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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No description available.

With a nation-wide aim toward reducing operational energy costs in buildings, it is important to understand the dynamics of controlled heating, cooling, and air circulation of an individual room, the "One-Room Model Problem." By understanding how one most efficiently regulates a room's climate, one can use this knowledge to help develop overall best-practice power reduction strategies. A key toward effectively analyzing the "One-Room Model Problem" is to understand the capabilities and limitations of existing commercial tools designed for similar problems. In this thesis we develop methodology to link commercial Computational Fluid Dynamics (CFD) software COMSOL with standard computational mathematics software MATLAB, and design controllers that apply inlet airflow and heating or cooling to a room and investigate their effects. First, an appropriate continuum model, the Boussinesq System, is described within the framework of this problem. Next, abstract and weak formulations of the problem are described and tied to a Finite Element Method (FEM) approximation as implemented in the interface between COMSOL and MATLAB. A methodology is developed to design Linear Quadratic Regulator (LQR) controllers and associated functional gains in MATLAB which can be implemented in COMSOL. These "closed-loop" methods are then tested numerically in COMSOL and compared against "open-loop" and average state closed-loop controllers. / Ph. D.

A wide range of applications involve interface problems. In most of the cases, mathematical modeling of these interface problems leads to partial differential equations with non-smooth or discontinuous inputs and solutions, especially across material interfaces. Different numerical methods have been developed to solve these kinds of problems and handle the non-smooth behavior of the input data and/or the solution across the interface. The main focus of our work is the immersed finite element method to obtain optimal numerical solutions for interface problems. In this thesis, we present piecewise quadratic immersed finite element (IFE) spaces that are used with an immersed finite element (IFE) method with interior penalty (IP) for solving two-dimensional second-order elliptic interface problems without requiring the mesh to be aligned with the material interfaces. An analysis of the constructed IFE spaces and their dimensions is presented. Shape functions of Lagrange and hierarchical types are constructed for these spaces, and a proof for the existence is established. The interpolation errors in the proposed piecewise quadratic spaces yield optimal <i>O</i>(h³) and <i>O</i>(h²) convergence rates, respectively, in the L² and broken H¹ norms under mesh refinement. Furthermore, numerical results are presented to validate our theory and show the optimality of our quadratic IFE method. Our approach in this thesis is, first, to establish a theory for the simplified case of a linear interface. After that, we extend the framework to quadratic interfaces. We, then, describe a general procedure for handling arbitrary interfaces occurring in real physical practical applications and present computational examples showing the optimality of the proposed method. Furthermore, we investigate a general procedure for extending our quadratic IFE spaces to <i>p</i>-th degree and construct hierarchical shape functions for <i>p</i>=3. / Ph. D.