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You searched for subject:(Infinite elements). Showing records 1 – 3 of 3 total matches.

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Ohio University

1. Bossaller, Daniel P. Some Topics in Infinite Dimensional Algebra.

Degree: PhD, Mathematics (Arts and Sciences), 2018, Ohio University

The following dissertation is a combination of three papers, emanating from two separate and mostly disjoint projects. The first project is an investigation of when the product of arbitrary infinite matrices is defined and associative. In the case where infinite matrices represent endomorphisms on an infinite-dimensional vector space, this question is trivial since multiplication of these matrices amounts to composition of the endomorphisms, a well-defined and associative operation. In the case of infinite matrices in general, this question becomes very nontrivial. In Chapter 2 we will explore this question of associativity and give necessary and sufficient conditions for a set of three infinite matrices A, B, and C to have an associative product. Afterwards we will give some applications for this characterization.The second project which makes up this dissertation is an exploration of R-algebras which have the property that there exists a basis B for the algebra which consists solely of strongly regular elements. This work was originally inspired by [26] and [27] which investigated algebras which have bases consisting solely of invertible elements. In the third chapter, it is shown that these strongly regular elements are also satisfy a slightly weaker version of invertibility which is dubbed “local invertibility.” Because local invertibility does not presuppose the existence of a multiplicative identity, we may examine algebras which fail to have a unit. Among algebras which satisfy the local invertibility property are all finite dimensional unital algebrs over a division ring D, and many examples of infinite matrix algebras such as the R-algebra of infinite matrices with finitely many nonzero entries, and the column-finite, and row-and-column finite matrix algebras.The fourth chapter is work towards determining when Leavitt path algebras have the invertibility and local invertibility properties. In [28–30], the authors completely classify when the Leavitt path algebra arising from a finite graph is invertible. I follow up on these author’s research in two ways. First, using the author’s analysis of “source loops,” I show that so long as the finite graph has no non-isolated source loops, the Leavitt path algebra is locally invertible. Secondly I give various conditions under which certain elements of Leavitt path algebras are locally invertible. Then I give some graph theoretic characterizations which are sufficient for local invertibility of the Leavitt path algebra. Among other characterizations it is shown that every von Neumann regular Leavitt path algebra and every directly finite Leavitt path algebra is locally invertible.Finally in the fifth chapter I will outline some avenues for future research on the problems described above, in many cases giving partial results towards the resolutions of the questions. Advisors/Committee Members: Lopez-Permouth, Sergio (Advisor).

Subjects/Keywords: Mathematics; Associativity; Infinite Matrices; Bases; Strongly Regular Elements; Leavitt Path Algebras

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Bossaller, D. P. (2018). Some Topics in Infinite Dimensional Algebra. (Doctoral Dissertation). Ohio University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520332321386827

Chicago Manual of Style (16th Edition):

Bossaller, Daniel P. “Some Topics in Infinite Dimensional Algebra.” 2018. Doctoral Dissertation, Ohio University. Accessed November 14, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520332321386827.

MLA Handbook (7th Edition):

Bossaller, Daniel P. “Some Topics in Infinite Dimensional Algebra.” 2018. Web. 14 Nov 2019.

Vancouver:

Bossaller DP. Some Topics in Infinite Dimensional Algebra. [Internet] [Doctoral dissertation]. Ohio University; 2018. [cited 2019 Nov 14]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520332321386827.

Council of Science Editors:

Bossaller DP. Some Topics in Infinite Dimensional Algebra. [Doctoral Dissertation]. Ohio University; 2018. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1520332321386827

2. Ribeiro, Dimas Betioli. Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF.

Degree: PhD, Estruturas, 2009, University of São Paulo

Neste trabalho, é desenvolvido um programa de computador para a análise estática e tridimensional de problemas de interação solo-estrutura. O programa permite considerar várias camadas de solo, cada qual com características físicas diferentes. Sobre este solo, o qual pode conter estacas, podem ser apoiados diversos tipos de estruturas, tais como placas e até um edifício. Todos os materiais considerados são homogêneos, isotrópicos, elásticos e lineares. O solo tridimensional é modelado com o método dos elementos de contorno (MEC), empregando as soluções fundamentais de Kelvin e uma técnica alternativa na consideração do maciço não-homogêneo. Esta técnica, que é uma contribuição original deste trabalho, é baseada no relacionamento das soluções fundamentais de deslocamento dos diferentes domínios, permitindo que sejam analisados como um único sólido sem a necessidade de equações de equilíbrio e compatibilidade. Isso reduz o sistema de equações final e melhora a precisão dos resultados, conforme comprovado nos exemplos apresentados. Para reduzir o custo computacional sem prejudicar a precisão dos resultados, é utilizada uma malha de elementos de contorno infinitos (ECI) nas bordas da malha de ECs para modelar o comportamento das variáveis de campo em longas distâncias. A formulação do ECI mapeado utilizado é outra contribuição original deste trabalho, sendo baseado em um EC triangular. É demonstrado por meio de exemplos que tal formulação é eficiente para a redução de malha, contribuindo de forma significativa na redução do custo computacional. Todas as estruturas que interagem com o solo, incluindo as de fundação, são simuladas empregando o método dos elementos finitos (MEF). Cada estaca é modelada como uma linha de carga empregando um único elemento finito com 14 parâmetros nodais, o qual utiliza funções de forma do quarto grau para aproximar os deslocamentos horizontais, do terceiro grau para as forças horizontais e deslocamentos verticais, do segundo grau para as forças cisalhantes verticais e constantes para as reações da base. Este elemento é empregado em outros trabalhos, no entanto os autores utilizam as soluções fundamentais de Mindlin na consideração da presença da estaca no solo. Desta forma, a formulação desenvolvida neste trabalho com as soluções fundamentais de Kelvin pode ser considerada mais uma contribuição original. No edifício, que pode incluir um radier como estrutura de fundação, são utilizados dois tipos de EFs. Os pilares e vigas são simulados com elementos de barra, os quais possuem dois nós e seis graus de liberdade por nó. As lajes e o radier são modelados empregando elementos planos, triangulares e com três nós. Nestes EFs triangulares são superpostos efeitos de membrana e flexão, totalizando também seis graus de liberdade por nó. O acoplamento MEC/MEF é feito transformando as cargas de superfície do MEC em carregamentos nodais reativos no MEF. Além de exemplos específicos nos Capítulos teóricos, um Capítulo inteiro é dedicado a demonstrar a abrangência e precisão da formulação desenvolvida,… Advisors/Committee Members: Paiva, João Batista de.

Subjects/Keywords: Acoplamento MEC/MEF; Building; Edifício; Elementos de contorno infinitos; FEM/BEM coupling; Infinite boundary elements; Interação solo/estrutura; Layered soil; Soil-structure interaction; Solo não-homogêneo

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Ribeiro, D. B. (2009). Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF. (Doctoral Dissertation). University of São Paulo. Retrieved from http://www.teses.usp.br/teses/disponiveis/18/18134/tde-14012011-102258/ ;

Chicago Manual of Style (16th Edition):

Ribeiro, Dimas Betioli. “Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF.” 2009. Doctoral Dissertation, University of São Paulo. Accessed November 14, 2019. http://www.teses.usp.br/teses/disponiveis/18/18134/tde-14012011-102258/ ;.

MLA Handbook (7th Edition):

Ribeiro, Dimas Betioli. “Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF.” 2009. Web. 14 Nov 2019.

Vancouver:

Ribeiro DB. Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF. [Internet] [Doctoral dissertation]. University of São Paulo; 2009. [cited 2019 Nov 14]. Available from: http://www.teses.usp.br/teses/disponiveis/18/18134/tde-14012011-102258/ ;.

Council of Science Editors:

Ribeiro DB. Estudo e aplicação de um elemento de contorno infinito na análise da interação solo-estrutura via combinação MEC/MEF. [Doctoral Dissertation]. University of São Paulo; 2009. Available from: http://www.teses.usp.br/teses/disponiveis/18/18134/tde-14012011-102258/ ;


University of Alberta

3. Lecoanet, Alexandre J L. Finite Element Model of the Thermal Profile During Submerged Arc Welding with One and Two Electrodes.

Degree: MS, Department of Chemical and Materials Engineering, 2016, University of Alberta

The submerged-arc welding (SAW) process is used extensively in the manufacturing of pipes. The heat flow introduced by the welding operation has a significant impact on the properties of both the weld metal and the heat affected zone (HAZ). The work presented in this thesis aims to develop a numerical heat flow model to predict the temperature profile in piece welded using SAW as a function of the welding parameters. Measurement were done using instrumented thermocouples during an operation of SAW with one electrode. The models were then compared to the measurements and a sensitivity analysis was carried out on the density, the specific heat, the parameter called “ff” in the double ellipsoid model, and the Neumann boundary condition. The three models used are a point source model giving results similar to Rosenthal’s results, a model using a double ellipsoid heat source with constant thermal properties, and a model using a double ellipsoid heat source with varying thermal properties. The presence of the thermocouples linked to the data acquisition system used in the experiment disturbed the weld but workable data were still extracted. Then the comparison between the measurement and the simulations showed that the most accurate model is the one using a double ellipsoid heat source with varying thermal properties. It predicts well the heating and the cooling phases of all the temperature profiles recorded but it predicts the peak well only for the thermocouples located around 12 mm from the center of the plate closer it overestimates the peak. The sensitivity analysis showed that the most sensitive parameters are the thermal properties. It also showed that the parameter called “ff” in Goldak’s approach is sensitive. The Neumann boundary condition is not a sensitive parameter. Also when measurements are done using thermocouples close to the knowing the exact location of the thermocouples is crucial.

Subjects/Keywords: Submerged arc welding; SAW; Modelling of submerged arc welding; Modelling of SAW; Modelling; Finite element method; FEM; Finite element method SAW; Thermal profile; Temperature profile; Modelling temperature profile; Instrumented thermocouples; Varying thermal properties; Simulation; Simulation of SAW; Simulation of welding; FEM modelling of SAW; Quasi-steady state; Heat transfer in welding; Point source; Double ellipsoid source; Two electrode welding; Welding with two electrodes; Instrumented welds; Sensitivity of the thermal properties; Welding of X70; Welding of pipelines; Statistical analysis; Bead shape parameters; Removing outliers; Simulation of welding with COMSOL; Mixed boundary condition; Simulation with two point sources; Infinite elements; Application of infinite elements to welding; Heat tranfer in moving coordinate system; Welding; Multiple electrode welding; Sensitivity analysis; Sensitivity analysis on submerged arc welding; Sensitivity analysis on SAW; Temperature measurement during a welding operation; Temperature measurement during submerged arc welding; Temperature measurement during SAW; Modelling temperature profile during welding; Modelling temperature profile during submerged arc welding; Modelling temperature profile during SAW

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Lecoanet, A. J. L. (2016). Finite Element Model of the Thermal Profile During Submerged Arc Welding with One and Two Electrodes. (Masters Thesis). University of Alberta. Retrieved from https://era.library.ualberta.ca/files/czk51vg98f

Chicago Manual of Style (16th Edition):

Lecoanet, Alexandre J L. “Finite Element Model of the Thermal Profile During Submerged Arc Welding with One and Two Electrodes.” 2016. Masters Thesis, University of Alberta. Accessed November 14, 2019. https://era.library.ualberta.ca/files/czk51vg98f.

MLA Handbook (7th Edition):

Lecoanet, Alexandre J L. “Finite Element Model of the Thermal Profile During Submerged Arc Welding with One and Two Electrodes.” 2016. Web. 14 Nov 2019.

Vancouver:

Lecoanet AJL. Finite Element Model of the Thermal Profile During Submerged Arc Welding with One and Two Electrodes. [Internet] [Masters thesis]. University of Alberta; 2016. [cited 2019 Nov 14]. Available from: https://era.library.ualberta.ca/files/czk51vg98f.

Council of Science Editors:

Lecoanet AJL. Finite Element Model of the Thermal Profile During Submerged Arc Welding with One and Two Electrodes. [Masters Thesis]. University of Alberta; 2016. Available from: https://era.library.ualberta.ca/files/czk51vg98f

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