We develop a coarse-grained model of lipids and proteins in which the lipids are modelled as diblock copolymers and the proteins as rigid cylinders. The generic protein model allows the possibility of amphipathic proteins with intrinsic curvature. Self-consistent field theory (SCFT) is used to determine the morphology of the lipid bilayer in the vicinity of the proteins. In particular, we focus on the case of a long transmembrane protein inserted perpendicular to the bilayer. For this system we use SCFT to determine the mechanical properties of the membrane and the thickness profile as a function of distance from the protein inclusion. The mechanical constants are also used in an elastic theory to predict the thickness profile. Good agreement between the full SCFT and elastic theory is obtained. We also use SCFT to determine systematic trends of the boundary conditions for the thickness profile at the protein interface. Such results could be used as boundary conditions for the description of bilayers using elastic theory. We show that this system undergoes a second order wetting transition as the interaction strength between the protein and membrane is varied. / Thesis / Master of Science (MSc)

Two problems in the study of elastic filaments are considered.First, a reliable numerical algorithm is developed that candetermine the shape of a static elastic rod under a variety ofconditions. In this algorithm the governing equations are writtenentirely in terms of local coordinates and are discretized usingfinite differences. The algorithm has two significant advantages:firstly, it can be implemented for a wide variety of the boundaryconditions and, secondly, it enables the user to work with generalconstitutive relationships with only minor changes to thealgorithm. In the second problem a model is presented describingthe dynamics of an elastic tube conveying a fluid. First weanalyze instabilities that are present in a straight rod or tubeunder tension subject to increasing twist in the absence of afluid. As the twist is increased beyond a critical value, thefilament undergoes a twist-to-writhe bifurcation. A multiplescales expansion is used to derive nonlinear amplitude equationsto examine the dynamics of the elastic rod beyond the bifurcationthreshold. This problem is then reinvestigated for an elastic tubeconveying a fluid to study the effect of fluid flow on thetwist-to-writhe instability. A linear stability analysisdemonstrates that for an infinite rod the twist-to-writhethreshold is lowered by the presence of a fluid flow. Amplitudeequations are then derived from which the delay of bifurcation dueto finite tube length is determined. It is shown that the delayedbifurcation threshold depends delicately on the length of the tubeand that it can be either raised or lowered relative to thefluid-free case. The amplitude equations derived for the case of aconstant average fluid flux are compared to the case where theflux depends on the curvature. In this latter case it is shownthat inclusion of curvature results in small changes in some ofthe coefficients in the amplitude equations and has only a smalleffect on the post-bifurcation dynamics.

The Eshelby-type problems of an arbitrary-shape polygonal or polyhedral inclusion embedded in an infinite homogeneous isotropic elastic material are analytically solved using a simplified strain gradient elasticity theory (SSGET) that contains a material length scale parameter. The Eshelby tensors for a plane strain inclusion with an arbitrary polygonal cross section and for an arbitrary-shape polyhedral inclusion are analytically derived in general forms in terms of three potential functions. These potential functions, as area integrals over the polygonal cross section and volume integrals over the polyhedral inclusion, are evaluated. For the polygonal inclusion problem, the three area integrals are first transformed to three line integrals using the Green's theorem, which are then evaluated analytically by direct integration. In the polyhedral inclusion case, each of the three volume integrals is first transformed to a surface integral by applying the divergence theorem, which is then transformed to a contour (line) integral based on Stokes' theorem and using an inverse approach. In addition, the Eshelby tensor for an anti-plane strain inclusion with an arbitrary polygonal cross section embedded in an infinite homogeneous isotropic elastic material is analytically solved. Each of the newly derived Eshelby tensors is separated into a classical part and a gradient part. The latter includes the material length scale parameter additionally, thereby enabling the interpretation of the inclusion size effect. For homogenization applications, the area or volume average of each newly derived Eshelby tensor over the polygonal cross section or the polyhedral inclusion domain is also provided in a general form. To illustrate the newly obtained Eshelby tensors and their area or volume averages, different types of polygonal and polyhedral inclusions are quantitatively studied by directly using the general formulas derived. The numerical results show that the components of the each SSGET-based Eshelby tensor for all inclusion shapes considered vary with both the position and the inclusion size. It is also observed that the components of each averaged Eshelby tensor based on the SSGET change with the inclusion size.

No description available.

No / Closed-form expressions are derived for the torsional stiffness, radial stiffness and tilting stiffness of annular rubber flanged bushes of finite length in three principal modes of deformation, based upon the classical theory of elasticity. Illustrative numerical results are deduced with realistic physical data of typical flanged bushes.

O escopo do trabalho é estudar o problema da torção uniforme em barras de seção maciça e resolvê-lo analiticamente para obter o momento de inércia à torção da seção transversal e os deslocamentos ao longo de toda a barra. Este trabalho foi desenvolvido no contexto da Teoria da Elasticidade, utilizando o método semi-inverso para determinar as equações de Saint-Venant para a torção uniforme. As seções em forma de elipse e triângulo eqüilátero foram resolvidas utilizando a função de tensão de Prandtl, a função empenamento e a sua conjugada harmônica. A seção retangular foi resolvida utilizando as funções empenamento e de Prandtl desenvolvidas em séries infinitas. Foi desenvolvida uma formulação matricial utilizando o Método de Galerkin para resolver problemas que não possuem solução fechada. / The main purpose of this essay is to present the issue of the uniform torsion in solid section bars and to solve it analytically to achieve the moment of inertia to the torsion of the transversal section and the displacements throughout the whole bar. This essay was developed in the Elasticity Theory context, using the semi-inverse method to determine the Saint-Venant equations to the uniform torsion. The sections in ellipse and equilateral triangle were solved using the Prandtl stress function, the warping function and its harmonic conjugate. The rectangular section was solved using the warping and the Prandtl functions developed in infinite series. A formulation based on matrixes was developed using the Galerkin method to solve problems that do not have closed solution.

O escopo do trabalho é estudar o problema da torção uniforme em barras de seção maciça e resolvê-lo analiticamente para obter o momento de inércia à torção da seção transversal e os deslocamentos ao longo de toda a barra. Este trabalho foi desenvolvido no contexto da Teoria da Elasticidade, utilizando o método semi-inverso para determinar as equações de Saint-Venant para a torção uniforme. As seções em forma de elipse e triângulo eqüilátero foram resolvidas utilizando a função de tensão de Prandtl, a função empenamento e a sua conjugada harmônica. A seção retangular foi resolvida utilizando as funções empenamento e de Prandtl desenvolvidas em séries infinitas. Foi desenvolvida uma formulação matricial utilizando o Método de Galerkin para resolver problemas que não possuem solução fechada. / The main purpose of this essay is to present the issue of the uniform torsion in solid section bars and to solve it analytically to achieve the moment of inertia to the torsion of the transversal section and the displacements throughout the whole bar. This essay was developed in the Elasticity Theory context, using the semi-inverse method to determine the Saint-Venant equations to the uniform torsion. The sections in ellipse and equilateral triangle were solved using the Prandtl stress function, the warping function and its harmonic conjugate. The rectangular section was solved using the warping and the Prandtl functions developed in infinite series. A formulation based on matrixes was developed using the Galerkin method to solve problems that do not have closed solution.

<p dir="ltr">The continuous advancements in material science and manufacturing engineering have revolutionized the material design and fabrication techniques therefore drastically accelerating the development of complex structured materials. These novel materials, such as micro/nano-structures, composites, porous media, and metamaterials, have found important applications in the most diverse fields including, but not limited to, micro/nano-electromechanical devices, aerospace structures, and even biological implants. Experimental and theoretical investigations have uncovered that as a result of structural and architectural complexity, many of the above-mentioned material classes exhibit non-negligible nonlocal effects (where the response of a point within the solid is affected by a collection of other distant points), that are distributed across dissimilar material scales.</p><p dir="ltr">The recognition that nonlocality can arise within various physical systems leads to a challenging scenario in solid mechanics, where the occurrence and interaction of nonlocal elastic effects need to be taken into account. Despite the rapidly growing popularity of nonlocal elasticity, existing modeling approaches primarily been concerned with the most simplified form of nonlocality (such as low-dimensional, isotropic, and homogeneous nonlocal problems), which are often inadequate to identify the nonlocal phenomena characterizing real-world problems. Further limitations of existing approaches also include the inability to achieve a mathematically well-posed theoretical and physically consistent framework for nonlocal elasticity, as well as the absence of numerical approaches to achieving efficient and accurate nonlocal simulations. </p><p dir="ltr">The above discussion identifies the significance of developing theoretical and numerical methodologies capable of capturing the effect of nonlocal elastic behavior. In order to address these technical limitations, this dissertation develops an advanced continuum mechanics-based approach to nonlocal elasticity by using fractional calculus - the calculus of integrals and derivatives of arbitrary real or even complex order. Owing to the differ-integral definition, fractional operators automatically possess unusual characteristics such as memory effects, nonlocality, and multiscale capabilities, that make fractional operators mathematically advantageous and also physically interpretable to develop advanced nonlocal elasticity theories. In an effort to leverage the unique nonlocal features and the mathematical properties of fractional operators, this dissertation develops a generalized theoretical framework for fractional-order nonlocal elasticity by implementing force-flux-based fractional-order nonlocal constitutive relations. In contrast to the class of existing nonlocal approaches, the proposed fractional-order approach exhibits significant modeling advantages in both mathematical and physical perspectives: on the one hand, the mathematical framework only involves nonlocal formulations in stress-strain constitutive relationships, hence allowing extensions (by incorporating advanced fractional operator definitions) to model more complex physical processes, such as, for example, anisotropic and heterogeneous nonlocal effects. On the other hand, the nonlocal effects characterized by force-flux fractional-order formulations can be physically interpreted as long-range elastic spring forces. These advantages grant the fractional-order nonlocal elasticity theory the ability not only to capture complex nonlocal effects, but more remarkably, to bridge gaps between mathematical formulations and nonlocal physics in real-world problems.</p><p>An efficient nonlocal multimesh finite element method is then developed to solve partial integro-differential governing equations in the fractional-order nonlocal elasticity to further enable nonlocal simulations as well as practical applications. The most remarkable consequence of this numerical method is the mesh-decoupling technique. By separating the numerical discretization and approximation between the weak-form integral and nonlocal integral, this approach surpasses the limitations of existing nonlocal algorithms and achieves both accurate and efficient finite element solutions. Several applications are conducted to verify the effectiveness of the proposed fractional-order nonlocal theory and the associated multimesh finite element method in simulating nonlocal problems. By considering problems with increasing complexity ranging from one-dimensional to three-dimensional problems, from isotropic to anisotropic problems, and from homogeneous to heterogeneous nonlocality, these applications have demonstrated the effectiveness and robustness of the theory and numerical approach, and further highlighted their potential to effectively model a wider range of nonlocal problems encountered in real-world applications.</p>

Made available in DSpace on 2014-07-29T15:18:23Z (GMT). No. of bitstreams: 1 Dissertacao Floriano Rodrigues de Moraes Neto.pdf: 3384428 bytes, checksum: 25598c7b69ec1f6df8596059eb0b923b (MD5) Previous issue date: 2011-08-29 / With the accelerated occupation of the space, the use of tunnels play an important role in engineering, in this sense, the deformations control during it s construction process is very important for the best performance of tunnels. In this sense the numerical analyzes represent a likely economy in the design process. This paper uses a theory of elasticity in the FlexPDE, the same allows the solution of a system of partial differential equations using the finite elements method and producing a graphical output of the problem. In this sense simulations were performed using three-dimensional numerical deep tunnel under the elastic rock in a physical environment continuously, equivalent to the rock mass. Analyzes were made of three-dimensional numerical condition and constructive process of a circular tunnel deep in the rock. These results were compared with the elastic solution of Kirsch for a cross section corresponding to the plane strain state, showing good concordance of numerical results with the analytical. After the verification stage of the numeric model has also been given to the numerical simulation 3D and analyses based on monitoring data from the tunnel auxiliary of the Hydroelectric Power Plant (HPP) of Simplicio/Anta, located in Paraiba do Sul River, in the state of Rio de January - RJ. In this work were carried out measurements of convergence in various sections of the tunnel at the same time of excavation progress. These results and the parameters of characterisation, strength and deformation were colected from Vissoto Junior (2009). Finally the results of the analyzes numerical 3D were compared with the results of field, and after the adjustment of geotechnical parameters in back analyses was obtained a good concordance of numerical results with field data. In this case studied the excavation of the tunnel had a linear elastic behavior since the rock mass is of good quality and the tunnel relatively small. / Com a ocupação acelerada dos espaços superficiais, a utilização de túneis passa a desempenhar um papel importante na engenharia, neste sentido o controle de suas deformações durante o processo construtivo dos mesmos, é de vital importância para o melhor desempenho de túneis. Nesse sentido as análises numéricas representam uma provável economia na fase de projeto. Este trabalho utiliza-se a teoria da elasticidade no programa FlexPDE, o mesmo permite a solução de um sistema de equações diferenciais parciais utilizando o método de elementos finitos e produzindo uma saída gráfica do problema. Neste sentido foram realizadas simulações numéricas tridimensionais de escavação de túneis profundos em regime elástico em maciços rochosos num meio físico contínuo, equivalente ao maciço fraturado. Foram feitas análises numéricas tridimensionais da condição e processo construtivo de um túnel circular profundo escavado em rocha. Estes resultados foram comparados com a solução elástica de Kirsch para uma seção transversal correspondente ao estado de deformação plana, observando-se boa concordância dos resultados numéricos com os analíticos. Após a etapa de verificação do modelo numérico deu-se também a simulação numérica 3D e retroanálise com base em dados de monitoramento do túnel auxiliar de jusante da Usina Hidroelétrica (UHE) de Simplício/Anta, localizada no Rio Paraíba do Sul, município do Rio de Janeiro RJ. Nesta obra foram realizadas medições da convergência em diversas seções do túnel ao mesmo tempo em que ocorria o avanço da frente de escavação. Estes resultados e os parâmetros de caracterização, resistência e deformação foram retirados do trabalho de Vissoto Junior (2009). Finalmente os resultados obtidos das análises numéricas 3D foram comparados com os resultados de campo, e após o ajuste dos parâmetros geotécnicos realizados na retroanálise foi obtida uma boa concordância dos resultados numéricos com os dados de campo. Neste caso estudado a escavação do túnel teve um comportamento elástico linear já que o maciço rochoso é de boa qualidade e o túnel relativamente pequeno.

No description available.