Tool wear is a significant problem for manufacturing companies and represents a major challenge in their operations, but it is also a way they can gain a competitive advantage. To do this it is important to set up a standard procedure to develop high performing tooling. This thesis outlines how the Finite Element (FE) method can be used to understand and develop tool geometry. FE based simulation, as a numerical method, is a reliable method to assess the performance of a cutting tool before conducting machining tests based on the force and temperature profile predicted by the FE model. Defining a mathematical model which can be used as a built-in algorithm for tool wear prediction is very challenging and time consuming. Instead there is a possibility of using other factors such as stress distribution and temperature profile and correlate them to tool wear. In this research, the performance of different tool edge radius in cutting has been studied through experiments and in parallel Updated Lagrangian Models have been developed through ABAQUS/EXPLICIT for various cutting conditions, and experimental data was used to validate the data that has been generated from the finite element models. These models are very convenient to develop and capable of being applied for other types of material and cutting conditions. Thus, they represent an efficient way to reduce the amount of experiments needed to improve a tooling, the machining process, and thereby provide an effective way to increase the machining productivity of manufacturing companies. / Thesis / Master of Applied Science (MASc)

The global Meridional Overturning Circulation (MOC) plays a significant role in the Earth\'s climate system by redistributing all over the world the excess heat gained by Earth in low latitudes. In its superficial branch, warm waters are exchanged throughout the world\'s ocean basins. The Indonesian Throughflow (ITF) and the Agulhas Leakage (AL) are the main processes responsible, respectively, for importing Pacific Ocean waters into the Indian Ocean, and for exporting Indian Ocean waters into the Atlantic Ocean. Recently, changes in both systems have been reported and can be related to global warming consequences, processes of air-sea interactions and variabilities in the ocean circulation and wind patterns. In the present work, output of a high-resolution, global implementation of HYCOM (Hybrid Coordinate Ocean Model) from different runs were used, aiming at a study of the structure and variability of the ITF, and to evaluate the use of a numerical tool for tracking virtual Lagrangian particles to correlate circulation patterns of the ITF and the AL. For the ITF, analysis of the models\' output provided a mean volume transport in the upper 700 m depth of about 13 Sv, what is in the range of values reported by observations and other numerical simulations in the region. The seasonal variability was found to be related to the monsoons wind regimes, and the ITF\'s response to the El Niño-Southern Oscillation (ENSO) was evaluated. During five La Niña events, the mean volume transport was of approximately 16 Sv, and for also five El Niño events, of approximately 12 Sv. Results show an abrupt increase in the heat transport between 2002 and 2012, what could be related to changes in the heat content within the Indian Ocean for the same period. Heat transport anomalies were analyzed in the last years of the time series and present a clear correlation with Nino3.4 index, denoting a strong response of the ITF to the 2014/16 El Niño. Numerical test-experiments simulating Lagrangian particles have been performed, to identify and quantify water masses\' origins compounding the ITF and to correlate variabilities signals of ITF in the Indian Ocean\'s basin circulation and in the Agulhas Leakage. / A Circulação de Revolvimento Meridional do oceano desempenha um papel importante no sistema climático da Terra, através da redistribuição do excesso de calor ganho pelo planeta em baixas latitudes. No seu ramo superficial, massas de águas quentes são carregadas entre as diferentes bacias oceânicas no mundo. O fluxo que ocorre através dos estreitos dos mares da Indonésia (ITF, Indonesian Throughflow), e o Vazamento das Agulhas (VA) são dois importantes processos responsáveis, respectivamente, por importar águas do Pacífico para o Oceano Índico, e por exportar águas do Índico para o Oceano Atlântico. Recentemente, mudanças em ambos sistemas têm sido reportados e podem estar relacionados a consequências do aquecimento global, a processos de interação ar-mar e a variabilidades da circulação oceânica e de padrões de vento. No presente trabalho foram usadas saídas de diferentes rodadas usando uma implementação global em alta resolução do HYCOM (Hybrid Coordinate Ocean Model), com o objetivo de estudar a estrutura e variabilidade do ITF e avaliar o uso de uma ferramenta numérica para rastrear virtualmente a trajetória de partículas Lagrangianas e correlacionar padrões de circulação do ITF e do VA. Para o ITF, análises dos resultados dos modelos forneceram um valor de transporte de volume de ≈13 Sv para os primeiros 700 m de profundidade, o qual está em acordo com valores obtidos por observações e outras simulações numéricas. A variabilidade sazonal foi demonstrada estar relacionada aos regimes de vento de monções, e a resposta do ITF para o El Niño-Oscilação Sul (ENOS) foi avaliada. Durante cinco eventos de La Niña o transporte de volume médio foi de ≈16 Sv, e para cinco eventos de El Niño, em ≈12 Sv. Os resultados mostram um aumento abrupto no transporte de calor entre 2002 e 2012, o qual pode estar relacionado a mudanças na quantidade de calor dentro do Oceano Índico para o mesmo período. Anomalias no transporte de calor foram analisadas para os últimos anos da mesma série temporal e também apresentou clara correlação com o índice Nino3.4, configurando uma forte resposta do ITF para o El Niño de 2014/16. Experimentos numéricos simulando partículas Lagrangianas foram implementados, com o objetivo de identificar origens de massas de águas que compõem o ITF e correlacionar sinais de variabilidade do ITF na bacia de circulação do Índico e do Vazamento das Agulhas.

Orientador: Silvio Alexandre de Araújo / Banca: Reinaldo Morabito Neto / Banca: Franklina Maria Bragion de Toledo / Resumo: Este trabalho consiste numa extensão do estudo de um problema de dimensionamento de lotes com custo de transporte feito por Norden e Velde [53], onde a produção dos itens é transportada, em paletes, para um armazém. O transporte é feito por uma empresa terceirizada sob um contrato com os seguintes custos pré-estabelecidos: um custo fixo de contrato, um custo para o transporte de um determinado volume de paletes e um custo adicional para paletes extras. O problema foi estendido, no presente trabalho, considerando restrições de capacidade e a possibilidade de atrasos no atendimento a demanda. Nosso objetivo é propor um modelo matemático para o problema estendido e desenvolver dois métodos heurísticos de resolução. Tais métodos são baseados em dois tipos de relaxação: relaxação Lagrangiana e relaxação Lagrangiana/Surrogate. Os resultados obtidos pelas heurísticas são comparados com os resultados obtidos pelo pacote de otimização CPLEX 10.0. Além disso, é feita uma comparação entre os métodos heurísticos. / Abstract: This work consist of an extension of a study of the capacitated lot-sizing problems with transportation cost by Norden and Velde [53], where the production of itens is transported into pallets to an warehouse. The transportation is executed by another company, under a contract with the following transportation cost established: a fixed contract cost, a transportation cost for determined quantity of pallets and an additional cost for extra pallets. The problem was extended, in this work, considering capacity constraint and backlogging. Our objective is to propose a mathematical model for the extended problem and to develop two heuristics methods of resolution. The methods are based on two types of relaxation: Lagrangian relaxation and Lagrangian/Surrogate relaxation. The results obtained by heuristics are compared with the results obtained by CPLEX 10.0. Furthermore, a comparison between the heuristics is made. / Mestre

In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is revealed to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L¹.

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No description available.

Dans cette thèse, on étudie les propriétés des sous-variétés lagrangiennes dans une variété symplectique en utilisant la relation de cobordisme lagrangien. Plus précisément, on s'intéresse à déterminer les conditions pour lesquelles les cobordismes lagrangiens élémentaires sont en fait triviaux. En utilisant des techniques de l'homologie de Floer et le théorème du s-cobordisme on démontre que, sous certaines hypothèses topologiques, un cobordisme lagrangien exact est une pseudo-isotopie lagrangienne. Ce resultat est une forme faible d'une conjecture due à Biran et Cornea qui stipule qu'un cobordisme lagrangien exact est hamiltonien isotope à une suspension lagrangianenne. / In this thesis we study the properties of Lagrangian submanifolds of a symplectic manifold by using the relation of Lagrangian cobordism. More precisely, we are interested in determining when an elementary Lagrangian cobordism is trivial. Using techniques coming from Floer homology and the s-cobordism theorem, we show that under some topological assumptions, an exact Lagrangian cobordism is a Lagrangian pseudo-isotopy. This is a weaker version of a conjecture proposed by Biran and Cornea, which states that any exact Lagrangian cobordism is Hamiltonian isotopic to a Lagrangian suspension.

Ce mémoire traite de la construction d’un nouvel invariant des cobordismes lagrangiens. Cette construction est inspirée des travaux récents de Solomon dans lesquels une extension de l’homomorphisme de Calabi aux chemins lagrangiens exacts est donnée. Cette extension fut entre autres motivée par le fait que le graphe d’une isotopie hamiltonienne est un chemin lagrangien exact. Nous utilisons la suspension lagrangienne, qui associe à chaque chemin lagrangien exact un cobordisme lagrangien, pour étendre la construction de Solomon aux cobordismes lagrangiens. Au premier chapitre nous donnons une brève exposition des propriétés élémentaires des variétés symplectiques et des sous-variétés lagrangiennes. Le second chapitre traite du groupe des difféomorphismes hamiltoniens et des propriétés fondamentales de l’homomorphisme de Calabi. Le chapitre 3 est dédié aux chemins lagrangiens, l’invariant de Solomon et ses points critiques. Au dernier chapitre nous introduisons la notion de cobordisme lagrangien et construisons le nouvel invariant pour finalement analyser ses points critiques et l’évaluer sur la trace de la chirurgie de deux courbes sur le tore. Dans le cadre de ce calcul, nous serons en mesure de borner la valeur du nouvel invariant en fonction de l’ombre du cobordisme, une notion récemment introduite par Cornea et Shelukhin. / In this master's thesis, we construct a new invariant of Lagrangian cobordisms. This construction is inspired by the recent works of Solomon in which an extension of the Calabi homomorphism to exact Lagrangian paths is given. Solomon's extension was motivated by the fact that the graph of any Hamiltonian isotopy is an exact Lagrangian path. We use the Lagrangian suspension construction, which associates to every exact Lagrangian path a Lagrangian cobordism, to extend Solomon's invariant to Lagrangian cobordisms. In the first chapter, we give a brief introduction to the elementary properties of symplectic manifolds and their Lagrangian submanifolds. In the second chapter, we present an introduction to the group of Hamiltonian diffeomorphisms and discuss the fundamental properties of the Calabi homomorphism. Chapter 3 is dedicated to Lagrangian paths, Solomon's invariant and its critical points. In the last chapter, we introduce the notion of Lagrangian cobordism and we construct the new invariant. We analyze its critical points and evaluate it on the trace of the Lagrangian surgery of two curves on the torus. In this setting we further bound the new invariant in terms of the shadow of the cobordism, a notion recently introduced by Cornea and Shelukhin.

This work is a stepping stone towards developing higher order shell element for simulating composite manufacturing procedure. In this study, a continuum approach suitable for combined material and geometrically nonlinear analysis for an eight node solid shell element SS8 is explained. The formulation of SS8 comprises two ingredients to alleviate undesirable locking effects: 1) Assumed Natural Strain concept, which has proven to alleviate the curvature thickness and transverse shear locking problems. 2) Enhanced Assumed Strain, which adds enhanced degrees of freedom to improve the in-plane response of the element and the curvature thickness locking problem. This formulation has been extended to represent geometric and material non-linearity using Total Lagrangian approach. Finally, finite strain formulation has been verified by numerical examples. Results when compared to continuum shell element in ABAQUS show a reasonable agreement with a relative error of less than 2%.

Although the flow of granular material in silos and the pressure acting on the silo walls have been studied for over a century, many challenges still remain in silo design. In particular, during the discharge process some dynamic phenomena in silos can often be observed to display large, self-induced and dynamic pulsations which may endanger the stability of the silo structure. The aim of this thesis is to study the flow and pressure in silos using numerical modelling and analytical methods, and to further understand the mechanical behaviour of granular material and mechanism of dynamic phenomena during silo discharge. The Finite Element (FE) method can be used to analyse the behaviour of the granular material in silos by considering the material as a continuum. In this thesis, FEM modelling of silo flow was developed using the Arbitrary Lagrangian-Eulerian (ALE) formulation in the Abaqus/Explicit program and the key parameters that affect the predictions of the flow and pressure during discharge were identified. Using the ALE technique, almost the entire silo discharge process can be simulated without mesh distortion problems. The mass flow rate and temporally averaged discharge pressure predicted by the FE model were first investigated in a conical hopper and were found to be in good agreement with those from the most commonly quoted theoretical solutions. The transient dynamic pressure fluctuations during incipient silo discharge were predicted and the causes for these dynamic events have been investigated which led to the conclusion that the stress wave propagation and the moving shear zone phenomena within the bulk solid were responsible for the dominant higher and lower frequencies effects respectively. A one-dimensional dynamic model of granular columns subject to Coulomb wall friction was developed to investigate the propagation of stress waves, focusing on the effect of geometry by examining converging and diverging tapered columns. The analytical solutions of this model are compared to the FE model based on the ALE formulation. This FE model was first validated using the known behaviour for cylindrical columns. In all cases, the stress impulse set off by incipient discharge at the silo outlet grew with the distance travelled up the column, however the rate was shown to depend on the halfangle of the taper. Over a range of small angles, the proposed analytical model was found to accurately predict this behaviour. After the successful application of the ALE technique for a conical hopper, the FE model was extended to simulate the granular flow in a flat-bottomed model silo. The FE predictions were compared with the silo pressure measurements in a model silo (Rotter et al, 2004). Pressure cells mounted along a vertical line on the silo walls were used to measure the pressure distribution in the silo tests using dry sand. The FE model was further extended to simulate the granular flow in a model silo consisting of a cylindrical section with a conical hopper. The prediction was compared with the experimental observations from a model silo (Munch-Andersen et al, 1992), together with the well-known theoretical solutions. Two numerical issues were addressed in some detail: one is the numerical treatment of the abrupt transition between the cylinder section and the conical hopper, the other is the interaction between the granular solid and the silo walls that was modelled using a dynamic friction model. In addition, the dynamic pressure events during discharge were examined and plausible explanations were given. Finally, this thesis deployed a non-coaxial elastoplastic constitutive model to explore the effect of non-coaxiality on silo phenomena. The non-coaxial FE modelling was performed on three problems: a simple shear test under various initial conditions, a steep hopper and a flat-bottomed silo. The results show that non-coaxiality did not influence the prediction of wall pressure during filling and storing, on the other hand, the discharge pressure was predicted to be larger when non-coaxiality is considered.