Yes / Polypropylene has been oriented by solid-phase deformation processing to draw ratios up to ∼16, increasing tensile stiffness along the draw direction by factors up to 12. Nanoindentation of these materials showed that moduli obtained for indenter tip motion along the drawing direction (3) into to 1–2 plane (axial indentation) were up to 60% higher than for indenter tip motion along the 2 direction into the 1–3 plane (transverse indentation). In static tests, tensile and compressive determinations of elastic modulus gave results differing by factors up to ∼5 for strain along the draw direction. A material model incorporating both orthotropic elasticity and tension/compression asymmetry was developed for use with Finite Element simulations. Elastic constants for the oriented polypropylene were obtained by combining static testing and published ultrasonic data, and used as input for nanoindentation simulations that were quantitatively successful. The significance of the tension/compression asymmetry was demonstrated by comparing these predictions with those obtained using tensile data only, which gave predictions of indentation modulus higher by up to 70%.

A new method called the Direct Method is developed to solve for the propagating modes in waveguides via the finite-element method. The variational form of the Direct method is derived to ensure that an extremum is reached. The Direct method uses Maxwell's equations directly, both zero and first-order, scalar and vector bases that are used in the finite-element formulation. The direct solution method solves for both the magnetic and electric fields simultaneously. Comparisons are made with the traditionally used vector-Helmholtz equation set. The advantages and disadvantages of the newly developed method is described as well as several results displayed using the WR-90 waveguide and a circular waveguide as test waveguides. Results include a partially filled dielectric loaded rectangular waveguide. The effects of including the divergence of the fields in the functional as penalty terms on the quality of results obtained by the Direct method and the vector-Helmholtz method is explored. The quality of results is gauged on the accuracy of the computed modes as well as the elimination or a significant reduction in the number of 'spurious modes' that are often encountered in solutions to waveguide problems. It is shown that computational time for the solution and computer storage requirements exceed the typically used Helmholtz equation method but the results obtained can be more accurate. Future work may include developing a sparse eigenvalue solution method that could reduce the solution time and storage requirements significantly. The Direct method of solution in dynamics resulted after an initial search in magnetostatics for methods to solve for the magnetic field without using the magnetic-vector potential using finite-element methods. A variational derivation that includes the boundary conditions is developed for the magnetic-vector potential method. Several techniques that were used to attempt accurate solutions for the magnetostatic fields with multiple materials and without the use of the magnetic-vector potential are described. It was found that some of the newly developed general techniques for magnetostatics are only accurate when homogeneous media are present. A method using two curl equations is developed which is a Direct method in magnetostatics and reveals the interaction between the bases used. The transition from magnetostatics to dynamics is made and similar Direct methods are applied to the waveguide problem using different bases. / Ph. D.

In soil and rock mechanics, coupling effects between geomechanics field and fluid-flow field are important to understand many physical phenomena. Coupling effects in fluid-saturated porous media comes from the interaction between the geomechanics field and the fluid flow. Stresses subjected on the porous material result volumetric strains and fluid diffusion in the pores. In turn, pore pressure change cause effective stresses change that leads to the deformation of the geomechanics field. Coupling effects have been neglected in traditional geotechnical engineering and petroleum engineering however, it should not be ignored or simplified to increases reliability of the results. The coupling effect in porous media was theoretically established in the poroelasticity theory developed by Biot, and it has become a powerful theory for modeling three-dimensional consolidation type of problem. The analysis of the porous media with fully-coupled simulations based on the Biot's theory requires intensive computational effort due to the large number of interacting fields. Therefore, advanced computational techniques need to be exploited to reduce computational time. In order to solve the coupled problem, several techniques are currently available such as one-way coupling, partial-coupling, and full-coupling. The fully-coupled approach is the most rigorous approach and produces the most correct results. However, it needs large computational efforts because it solves the geomechanics and the fluid-flow unknowns simultaneously and monolithically. In order to overcome this limitation, staggered solution based on the Biot's theory is proposed and implemented using a modular approach. In this thesis, Biot's equations are implemented using a Finite Element method and/or Finite Difference method with expansion of nonlinear stress-strain constitutive relation and multi-phase fluid flow. Fully-coupled effects are achieved by updating the compressibility matrix and by using an additional source term in the conventional fluid flow equation. The proposed method is tested in multi-phase FE and FD fluid flow codes coupled with a FE geomechanical code and numerical results are compared with analytical solutions and published results. / Ph. D.

This thesis concerns itself with a finite element model of nonproportional viscoelastic damping and its subsequent reduction. The Golla-Hughes-McTavish viscoelastic finite element has been shown to be an effective tool in modeling viscoelastic damping. Unlike previous models, it incorporates physical data into the model in the form of a curve fit of the complex modulus. This curve fit is expressed by minioscillators. The frequency dependence of the complex modulus is accounted for by the addition of internal, or dissipation, coordinates. The dissipation coordinates make the viscoelastic model several times larger than the original. The trade off for more accurate modeling of viscoelasticity is increased model size. Internally balanced model order reduction reduces the order of a state space model by considering the controllability/observability of each state. By definition, a model is internally balanced if its controllability and observability grammians are equal and diagonal. The grammians serve as a ranking of the controllability/observability of the states. The system can then be partitioned into most and least controllable/observable states; the latter can be statically reduced out of the system. The resulting model is smaller, but the transformed coordinates bear little resemblance to the original coordinates. A transformation matrix exists that transforms the reduced model back into original coordinates, and it is a subset of the transformation matrix leading to the balanced model. This whole procedure will be referred to as Yae's method within this thesis. By combining GHM and Yae's method, a finite element code results that models nonproportional viscoelastic damping of a clamped-free, homogeneous, Euler-Bernoulli beam, and is of a size comparable to the original elastic finite element model. The modal data before reduction compares well with published GHM results, and the modal data from the reduced model compares well with both. The error between the impulse response before and after reduction is negligible. The limitation of the code is that it cannot model sandwich beam behavior because it is based on Euler-Bernoulli beam theory; it can, however, model a purely viscoelastic beam. The same method, though, can be applied to more sophisticated beam models. Inaccurate results occur when modes with frequencies beyond the range covered by the curve fit appear in the model, or when poor data are used. For good data, and within the range modeled by the curve fit, the code gives accurate modal data and good impulse response predictions. / Master of Science

Formula SAE (FSAE) chassis systems are increasing being manufactured with integrated composite structures in an effort to increase the performance of the system while decreasing weight. The increased use of composite structures requires more details of the loading conditions and evaluation metrics than the mild steel structures they are replacing. The prototypical FSAE steel space frame chassis designs are heavily structured around the mandated safety rules that doubled as mostly satisfactory structures for vehicle loads. The use of composite structures and the directionality of their material properties has created a need for more detailed loading scenarios to evaluate their ability to transfer load. This thesis presents a framework for evaluating the chassis structure not only through the standard static twist analysis, but increased use of modal analysis and dynamic vehicle maneuvers using an attached suspension. The suspension joints and springs/dampers are modeled using Abaqus Connector Elements, allowing for the use of complex kinematic degrees of freedom definitions required to accurately model the suspension behavior. The elements used to represent the joints and springs are detailed as well as their superiority over traditional multi-point constraints in this context. The use of modal analysis is used for a more direct comparison of not only the efficiency of stiffness in the chassis alone, but also how the chassis interacts with the suspension. The natural frequencies from the modal analysis along with the static twist distribution along the chassis are presented as a replacement for the static torsional stiffness performance metric. By using dynamic vehicle maneuvers the chassis-suspension structure can be evaluated based on loads developed during the typical use of the FSAE vehicle. The dynamic nature of the analysis also allows for the inclusion of mass in the loading profile as well as the load variation with time that can be hard to achieve with static analysis. The framework for a bump event as well as a constant-speed-constant-radius turn are presented. The bump analysis is designed to evaluate the system's response to straight line dynamic events, while the turning maneuver evaluates the lateral components of the suspension load transfer capabilities. For the turn analysis both a spring/damper tire model using connector elements and a rolling tire model are presented. Intermediate checks on suspension and chassis behavior are evaluated to verify the modeling techniques; while the maneuver results are evaluated based on trends and overall motion rather than magnitudes due to lack of data at the time of the analysis. / Master of Science

Finite Element Method (FEM) is a powerful numerical tool which, combined with the fast development of Computer Science in the lastdecades, had made possible to perform mechanical analysis of a widerange of bodies and boundary conditions. However, the complexity of some cases may turn the calculationprocess too slow and sometimes even unaffordable for most computers. This work aims to simplify an intricate system of layers withdifferent geometries and material properties by approximating itthrough a homogeneous material, with unique mechanical parameters.Besides the Finite Element analysis, a theoretical model is created, in order to understand the basis of the problem, and, as a firstapproach, check whether the assumptions made in the FEM model areacceptable or not. This work intends to make a small contribution to the understandingof the mechanical behaviour of the Vasa vessel, which will eventuallylead to the design of a new support structure for the ship. The preservation of the Vasa is a priority for the Swedish Property Board, as it is one of the main monuments of Sweden.

In this thesis, we investigate the regularity and approximation of a hyperbolic-elliptic coupled problem. In particular, we consider the Poisson and the transport equation where both are assigned nonhomogeneous Dirichlet boundary conditions. The coupling of the two problems is executed as follows. The right hand side function of the Poisson equation is the solution ρ of the transport equation whereas the gradient field E = −∇u, with u being solution of the Poisson problem, is the convective field for the transport equation. The analysis is done throughout on a nonconvex, not simply connected domain that is supposed to be homeomorph to an annular domain. In the first part of this thesis, we will focus on the existence and uniqueness of a classical solution to this highly nonlinear problem using the framework of Hölder continuous functions. Herein, we distinguish between a time dependent and time independent formulation. In both cases, we investigate the streamline functions defined by the convective field E. These are used in the time dependent case to derive an operator equation whose fixed point is the streamline function to the gradient of the classical solution u. In the time independent setting, we formulate explicitly the solution operators L for the Poisson and T for the transport equation and show with a fixed point argument the existence and uniqueness of a classical solution (u,ρ). The second part of this thesis deals with the approximation of the coupled problem in Sobolev spaces. First, we show that the nonlinear transport equation can be formulated equivalently as variational inequality and analyse its Galerkin finite element discretization. Due to the nonlinearity of the coupled problem, it is necessary to use iterative solvers. We will introduce the staggered algorithm which is an iterative method solving alternating the Poisson and transport equation until convergence is obtained. Assuming that LοT is a contraction in the Sobolev space H1(Ω), we will investigate the convergence of the discrete staggered algorithm and obtain an error estimate. Subsequently, we present numerical results in two and three dimensions. Beside the staggered algorithm, we will introduce other iterative solvers that are based on linearizing the coupled problem by Newton’s method. We illustrate that all iterative solvers converge satisfactorily to the solution (u, ρ).

[pt] Este trabalho apresenta a previsão do desempenho de três acessórios de união (manilha de união, elo Kenter e elo Multifuncional) utilizados em sistemas de ancoragem de unidades offshore, sob carregamentos monotônicos e cíclicos. Cinqüenta e sete modelos foram analisados pelo método de Elementos Finitos utilizando o software Ansys 10. Inicialmente, com o objetivo de quantificar a influência do contato e mensurar a área onde este ocorre, três modelos com contatos entre manilha de união e elos foram analisados com variações no diâmetro (76, 95 e 120 mm) e mantendo-se constante as propriedades mecânicas do material e a carga aplicada. Em seqüência, cinqüenta e quatro outros modelos foram elaborados sem condições de contato, isto é, com as cargas aplicadas diretamente nos componentes de estudo, que sofreram variações de diâmetros (76, 95 e 120 mm), de propriedades mecânicas (limites de escoamento e resistência mecânica) e de carregamento (proof load e minimum break load). Comparativamente, as manilhas de união apresentaram os menores níveis de tensões e as melhores distribuições de tensões dentre os três componentes para todos os casos analisados. Dos cinqüenta e quatro modelos citados acima, três foram selecionados para análise da vida em fadiga com o software FE-Fatigue. Estes representavam um acessório de união de cada tipo com o diâmetro considerado crítico (120 mm) e sem variações nas propriedades mecânicas do material. Os resultados mostraram que a geometria do componente é determinante para os valores das tensões e da vida-fadiga. A manilha apresentou os melhores resultados de resistência e de vida-fadiga, que para o diâmetro e material escolhidos, foi cerca de três vezes maior do que aquela relativa aos elos Kenter e Multifuncional. / [en] This work represents an approach to predict the performance of three joining accessories (shackle, Kenter link and Multifunctional link) for offshore mooring systems under monotonic and cyclic loading. Fifty seven models were analyzed by the Finite Element method using the software Ansys 10. Initially, in order to quantify the influence of the contact conditions and to measure the area where it occurs, three models presenting contacts between the joining shackle and chain links were analyzed varying the diameter (76, 95, 120 mm) and maintaining constant the material’s mechanical properties as well as the applied loads. In sequence, fifty four other models were created without contact conditions, which means that the loads were applied directly on the components in question, with variations in link diameter (76, 95 and 120 mm), in mechanical properties (yield stress and ultimate strength) and in load conditions (proof and minimum break loads). Comparing the joining shackles with the other accessories, the shackles present the lowest stress levels and the best stress distributions with regard to all the cases studied. Three of the fifty four models cited above were selected for predicting their fatigue life making use of the FE-Fatigue software. These represented one of each joining accessory with a diameter considered critical (120 mm), keeping constant the mechanical properties of the material. The results showed that the influence of the component geometry is determinant for the stress values developed during the loading tests as well as its fatigue life. The shackle presented the best results in terms of strength and fatigue life, which was about three times greater than that for the Kenter and Multifunctional links.

Este trabalho avaliou, utilizando o Método dos Elementos Finitos, o comportamento mecânico em seis ensaios, quatro de flexo compressão com variação apenas no comprimento da haste de fixação, um de flexão ântero-posterior e um de flexão lateral, em um modelo tridimensional de fixador externo construído com auxílio do computador. Para a validação desses ensaios os mesmos testes também foram realizados na máquina universal de ensaio e depois comparados com o método dos elementos finitos. A rigidez no ensaio de flexão lateral obtida no método dos elementos finitos apresentou um valor 106% maior do que o obtido na máquina universal de ensaio, possivelmente por ocorrência de afrouxamento entre as partes adjacentes elo fixador externo no ensaio mecânico, e no ensaio de flexo compressão (número 1) a rigidez obtida pelo método dos elementos finitos foi 7,39% menor elo que a obtida na máquina universal de ensaio. No ensaio número 4 (flexo-compressão) os deslocamentos obtidos, correspondentes a aplicação de uma carga de 15,4 N, utilizando tanto o método dos elementos finitos como a máquina universal ele ensaio, divergiram em 8,5%. Já no ensaio número 5 (flexão ântero-posterior) a divergência foi de 0,9%, para os deslocamentos correspondentes a aplicação de uma carga de 14,4 N. O Métodos dos Elementos Finitos é um eficiente método para prever comportamento mecânico de estruturas complexas. / This work evaluates the mechanical behavior of an external device on a CAD (Computer Aided Design) 3D model in six tests, four of them of flexion-compression with a single variation of the external device stick length, one of longitudinal flexion and one of lateral flexion. They all were carried out applying the Method of the Finite Elements (MFE). For the comparison with the MFE the same mechanical testes were made. The stiffness achieved in the MFE showed a value 106% greater than that of the mechanical test. The test number one of flexion-compression showed a value 7,39% smaller in the MFE than that of the mechanical test. In the test number four (flexion-compression) the corresponding displacement after the application of a 15,4 N working stress showed a difference of 8,5%. The variation of the number five test was of 0,9% for the displacement after the application of a 14,4N working stress. The MEF showed efficient to evaluate the behavior of complex mechanical structures.

Os problemas freqüentes de patologias ortopédicas e traumáticas da coluna vertebral envolvem a colocação de fixadores internos (parafusos longos, os quais são inseridos nos pedículos posteriores até os corpos vertebrais e conectados por fios nas hastes longitudinais podendo ser fixados em todas as posições pelas porcas). Estes fixadores foram simulados no computador através da construção de modelos geométricos dos mesmos, utilizando o software ANSYS 5.5, que consiste de várias ferramentas para análise do projeto baseado no método dos elementos finitos. Foi também utilizado um software para a modelagem das peças e do conjunto do fixador já existente chamado SOLID EDGE, e logo em seguida o mesmo foi transferido para o software ANSYS 5.5 e simulado. Esta comparação servirá como complemento para possíveis modificações das montagens, dimensões e aplicações, não necessitando de novos ensaios mecânicos na máquina universal de ensaios e sim realizando simulações computadorizadas / The frequent problems of orthopedic and traumatic pathologies of the spinal column that involves the placement of an internal fixator (long screws, which are inserted in the subsequent pedicle until the vertebral and connected by bodies for wires in the longitudinal stems could be fastened in all the positions by the screw). These fixators were simulate in the computer through the construction of geometric models of the same ones, using the software ANSYS 5.5, that consists of several tools for analysis of the project based on the method of the finite elements. It was also used a software for the modelling of the pieces and of the group of the fixador already called existent SOLID EDGE, and then the same was transferred to the software ANSYS 5.5 and simulated. This comparison will serve a complement for possible modifications of the assemblies, dimensions and applications, not needing new mechanical test in the universal machine test but accomplishing computerized simulations