The increase of new and ever more stringent emission legislation has brought about with it a surge in the demand for more sustainable automotive solutions. This has particularly been the case for automobiles, including heavy-duty vehicles like trucks and buses, with internal combustion engines, which now require the design and manufacturing of more durable and reliable components. An important component of internal combustion engine automobiles, which helps achieve this target, is the exhaust after-treatment system. Exhaust after-treatment systems are usually equipped with some type of catalytic converter, treating the combustion gases from the engine exhaust manifold to reduce the concentration of pollutants. The catalytic converter assembly usually consists of an assembly of an outer metallic canning, an inner substrate and a packaging mat in between the two. The packaging mat, commonly known as the support mat, is an important component in the assembly, protecting the ceramic substrate from road induced and thermal loads, thereby preventing any damage to the latter. This thesis involves further development of a finite element model for the support mat that could be used in catalytic converter simulations with a reasonable degree of accuracy and reliability. In line with this objective, the characteristic mechanical response of the mat is first studied through a series of material tests: namely compression, friction, and shear tests. Different non-linear material models like hyperfoam, hyperelastic and viscoelastic models, are then created in ABAQUS to simulate the mat behaviour in the tests. The material model correlating most closely with the test is then implemented in the simulation of the assembly process, canning of a catalytic converter. This report includes the material tests conducted on the mats in new and aged condition, findings of the characteristic response of the mats in these tests as well as the constitutive material modelling and finite element simulations carried out for correlation with test data from the new mats. The most appropriate material model was also implemented in a canning assembly simulation to evaluate the efficacy of the material model in predicting the mat pressure, gap bulk density, and push-in force.

No description available.

[pt] Nas últimas décadas, tem-se observado um crescente número de pesquisas e aplicações envolvendo estruturas hiperelásticas, integrando diferentes áreas da engenharia de estruturas e de materiais, impulsionados pelos avanços tecnológicos do processo de manufatura por adição (impressões 3D e 4D), muitas envolvendo flambagem. Entretanto têm-se poucas informações sobre a estabilidade de elementos estruturais hiperelásticos. O objetivo desta tese é, pois, estudar a estabilidade de colunas e arcos hiperelásticos. Com esta finalidade, desenvolve-se inicialmente uma formulação variacional não linear pseudo-3d para vigas hiperelásticas incompressíveis, seguindo as hipóteses de Euler-Bernoulli. Para avaliar esta formulação, o problema de flexão pura de uma viga hiperelástica é investigado numericamente usando elementos finitos, e experimentalmente. Diversos modelos constitutivos para materiais hiperelásticos não lineares submetidos a deformações finitas são adotados. Ensaios uniaxiais são usados para determinação das constantes de cada modelo constitutivo e determinação do modelo mais preciso para o material considerado (polivinilsiloxano). Diversos elementos finitos uni- e tridimensionais são testados. A comparação entre resultados obtidos pela formulação proposta e por elementos finitos com os dados experimentais permitem determinar a precisão da formulação bem como o tipo de elemento e a discretização mais apropriada para as análises. Adicionalmente, estes resultados permitem aferir a importância das deformações axiais e cisalhantes e do peso próprio em barras hiperelásticas. O auxílio de um software de medição por correlação de imagem digital durante os ensaios permite uma análise aprofundada do campo de deformações, juntamente com as análises por elementos finitos tridimensionais. A seguir estuda-se a flambagem de colunas hiperelásticas com diferentes condições de contorno. Sob solicitações de flexo-compressão, observase que as deformações da estrutura ao longo do caminho não linear de equilíbrio são influenciadas pelas deformações axiais e cisalhantes, que se mostram importantes mesmo sob pequenas deformações. Tendo em vista a importância das imperfeições iniciais em problemas de estabilidade, propõe-se aqui uma modificação do método de Southwell para incluir tais deformações. Finalmente, analisa-se o comportamento multiestável de arcos hiperelásticos pré-tensionados considerando um ou múltiplos arcos associados em paralelo, obtendo-se boa correlação entre resultados numéricos e experimentais. Os resultados obtidos na análise experimental mostram que flexibilidade dos materiais hiperelásticos altera os caminhos de equilíbrio e que a estrutura é capaz de apresentar níveis elevados de deformação sem danos ao material, conferindo-as um grande potencial de absorção e armazenamento de energia. Observa-se também o papel importante do peso próprio nessas trajetórias. A compreensão do comportamento não linear e estabilidade desses sistemas estruturais são importantes em aplicações práticas como controle de vibrações, absorção e coleta de energia, desenvolvimento de metamateriais, bioengenharia e medicina e robôs flexíveis, dentre outras. / [en] In recent decades, there has been an increasing number of researches and applications involving hyperelastic structures, integrating different areas of engineering structures and materials, driven by technological advances in the manufacturing process by addition (3D and 4D printing), many involving buckling. However, there is little information about the stability of hyperelastic structural elements. The objective of this thesis is, therefore, to study the stability of hyperelastic columns and arches. For this purpose, a non-linear pseudo-3d variational formulation is initially developed for incompressible hyperelastic beams, following the Euler-Bernoulli hypotheses. To evaluate this formulation, a pure bending problem of a hyperelastic beam is investigated numerically using finite elements, and experimentally. Several constitutive models for nonlinear hyperelastic materials subjected to finite strains are adopted. Uniaxial tests are used to determine the constants of each constitutive model and to determine the most accurate model for the material considered (polyvinylsiloxane). Several one- and three-dimensional finite elements are tested. The comparison between results obtained by the proposed formulation and by finite elements with the experimental data allows determining the accuracy of the formulation as well as the type of element and the most appropriate discretization for the analyses. Additionally, these results allow evaluating the importance of axial and shear strains and self-weight in hyperelastic bars. The aid of a digital image correlation measurement software during the tests allows an in-depth analysis of the deformation field, along with three-dimensional finite element analyses. Next, the buckling of hyperelastic columns with different boundary conditions is studied. Under bending and compression actions, it is observed that the deformations of the structure along the non-linear path of equilibrium are influenced by axial and shear deformations, which are important even under small deformations. Bearing in mind the importance of initial imperfections in stability problems, a modification of the Southwell method is proposed here to include such deformations. Finally, the multistable behavior of pre-compressed hyperelastic arches is analyzed considering one or multiple archess associated in parallel, obtaining a good correlation between numerical and experimental results. The results obtained in the experimental analysis show that the flexibility of hyperelastic materials alters the equilibrium paths and that the structure is capable of presenting high levels of deformation without damage to the material, giving them a great potential for energy absorption and storage. It is also observed the important role of self-weight in these trajectories. Understanding the non-linear behavior and stability of these structural systems are important in practical applications such as vibration control, energy absorption and harvesting, metamaterial development, bioengineering and medicine and flexible robots, among others.

Although several studies have proven the accuracy of using a non-contact, air-coupled receiver in nonlinear ultrasonic (NLU) Rayleigh wave measurements, inconsistent results have been observed when working with narrow specimens. The objectives of this research are first, to develop a 3D numerical finite element (FE) model which predicts nonlinear ultrasonic measurements and second, to apply the validated model on the narrow waveguide to determine causes of the previously observed experimental issues. The commercial FE-solver ABAQUS is used to perform these simulations. Constitutive law and excitation source properties are adjusted to match experiments conducted, considering inherent effects of the non-contact detection, such as frequency dependent pressure wave attenuation and signal averaging. Comparison of “infinite” and narrow width simulations outlines various influences which impair the nonlinear Rayleigh wave measurements. When the wave expansion is restricted, amplitudes of the fundamental and second harmonic components decrease more significantly and the Rayleigh wavefronts show an oscillating interaction with the boundary. Because of the air-coupled receiver’s finite width, it is sensitive to these edge effects which alter the observed signal. Thus, the narrow specimen adversely affects key factors needed for consistent measurement of material nonlinearity with an air-coupled, non-contact receiver.

In vielen industriellen Anwendungen sind Dichtungen im Einsatz. Vergleicht man den Preis mit dem eines Gesamtsystems, in denen Dichtungen verwendet werden, so sind Dichtungen verhältnismäßig günstig. Jedoch führt ein Versagen von Dichtungen meist zu schwerwiegenden Konsequenzen. Dichtungen sind komplexe Subsysteme und ihre Auslegung erfordert umfangreiche Kenntnisse im Bereich Materialmodellierung, Belastung und Versagenskriterien. Die heutige Simulationstechnologie ermöglicht einen parametrischen Workflow für die Berechnung des Verhaltens von Dichtungen mit den auftretenden Effekten wie nichtlinearem Materialverhalten, wechselnden Kontaktbedingungen und Flüssigkeitsunterwanderung bei Druck. Als ein führendes Simulationswerkzeug für diese physikalische Fragestellung wird ANSYS Mechanical für die Auslegung herangezogen. Desweiteren kann das Verständnis für das Produkt erhöht werden, was zu einer Verbesserung der Funktionalität und der Zuverlässigkeit führt. Versuchsdaten können als Spannungs-Dehnungskurven in ANSYS importiert werden, welche das Materialverhalten des hyperelastischen Werkstoffs mit traditionellen Materialmodellen wie Mooney Rivlin, Ogden and Yeoh oder einer neueren Formulierung, der Antwortfunktionsmethode, widerspiegeln. Robuste Kontakttechnologien beschleunigen die Simulation und Entwicklungszeit-Berechnungszeiten und gewährleisten ein genaues Verhalten des Simulationsmodells. Insbesondere bei Dichtungen ist die druckbeaufschlagte Fläche in 2D und 3D Anwendungen von Bedeutung. ANSYS berechnet diese automatisch in Abhängigkeit des aktuellen Kontaktzustandes. Diese benutzerfreundliche Unterstützung führt zu einer höheren Genauigkeit des Simulationsergebnisses, da ein manuelles Schätzen der Druckflächen entfällt. Mit einem parametrischen und durchgängigen Ansatz innerhalb von ANSYS Workbench, beginnend bei der CAD-Geometrie, über die Vernetzung, Material- und Randbedingungsdefinition und Lösung. können eine Reihe von Varianten in kurzer Zeit berechnet werden. Neben einem besseren Verständnis für das Produkt hilft dies dem Ingenieur Änderungen vorzunehmen, was zu exakten und aussagekräftigen Ergebnissen führt. Desweiteren kann der Einfluss von Unsicherheiten berücksichtigt werden, sodass der Berechnungsingenieur fernab von idealen Bedingungen robuste und zuverlässige Dichtungen entwickeln kann.

En struktur analys på Ericssons MINILINK-6352 har utförts för att undersöka spänningar och deformationer på enheten, främst med fokus på de termiska gränskiktsmaterialen och buktningar av kretskortet. Dessa är viktiga aspekter när man överväger om enheten är termiska lämpad ur en mekanisk synvinkel, där god ytkontakt mellan de olika kropparna är avgörande för ordentlig kylning genom värmeledning. Analysen kräver tillräcklig materialdata till gränskiktsmaterialen och kretskortet för att kunna skapa lämpliga matematiska modeller. Enaxliga kompressionstester har genomförts för att karakterisera de hyperelastiska och viskoelastiska lagar för fyllda silikongummimaterial som används som termiska gränskiktsmaterial, som ibland kallas för gappad. Böjning av ett kretskort simulerades och jämfördes med ett tre--punkts böjtest för att verifiera om befintlig materialdata i beräkningsprogrammen var tillräcklig, jämförelsen visade god överensstämmelse. Kretskortet med dess komponenter, som modellerades som styva block, med gappads ovanpå som komprimeras av en platta simulerades och ett svagt område hittades. Detta område var sedan tidigare känt och har i ett senare skede eliminerats genom att tillsätta ytterligare en stödpelare. Därav visar denna studie en metod för att hitta intressanta regioner tidigt i konstruktionsfasen som lätt kan ändras för att uppfylla nödvändiga krav och undvika brister i konstruktionen. Arbetet har visat sig användbart genom att hitta detta svaga område i exempel produkten, arbetet ger även tillräckligt med information och exempeldata för att ytterligare utreda liknande produkter. Kombinationen av erfarenhet och simulering möjliggör smartare designval. / A structural analysis on Ericssons MINILINK-6352 has been performed in order to investigate stresses and deformations of the unit, mainly focusing on the thermal interface materials and warpage of the printed circuit boards. These are important aspects when considering if the unit is thermally adequate from a mechanical point of view, where good surface contact between various bodies are critical for proper cooling through heat conductivity. The analysis requires sufficient materal data for the interface material and the circuit board in order to create suitable mathematical models. Uniaxial compression tests have been conducted to characterise the hyperelastic and viscoelastic constitutive laws of a filled silicone rubber material used as a thermal interface material, commonly referred to as a thermal pad. Bending of a printed circuit board was simulated and compared to a three-point bend test on the circuit board in order to verify material data already available in the computational software, which showed good agreement. The entire radio unit was mechanically analysed during its sealing process. The circuit board with attached components modelled as stiff blocks with thermal pads on top compressed by plates was simulated and a weak area was found. This area in question was already known and has in a later stage been eliminated by adding an additional supporting pillar. Hence this study shows a methodology to find regions of interest at an early design phase which can easily be altered to fulfil necessary requirements and eliminate design flaws. This work has proven useful in finding weak regions in the example product, it also provides enough information and example data to further investigate similar products. The combination of experience and simulation allows for smarter design choices.

The hands and feet account for half of the complexity of the musculoskeletal system, while the skin of the hand is specialised with many important structures. Much of the subtlety of the mechanism of the hand lies in the soft tissues, and the tactile and proprioceptive sensitivity depends on the large number of mechanoreceptors embedded in specific structures of the soft tissues. This thesis investigates synthetic materials and manufacturing techniques to enable building robots that reproduce the biomechanics and tactile sensitivity of vertebrates – histomimetic robotics. The material and mechanical anatomy of the hand is reviewed, highlighting difficulty of numerical measurement in soft-tissue anatomy, and the predictive nature of descriptive anatomical knowledge. The biomechanical mechanisms of the hand and their support of sensorimotor control are presented. A palate of materials and layup techniques are identified for emulating ligaments, joint surfaces, tendon networks, sheaths, soft matrices, and dermal structures. A method for thermoplastically drawing fine elastic fibres, with liquid metal amalgam cores, for connecting embedded sensors is demonstrated. The performance requirements of skeletal muscles are identified. Two classes of muscle-like bulk MEMS electrostatic actuators are shown theoretically to be capable of meeting these requirements. Means to manufacture them, and their additional application as mechanoreceptors are described. A novel machine perception algorithm is outlined as a solution to the problem of measuring soft tissue anatomy, CAD/CAE/CNC for layup of histomimetic robots, and sensory perception by such robots. The results of the work support the view that histomimetic robotics is a viable approach, and identify a number of areas for further investigation including: polymer modification by graft-polymerisation, automated layup tools, and machine perception.

Mechanical forces have been observed to affect various aspects of life, for example, cell differentiation, cell migration, locomotion and behavior of multicellular organisms etc. Such forces are generated either by external entities such as mechanical touch, fluid flow, electric and magnetic fields or by the living organisms themselves. Study of forces sensed and applied by living organisms is important to understand the interactions between organisms and their environment. Such studies may reveal molecular mechanisms involved in mechanosensation and locomotion. Several techniques have been successfully applied to measure forces exerted by single cells and cell monolayers. The earliest technique made use of functionalized soft surfaces and membranes as substrates on which cell monolayers were grown. The forces exerted by the cells could be measured by observing deformation of the substrates. Atomic Force Microscope (AFM) is another sensitive instrument that allows one to exert and measure forces in pico-Newton range. Advances in micromachining technology have enabled development of miniature force sensors and actuators. Latest techniques for mechanical force application and measurement use micromachined Silicon cantilevers in single as well as array form and micropillar arrays. Micropillar arrays fabricated using soft lithography enabled the use of biocompatible materials for force sensors. Together, these techniques provide access to a wide range of forces, from sub micro-Newton to milli-Newton. In the present work, types of forces experienced in biological systems and various force measurement and actuation techniques will be introduced. This will be followed by in depth description of the two major contributions of this thesis, 1) ―Colored polydimethylsiloxane micropillar arrays for high throughput measurements of forces applied by genetic model organisms‖. Biomicrofluidics, January 29, 2015. doi: 10.1063/1.4906905 2) ―Air microjet system for non-contact force application and the actuation of micro-structures‖. Journal of micromechanics and microengineering, December 15, 2015. doi: 10.1088/0960-1317/26/1/017001 Device developed for force measurement consists of an array of micropillars made of a biocompatible polymer Poly Dimethyl Siloxane (PDMS). Such devices have been used by researchers to measure traction forces exerted by single cells and also by nematode worm Caenorhabditis elegans (C. elegans). C. elegans is allowed to move in between the micropillars and the locomotion is video recorded. Deflection of the micropillar tips as the worm moves is converted into force exerted. Transparent appearance of C. elegans and PDMS poses difficulties in distinguishing micropillars from the worm, thus making it challenging to automate the analysis process. We address this problem by developing a technique to color the micropillars selectively. This enabled us to develop a semi-automated graphical user interface (GUI) for high throughput data extraction and analysis, reducing the analysis time for each worm to minutes. Moreover, increased contrast because of the color also delivered better images. Addition of color changed the Young‘s modulus of PDMS. Thus the dye-PDMS composite was characterized using hyper-elastic model. The micropillars were also calibrated using commercial force sensor. Analysis of forces exerted by wild type and mutant C. elegans moving on an agarose surface was performed. Wild type C. elegans exerted a total average force of 7.68 µN and an average force of ~1 µN on an individual pillar. We show that the middle of C. elegans exerts more force than its extremities. We find that C. elegans mutants with defective body wall muscles apply significantly lower force on individual pillars, while mutants defective in sensing externally applied mechanical forces still apply the same average force per pillar compared to wild type animals. Average forces applied per pillar are independent of the length, diameter, or cuticle stiffness of the animal. It was also observed that the motility of the worms with mechanosensation defects, lower cuticle stiffness, and body wall muscle defects was reduced with worms that have defective body wall muscle having the largest degree. Thus, we conclude that while reduced ability to apply forces affects the locomotion of the worm in the micropillar array, the reduced motility/locomotion may not indicate that the worm has reduced ability to apply forces on the micropillars. We also used the colored micropillar array for the first time to measure forces exerted by Drosophila larvae. Our device successfully captured the peristaltic rhythm of the body wall muscles of the larva and allowed us to measure the forces applied on each deflected pillar during this motion. Average force exerted by 1st instar wild type Drosophila larvae was measured to be ~ 1.5 µN per pillar. We demonstrated that a microjet of air can be used to apply forces in micro-Newton range. We developed a standalone system to generate a controlled air microjet. Microjet was generated using a controlled electromagnetic actuation of a diaphragm. With a nozzle diameter of 150 µm, the microjet diameter was maintained to a maximum of 1 mm at a distance of 5 mm from the nozzle. The force generated by the microjet was measured using a commercial force sensor to determine the velocity profile of the jet. Axial flow velocities of up to 25 m/s were obtained at distances as long as 6 mm. The microjet exerted a force up to 1 µN on a poly dimethyl siloxane (PDMS) micropillar (50 µm in diameter, 157 µm in height) and 415 µN on a PDMS membrane (3 mm in diameter, 28 µm thick). We also demonstrate that from a distance of 6 mm our microjet can exert a peak pressure of 187 Pa with a total force of about 84 µN on a flat surface with 8 V operating voltage. Next, we demonstrated that the response of C. elegans worms to the impinging air microjet is similar to the response evoked using a manual gentle touch. This contactless actuation tool avoids contamination and mechanical damage to the samples. Out of the cleanroom fabrication and robust design make this system cost effective and durable. Magnetic micropillars have been used as actuators. We fabricated magnetic micropillar arrays and designed actuation mechanisms using permanent magnet and a pulsed electromagnet. Force of about 19 µN was achievable using a permanent magnet actuation. In a pulsed electromagnetic field micropillar exerted a force of about 10 µN on a commercial force sensor. These techniques have promising applications when actuation needs to be controlled from long distances.

CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O câncer de mama é um problema de saúde pública e possui a maior incidência e mortalidade na população feminina em todo o mundo. A detecção precoce do câncer de mama é essencial para redução da morbidade e mortalidade associadas a esta doença. Alguns dos métodos usados para detecção dos tumores mamários são a ultrassonografia, a imagem por ressonância magnética (MRI), a tomografia por emissão de pósitrons (PET), a tomossíntese e a mamografia, recomendada como técnica de rastreamento. Cada um dos métodos apresenta vantagens e desvantagens, como provocar desconforto ao paciente durante a realização dos exames, possíveis reações ao agente de contraste, emissão de radiação, dependência do operador para análise dos resultados, dificuldade de detecção em tecidos densos, falta de acessibilidade para pessoas com deficiência ou baixa mobilidade, alto custo e produção de rejeitos radioativos. O objetivo principal deste trabalho é aplicar os métodos de impedância eletromecânica e térmica na detecção de inclusões para que possam ser futuramente usados como técnicas alternativas às já existentes na identificação de tumores mamários. A aplicação do método da impedância eletromecânica que utiliza transdutores piezelétricos, atuando simultaneamente como sensor e atuador, acoplados à estrutura analisada permite o monitoramento das mudanças da massa, rigidez e/ou amortecimento e a consequente detecção da inclusão. O mesmo procedimento é aplicado no método da impedância térmica que, por sua vez, consiste na razão entre a variação da resposta da temperatura superficial da estrutura em função da aplicação de um fluxo de calor externo. A detecção das inclusões torna-se possível devido a definições de métricas de dano que são parâmetros estatísticos capazes de representar numericamente a diferença entre duas medições antes e após o dano. A metodologia proposta é validada experimentalmente através da aplicação em materiais hiperplásticos de geometria simples e complexa. Amostras de silicone e modelos de aplicação médica são analisadas. Os métodos de impedância propostos apontaram, preliminarmente, para uma maior sensibilidade da técnica a inclusões menores, de 10 mm de diâmetro para os testes realizados. Além disso, observou-se que o aquecimento externo imposto aos modelos e a presença de geração de calor nas inclusões auxiliou na detecção. Um teste qualitativo foi realizado in vivo para a análise do potencial de uso da impedância eletromecânica em aplicações clínicas. Este trabalho apresenta contribuições importantes, não só no campo da engenharia biomecânica, mas também na análise do comportamento estrutural, ampliando as aplicações de técnicas de dano em materiais hiperelásticos, assim como, propondo o uso da impedância térmica como um novo parâmetro para identificação de inclusões ou falhas estruturais em ensaios não destrutivos. / Breast cancer is a public health problem and has the highest incidence and mortality in the female population worldwide. Early detection of breast cancer is essential for reducing the morbidity and mortality associated with this disease. Some of the methods used to detect breast tumors are ultrasonography, magnetic resonance imaging (MRI), positron emission tomography (PET), tomosynthesis and mammography, which is recommended as a screening technique. Each method has its advantages and disadvantages, such as discomfort to the patient during the exams, possible reactions to the contrast agent, radiation emission, operator dependence for the analysis of results, difficulty for detection in dense tissues, lack of accessibility for people with disabilities or low mobility, high cost and radioactive waste production. The main objective of this work is to apply the electromechanical and thermal impedance methods in the detection of inclusions, in order to be used, in the future, as alternative techniques to those already existent for the identification of breast tumors. The application of the electromechanical impedance method using piezoelectric transducers, acting simultaneously as a sensor and actuator, coupled to the analyzed structure allows the monitoring of mass, rigidity and/or damping variations, and consequent detection of the inclusion. The same procedure is applied in the thermal impedance method, which consists of the ratio between the gradient of the surface temperature response of the structure as a function of the application of an external heat flow. The detection of inclusions is possible due to the damage metrics that are statistical parameters capable of numerically representing the difference between two measurements before and after the damage. The proposed methodology is validated experimentally through the application in hyperplastic materials of simple and complex geometry. Silicone samples and medical application models are analyzed. The proposed impedance methods preliminarily presented a higher sensitivity of the technique to smaller inclusions of 10 mm in diameter for the tests performed. In addition, it was observed that the external heating imposed on the models and the presence of heat generation in the inclusions aided in the detection. A qualitative test was performed in vivo to analyze the potential of the use of electromechanical impedance in clinical applications. This work presents important contributions not only in the field of biomechanical engineering, but also in the analysis of structural behavior, expanding the applications of damage techniques in hyperelastic materials, as well as proposing the use of thermal impedance as a new parameter for identification of inclusions or structural failures in nondestructive testing. / Tese (Doutorado)

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2015-10-27T18:16:56Z No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2015.pdf: 7212801 bytes, checksum: 41d5a93b0ae749a6418b871cd4fea683 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-10-28T14:29:10Z (GMT) No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2015.pdf: 7212801 bytes, checksum: 41d5a93b0ae749a6418b871cd4fea683 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-10-28T14:29:10Z (GMT). No. of bitstreams: 2 Dissertação - Renato de Sousa e Silva - 2015.pdf: 7212801 bytes, checksum: 41d5a93b0ae749a6418b871cd4fea683 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-06-12 / Fundação de Amparo à Pesquisa do Estado de Goiás - FAPEG / Structural elements with large deformation capacity as hyperelastic membranes are gaining prominence in several engineering branches and have applications in biomechanics, thus the study of the dynamic behavior of hyperelastic structures is very important to minimize effects as the loss of the stability and undesirable vibrations. In this paper the elasticity theory for large deformations in the development of membrane theory, in order to investigate the linear and nonlinear dynamic behavior of hyperelastic membrane is used. A rectangular membrane composed of an elastomeric material, isotropic, homogeneous, incompressible and consisting of neo-Hookeano, Mooney-Rivlin and Yeoh models is considered. To model the membrane, the energy and work of external forces are used together with the application of the Hamilton on the Lagrange function. The Galerkin method is applied to obtain a discretized system of nonlinear Partial Differential Equations (PDE) and the Runge-Kutta method of 4th order is used to obtain its time response. Finally, the Brute Force and Continuation methods are applied to investigate the nonlinear dynamic behavior of the membrane. A parametric analysis is carried out looking to evaluate the influence of the material, geometry and initial tensions on the natural frequencies of the membrane. It is noted that increasing the size of a tensioned membrane, it is also increased the natural frequency for a given amplitude, and increasing the strength of a pre-tensioned membrane, the smaller the value of the frequency in relation to a range. Small differences are perceived in the behavior of the membrane for the three constitutive models of material, which are calibrated to represent the same material. Moreover, the main bifurcations of the analyzed membranes are of cyclic bending type, known as saddle-node bifurcation. / Elementos estruturais com grande capacidade de deformação como membranas hiperelásticas vêm ganhando destaque em diversas áreas da engenharia e têm várias aplicações na biomecânica, assim, o estudo do comportamento dinâmico de estruturas hiperelásticas é de grande importância visando minimizar os efeitos, como à perda de estabilidade e vibrações indesejáveis. No presente trabalho é utilizada a teoria da elasticidade para grandes deformações no desenvolvimento da teoria de membranas com o objetivo de investigar o comportamento dinâmico linear e não linear de membranas hiperelásticas. Considera-se a membrana retangular composta por um material elastomérico, isotrópico, homogêneo, incompressível e descrito pelos modelos constitutivos de neo-Hookeano, Mooney-Rivlin e Yeoh. Para obter as equações de equilíbrio estático e dinâmico da estrutura são utilizadas as energias e trabalhos atuantes, bem como o princípio de Hamilton aplicado na função de Lagrange. O Método de Galerkin é utilizado para discretizar as Equações Diferenciais Parciais (EDP) em um sistema de Equações Diferenciais Ordinárias (EDO). Para resolver esse sistema, utiliza-se o Método de Runge-Kutta de quarta ordem e utiliza-se o Método da Força Bruta e o Método da Continuação para investigar o comportamento dinâmico da membrana. É realizada uma análise paramétrica visando avaliar a influência do material e da geometria da membrana nas frequências naturais e nas tensões inicias. Constata-se que as bifurcações das membranas analisadas são do tipo Dobra Cíclica, conhecida como Nó-Sela. Além de verificar que quanto menor o nível de tração, maior será a não linearidade da curva de frequênciaamplitude da membrana e que há leves divergências no comportamento da membrana em relação aos três modelos constitutivos do material adotados.