nonlinear behavior of the column-foundation system. In order to study the free vibration problem, the energy functional of the system is obtained, allowing the derivation of the partial differential equations of motion for the buried and unburied parts of the pile. The possible solutions of these equations are then obtained as a function of a set of non-dimensional parameters characteristic of the problem. The consideration of the geometric nonlinearity of the beam leads to a set of nonlinear differential equations. The solution of these equations is obtained by employing the Ritz method to discretize the column in space and the methods of Galerkin- Urabe and Harmonic Balance to derive an approximate solution for the resulting equations of motion. Based on these results, the influence of the geometrical and physical parameters of the column-foundation system on the free and forced non-linear vibrations of the pile is analyzed.

No description available.

The measurement of the work of adhesion is of significant technical interest in a variety of applications, ranging from a basic understanding of material behavior to the practical aspects associated with making strong, durable adhesive bonds. The objective of this thesis is to investigate a novel technique using an elastica loop to measure the work of adhesion between solid materials. Considering the range and resolution of the measured parameters, a specially designed apparatus with a precise displacement control system, an analytical balance, an optical system, and a computer control and data acquisition interface is constructed. An elastica loop made of poly(dimethylsiloxane) [PDMS] is attached directly to a stepper motor in the apparatus. To perform the measurement, the loop is brought into contact with various substrates as controlled by the computer interface, and information including the contact patterns, contact lengths, and contact forces is obtained. Experimental results indicate that due to anticlastic bending, the contact first occurs at the edges of the loop, and then spreads across the width as the displacement continues to increase. The patterns observed show that the loop is eventually flattened in the contact region and the effect of anticlastic bending of the loop is reduced. Compared to the contact diameters observed in the classical JKR tests, the contact length obtained using this elastica loop technique is, in general, larger, which provides potential for applications of this technique in measuring interfacial energies between solid materials with high moduli. The contact procedure is also simulated to investigate the anticlastic bending effect using finite element analysis with ABAQUS. The numerical simulation is conducted using a special geometrically nonlinear, elastic, contact mechanics algorithm with appropriate displacement increments. Comparisons of the numerical simulation results, experimental data, and the analytical solution are made. / Master of Science

Dans un contexte où l'utilisation de structures déployables s'est généralisée, le département Recherche de la société Thales Alenia Space étudie un nouveau concept de télescope spatial dont le miroir secondaire est déployé grâce au déroulement de six mètres rubans. Des études antérieures ont permis la mise au point d'un prototype constitué de rubans métalliques dont le déploiement s'est avéré trop violent. Dans ce travail de thèse nous proposons d'une part un nouveau type de ruban à la vitesse de déroulement maîtrisable et d'autre part un modèle original décrivant le comportement dynamique de tels rubans, permettant de mieux appréhender les phénomènes complexes pouvant intervenir lors de scénarios de pliage, de déploiement ou de déroulement. La solution envisagée pour contrôler la vitesse de déroulement repose sur l'exploitation des propriétés mécaniques d'une couche de matériau viscoélastique collée à la surface du ruban. Ces propriétés variant avec la température permettent de garantir un maintien de la position enroulée à froid et assurent un déroulement régulé grâce à un réchauffage localisé. Ces phénomènes ont été mis en évidence expérimentalement et numériquement. La lourdeur des méthodes classiques de modélisation et le manque de richesse des méthodes simplifiées nous ont conduit à développer un modèle de poutre à section fortement déformable permettant de décrire le comportement dynamique des rubans en grands déplacements. Partant d'un modèle de coque, l'originalité de la méthode repose essentiellement sur l'introduction d'une cinématique de type elastica pour décrire les grandes variations de forme de la section. Un modèle énergétique 1D est obtenu en intégrant dans la section et le problème est résolu à l'aide du logiciel de modélisation par éléments finis COMSOL. On propose finalement un modèle continu 1D à 4 paramètres cinématiques qui permet de rendre compte d'une large gamme de phénomènes intervenant dans des scénarios complexes de pliage, de déroulement et de déploiement dynamique. / The research department of Thales Alenia Space is studying new concepts of space telescopes whose secondary mirror is deployed thanks to the unreeling of six tape-springs. A breadboard using metallic tape-springs has been built during preliminary studies and has exhibited a deployment that is too energetic and induce too important shocks.In this thesis a new kind of tape-spring with a controlled uncoiling speed is introduced. Secondly a rod model with highly deformable thin-walled cross-sections describing the dynamic behaviour of tape-springs is derived.In order to over come the deployment speed of a tape spring, a viscoelastic layer is stuck on its sides. Thanks to its properties varying with the temperature, the viscoelastic layer is used to maintain the tape-spring in a coiled configuration at low temperature whereas a local heating leads to a controlled uncoiling. These phenomenons have been underlined experimentally and numerically.Because of the high complexity of classical shell models and the lack of details of simplified models, smart modelling methods need to be developed to describe the highly non linear behaviour of a tape-spring. A planar rod model with highly deformable thin-walled cross-sections that accounts for large displacements and large rotations in dynamics is proposed. Starting from a classical shellmodel, the main additional assumption consists in introducing an elastica kinematics to describe thelarge changes of the cross-section shape with very few parameters. The expressions of the strain andkinetic energies are derived by performing an analytical integration over the section. The Hamilton principle is directly introduced in a suitable finite element software to solve the problem. Several examples (folding, coiling and deployment of a tape spring) are studied through the FEM software COMSOL to demonstrate the ability of the 4-parameter model to account for several phenomena: creation of a single fold and associated snap-through behaviour, splitting of a fold into two, motion of a fold along the tape during a dynamic deployment, scenarios of coiling and uncoiling of a bistable tape-spring.

[pt] Diversos acidentes envolvendo dutos submarinos já aconteceram no Brasil como o do Gasoduto PCR-01/Lubnor e o da plataforma P-55 de 2,3 km no campo de Roncador, na Bacia de Campos. Esses acidentes ocorrem em muitos casos devido à flambagem, à fadiga, ao intenso processo corrosivo, à deficiência de projeto, a falta de manutenção dos mesmos. Os dutos submarinos representam uma alta porcentagem no custo total de uma unidade de extração de petróleo. Sua importância se torna vital para a extração de petróleo em águas territoriais brasileiras. Seu projeto estrutural é uma atividade que pode ser dividida em várias etapas que devem ser seguidas à risca para garantir a conformidade do mesmo com as normas nacionais e internacionais sua operação em um dos mais inóspitos cenários da natureza: o fundo do mar. Nesta situação, o duto fica sujeito a carregamentos extremos, tanto estáticos quanto dinâmicos. Por este motivo, ele é constituído de uma estrutura de camadas bastante complexa. O objetivo deste trabalho é a avaliação das condições de operação de dutos submarinos sujeitos à ação de ondas e correntes marinhas. Um estudo paramétrico em elementos finitos é realizado para compreender a influência das condições de contorno, diferentes comprimentos de vão livre do duto submarino e variações do tipo de solo na resposta dinâmica do duto submarino. È desenvolvida também uma solução analítica para o problema. As soluções numérica, analítica e as recomendações da norma são confrontadas e tiradas conclusões sobre os principais fatores a serem considerados pelos engenheiros envolvidos na construção de estruturas deste tipo. / [en] Several accidents involving subsea pipelines have happened in Brazil as the pipeline PCR-01 / Lubnor and the P-55 platform 2.3 km in the Roncador field in the Campos Basin. These accidents occur in many cases due to buckling, fatigue, the intense corrosive process, design deficiency, lack of maintenance. The submarine pipelines represent a high percentage in the total cost of an oil extraction unit. Its importance becomes vital for the extraction of oil in Brazilian waters. Its structural design is an activity that can be divided into several steps that must be followed strictly to ensure its conformity with national and international standards operation in one of the harshest scenes of nature: the seabed. In this situation, the product is subject to extreme loads, both static and dynamic. For this reason, it consists of a complex layer structure. The objective of this study is the evaluation of the operating conditions of submarine pipelines subject to the action of waves and currents. A parametric study of finite element is performed to understand the influence of the boundary conditions, different span lengths of submarine pipeline and variations of soil type on the dynamic response of submarine pipeline. It is also developed an analytical solution to the problem. The numerical solutions, analytical and standard recommendations are compared and conclusions drawn on the main factors to be considered by the engineers involved in the construction of such structures.