This research is concerned with the development of a mathematical approach for energy and mass transport in solidification modelling involving a control volume (CV) technique and finite element method (FEM) and incorporating non-physical variables in its solution. The former technique is used to determine an equivalent capacitance to describe energy transport whilst the latter technique provides temperatures over the material domain. The numerical solution of the transport equations is achieved by the introduction of two concepts, i.e. weighted transport equations and non-physical variables. The main aim is to establish equivalent transport equations that allow exact temporal integration and describe the behaviour of non-physical variables to replace the original governing transport equations. The variables defined are non-physical in the sense that they are dependent on the velocity of the moving CV. This dependence is a consequence of constructing transport equations that do not include flux integrals. The form of the transport equations facilitate the construction of a FEM formulation that is applicable to heat and mass transport problems and caters for singularities arising from phase-change, which can prove difficult to model. However, applying the non-physical enthalpy method (NEM) any singularity involved in the solidification process is precisely identified and annihilated.

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

Les différents travaux de recherche menés dans le cadre de la présente thèse, ont pour objectifs de :(i) comprendre les mécanismes et phénomènes prenant part dans la plasticité des aciers en présence d’une transformation de phases diffusive ou martensitique. (ii) développer des outils de prédiction de TRIP capables d’une part de reproduire correctement cette déformation macroscopique pour des cas de chargements complexes et d’autre part de nous offrir des enseignements sur les interactions élasto-visco-plastiques locales entre phase naissante et phase parente. Pour ce faire, de nouvelles campagnes d'essais TRIP à chargements uni- et bi-axiaux constants ou variables ont été menées sur l'acier 35NCD16 pour une transformation austénitemartensite et l'acier 100C6 pour une transformation austénite-perlite. En complément, des essais de traction-compression et relaxation ont été réalisés pour caractériser les propriétés élastoviscoplastique ssur chacune des 2 phases de l’acier 100C6... / The objectives of this work are: (i) understand the mechanisms and phenomena involved in the plasticity of steels in the presence of a diffusive or martensitic phase transformation. (ii) develop tools for predicting TRIP, which are able to correctly reproduce the macroscopic deformation for cases of complex loading and could also provide information about local elasto-visco-plastic interactions between product and parent phases. To this purpose, new experimental tests are conducted on 35NCD16 steel for austenite tomartensite transformation and on 100C6 steel for austenite to pearlite transformation. The elasto viscoplasticproperties of austenite and pearlite of the 100C6 steel are characterized through tension compression and relaxation tests...

Las presas son estructuras de gran relevancia para un adecuado desarrollo de proyectos de agua potable y agrícola; sin embargo, su potencial falla representa grandes riesgos por las pérdidas de materiales y de vidas humanas que podría ocasionar. Por ello, resulta de gran importancia su estudio, para realizar diseños cada vez más seguros y funcionales. Es importante garantizar el desempeño de la obra durante su construcción y vida útil, para lo cual es fundamental conocer la distribución de esfuerzos, deformaciones y desplazamientos que ocurren en el dique. Este trabajo presenta los fundamentos suficientes para llevar a cabo un análisis de esfuerzos, deformaciones y desplazamientos en presas de enrocado. El estudio incluye desde las bases teóricas de estabilidad de taludes, hasta el método de elementos finitos. Para ello, se analizó la influencia del esfuerzo confinante en la disminución de los parámetros de resistencia en presas de enrocado de gran altura y se comparó los resultados obtenidos en términos de tensión - deformación. La teoría aplicada es de equilibrio límite con la metodología de Morgenstern y Price, en el cual mediante cortes realizados se satisface el equilibrio de fuerzas y momentos en los bloques individuales. El análisis de la presa de enrocado también se realizó con la herramienta computacional PLAXIS (elementos finitos), en la cual se determinó la tensión – deformación de los parámetros sometidos a la influencia del esfuerzo confinante determinados por la función bilineal propuesta por LEPS. / The dams are structures of great relevance for the adequate development of potable water and agricultural projects; However, its potential failure represents great risks due to the loss of materials and human life that it could cause. Therefore, its study is of great importance, to make designs that are increasingly safe and functional. It is important to guarantee the performance of the work during its construction and useful life, for which it is essential to know the distribution of stresses, deformations and displacements that occur in the dike. This work presents enough foundations to carry out an analysis of stresses, deformations and displacements in rockfill dams. The study includes from the theoretical bases of slope stability, to the finite element method. For this, the influence of the confining stress on the reduction of the resistance parameters in high-altitude rock fill dams was analyzed and the results obtained in terms of stress-strain were compared. The applied theory is of limit equilibrium with the Morgenstern and Price methodology, in which the equilibrium of forces and moments in the individual blocks is satisfied by means of cuts made. The analysis of the rockfill dam was also carried out with the PLAXIS (finite element) computational tool, in which the stress - deformation of the parameters subjected to the influence of the confining stress determined by the bilinear function proposed by LEPS was determined. / Tesis

The geometric alteration of slopes is a reality that can be observed in several districts of the Peruvian capital. The construction of houses, roads, and other infrastructure can produce some slope instability and cause tragic events. Thus, a stability analysis was carried out for a slope located in the San Juan de Lurigancho district, specifically in the Virgen de Fátima sector. Therefore, for the present investigation, two models were made with the help of Phase2 software to identify the resistance reduction factors (SFR), which is a finite element-based program. To start the analysis, possible failures were identified, demonstrating that the slope does not present any possibility of failure. For the first model, we worked with a dip of 30° and identified an SFR = 19.26 for static conditions and an SFR = 9.66 for pseudo-static conditions. For the second model, we worked with a dip of 55°, this change in slope geometry shows a possible wedge failure, according to the kinematic analysis. Also, an SFR = 0.89 was identified for static conditions and an SFR = 0.48 for pseudo-static conditions. The results show very considerable changes and are due to the geometry of the slope, the presence of discontinuities, and the participation of seismic forces.

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[pt] Pela observação e análise das condições dos locais atingidos por violentos sismos destrutivos, pode-se demostrar a grande importância do comportamento do maciço de solo na resposta dinâmica das estruturas na superfície. Embora esta importância tenha sido há muito reconhecida, só recentemente uma investigação sistemática dos fatores intervenientes na interação dinâmica solo-estrutura vem merecendo a atenção adequada. Graças ao avanço de técnicas numéricas e métodos de análise, é possível hoje estudar-se este problema de forma eficiente, ampla e racional. O presente trabalho consiste em uma análise pelo método dos elementos finitos do problema do comportamento dinâmico dos tanques de armazenamento de combustível da Refinaria Costarricense de Petróleo (RECOPE) freqüentemente sujeitos a abalos sísmicos. A avaliação da amplificação sísmica dos solos da região da refinaria, o comportamento estrutural dos tanques sob solicitações dinâmicas, a análise comparativa dos métodos de projeto recomendados na Costa Rica, os efeitos da interação dinâmica solo-tanque, etc., são alguns dos pontos examinados em detalhe neste trabalho. O conhecimento do comportamento dinâmico dos tanques da Refinaria de RECOPE, Costa Rica, foi significativamente aperfeiçoado pela realização deste trabalho. / [en] Through observation and analysis of the local conditions of regions subjected to violent seismic excitations, one can conclude the great importance of the dynamic behavior of the soil mass on the response of structural systems founded in it. Although the importance of the soil behavior has long been recognized in the literature, systematic investigations on the influencing factors on the dynamic soil-structure interaction problems have received the due attention only recently.Given the modern developments in numerical methods as well as the now common availability of powerful microcomputers in design offices, it is now possible to study this problem following a rational and efficient manner.In the present work, an analysis of the dynamic behavior of steel tanks for fuel storage at the industrial plant of RECOPE (Petroleum Refinery of Costa Rica), frequently subjected to severe earthquakes, has been carried out using the finite element method.The main points investigated in this thesis are: the evaluation of dynamic amplifications due to local soil properties, the structural behavior of tanks under dynamic forces, the soil-structure interaction effects as well as a comparative study with the design procedures currently employed in Costa Rica.The technical knowledge about the dynamic behavior of RECOPE`s fuel tanks has been significantly improved by this research. / [es] Por la observación y análisis de las condiciones de los locales castigados por violentos sismos destructivos, se puede demostrar la gran importancia del comportamiento del macizo de suelo en la respuesta dinámica de las extructuras en la superficie. Aunque esta importancia há sido reconocida hace mucho tiempo, solo recientemente una investigación sistemática de los factores que intervienen en la interacción dinámica suelo extructura ha merecido atención adecuada. Gracias al avance de técnicas numéricas y métodos de análisis, es posible hoy estudiar este problema de forma eficiente, amplia y racional. EL presente trabajo consiste en un análisis por el método de los elementos finitos del problema del comportamiento dinámico de los tanques de almacenamiento de combustible de la Refinaría Costarricense de Petróleo (RECOPE) frecuentemente sujetos a sacudidas sísmicas. La evaluación de la amplificación sísmica de los suelos de la región de la refinaria, el comportamiento extructural de los tanques bajo solicitaciones dinámicas, el análisis comparativo de los métodos de proyecto recomendados en la Costa Rica, los efectos de la interacción dinámica suelo-tanque, etc., son algunos de los puntos examinados en detalle en este trabajo. EL conocimiento del comportamiento dinámico de los tanques de la Refinaría de RECOPE, Costa Rica, fue significativamente perfeccionado por la realización de este trabajo.

This work is a numerical study of Burgers' equation with Neumann boundary conditions. The goal is to determine the long term behavior of solutions. We develop and test two separate finite element and Galerkin schemes and then use those schemes to compute the response to various initial conditions and Reynolds numbers. It is known that for sufficiently small initial data, all steady state solutions of Burgers' equation with Neumann boundary conditions are constant. The goal here is to investigate the case where initial data is large. Our numerical results indicate that for certain initial data the solution of Burgers' equation can approach non-constant functions as time goes to infinity. In addition, the numerical results raise some interesting questions about steady state solutions of nonlinear systems. / Master of Science