Thesis (Ph. D.)--Lehigh University, 2002. / Includes vita. Includes bibliographical references (leaves 70-74).

Kaiserslautern, Univ., Diss., 2002. / Computerdatei im Fernzugriff.

Kaiserslautern, Univ., Diss., 2002. / Computerdatei im Fernzugriff.

Kaiserslautern, Universiẗat, Diss., 2002.

Cette thèse vise à approfondir les liens entre la géométrie différentielle et la théorie de l'élasticité, linéaire ou nonlinéaire. En s'appuyant sur cette analogie, on établit des résultats nouveaux tant en élasticité, qu'en géométrie différentielle.<br /> Dans les deux premiers chapitres, on montre que l'inégalité de Korn sur une surface est une conséquence de l'inégalité de Korn tridimensionnelle en coordonnées curvilignes et l'on établit une inégalité de type Korn sur une surface compacte sans bord. Dans le deux derniers chapitres, on établit certains résultats de géométrie différentielle concernant les espaces riemanniens et les surfaces sous des hypothèses affablies de régularité sur les données.<br />Dans l'appendice, on présente quelques résultats d'analyse utilisés dans la thèse.

No description available.

by Fan Xuqian. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 99-100). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- The Theorem of Efimov --- p.7 / Chapter 2.1 --- The Idea of the Proof of the Efimov's Theorem --- p.8 / Chapter 2.2 --- Proof of the Efimov's Main Lemma --- p.12 / Chapter 2.3 --- Proof of Lemma 2.3 --- p.48 / Chapter 2.4 --- Proof of Lemma 2.4 --- p.52 / Chapter 3 --- Isometric Immersion into R3 of Complete Surfaces with Negative Curvature --- p.62 / Chapter 3.1 --- The Sketch of the Proof of Theorem 3.1 --- p.66 / Chapter 3.2 --- Proof of Lemma 3.4 --- p.75 / Chapter 3.3 --- Proof of Lemma 3.5 --- p.76 / Chapter 3.4 --- Proof of Lemma 3.6 --- p.86 / Chapter 3.5 --- Proof of Lemma 3.7 --- p.89 / Chapter 3.6 --- The Geometric Properties of the Immersion --- p.95

Les matériaux composites sont utilisés dans de nombreuses structures marines et de nouvelles applications sont en cours de développement telles que les pales d’hydroliennes. La fiabilité de ces composants dans un environnement très sévère est cruciale pour la rentabilité de ces systèmes récupérateurs d’énergie des courants marins. Ces structures sont sujettes à de nombreuses forces, telles que les courants marins, les vagues, tempêtes mais également diverses agressions marines telles que l’eau de mer et la corrosion. Une compréhension approfondie du comportement au long terme de ces parties mobiles est donc essentielle. La majorité des développeurs d’hydroliennes ont préféré des pales en carbone. Ainsi il est nécessaire de comprendre comment une longue immersion dans l’océan affecte ces composites. Dans cette étude, le comportement au long terme de différents composites carbone/époxy a été étudié en utilisant des essais de vieillissement accéléré. Une diminution significative des résistances des composites a été observée après saturation en eau de mer. Pour des temps d’immersion plus longs, seulement peu de changements des propriétés apparaissent. Peu d’effets significatifs ont été observés tant sur les modules que sur la ténacité. Ces changements de propriétés sont initialement dus à la plastification de la matrice, suivis par un affaiblissement de l’interface fibre/matrice. L’endommagement peut affecter le comportement au long terme des structures composites et créer de nouveaux chemins préférentiels pour la diffusion de l’eau. En conséquence un modèle basé sur un critère couplé résistance/ténacité a été proposé pour décrire le seuil d’endommagement et basé sur un critère en ténacité pour décrire la cinétique d’endommagement. Il permet de reproduire d’une manière correcte le seuil et la cinétique d’endommagement pour des matériaux vieillis et non vieillis. L’évolution de l’entrée d’eau dans les composites a été suivie dans le but de développer un modèle de diffusion prenant en compte le nature anisotrope des composites. Ainsi le modèle de diffusion a été utilisé sur pale d’hydrolienne. Finalement des premières investigations sur le couplage entre le modèle de diffusion et l’endommagement ont été réalisées. Cette étude a contribué au développement d’outils pour quantifier la durabilité au long terme des pales d’hydroliennes en composites. / Composite materials are used in many marine structures and new applications are being developed such as tidal turbine blades. The reliability of these components, in a very severe environment, is crucial to the profitability of tidal current energy systems. These structures are subject to many forces such as ocean tides, waves, storms but also to various marine aggressions, such as sea water and corrosion. A thorough understanding of the long term behavior of the moving parts is therefore essential. The majority of tidal turbine developers have preferred carbon blades, so there is a need to understand how long immersion in the ocean affects these composites. In this study the long term behavior of different carbon/epoxy composites has been studied using accelerated ageing tests. A significant reduction of composite strengths has been observed after saturation of the material in seawater. For longer immersions only small further changes in these properties occur. No significant changes have been observed for moduli nor for composite toughness. Changes in properties are initially due to matrix plasticization, followed by reductions due to fibre/matrix interface changes. Damage can affect the long term behavior of composites structures and create new pathways for water diffusion. As a consequence a damage model has been proposed based on a coupled strength/toughness criterion to describe the threshold of damage and on a toughness criterion to describe the crack development kinetics. It describes in a correct manner the damage threshold and kinetics for the as-received material and for material after sea water ageing. The evolution of the rate of water ingress into composite materials has been followed, in order to develop a diffusion model taking into account the anisotropic nature of composites. Then the diffusion model has been applied on a tidal turbine blade. Finally a first investigation of the coupling between the diffusion model and damage has been performed. This study has contributed to the development of tools to quantify long term durability of composite tidal turbine blades.

Neste trabalho estudamos essencialmente problemas relacionados aos conceitos de superfícies e curvas bi-harmônicas e de superfícies de ângulo constante. Caracterizamos as curva bi-harmônicas do grupo especial linear SL(2,R). Em particular, mostramos que todas as curvas bi-harmônicas de SL(2,R) são hélices e damos suas parametrizações explícitas como curvas do espaço pseudo-Euclidiano R42. Estudamos as superfícies biconservativas (as quais representam uma grande família que inclui as superfícies bi-harmônicas) nos espaços de Bianchi-Cartan-Vranceanu, obtendo a caracterização daquelas de ângulo constante e daquelas SO(2)-invariantes. Também, caracterizamos as superfícies de ângulo constante do espaço Euclidiano tridimensional que possuem aplicação de Gauss bi-harmônica, provando que são cilindros de Hopf sobre uma clotóide. Além disto, caracterizamos as superfícies de ângulo contante de SL(2,R). Mais especificamente, damos uma descrição local explícita para estas superfícies em termos de uma determinada curva de SL(2,R) e de uma família a um parâmetro de isometrias do espaço ambiente. / In this work we mainly study some problems related to the concept of biharmonic curves and surfaces and to surfaces of constant angle. We characterize the biharmonic curves in the special linear group SL(2,R). In particular, we show that all proper biharmonic curves in SL(2,R) are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean space R42</sub. We study the biconservative surfaces (which represent a large family including the biharmonic surfaces) in the Bianchi-Cartan-Vranceanu spaces, obtaining the characterization of those with constant angle and of those which are SO(2)-invariant. Furthermore, we characterize the constant angle surfaces of the three-dimensional Euclidean space which have bi-harmonic Gauss map, proving that they are Hopf cylinders over a clothoid. Also, we characterize the constant angle surfaces of SL(2,R). In particular, we give an explicit local description of these surfaces by means of a suitable curve of SL(2,R) and a 1-parameter family of isometries of SL(2,R).

Neste trabalho estudamos essencialmente problemas relacionados aos conceitos de superfícies e curvas bi-harmônicas e de superfícies de ângulo constante. Caracterizamos as curva bi-harmônicas do grupo especial linear SL(2,R). Em particular, mostramos que todas as curvas bi-harmônicas de SL(2,R) são hélices e damos suas parametrizações explícitas como curvas do espaço pseudo-Euclidiano R42. Estudamos as superfícies biconservativas (as quais representam uma grande família que inclui as superfícies bi-harmônicas) nos espaços de Bianchi-Cartan-Vranceanu, obtendo a caracterização daquelas de ângulo constante e daquelas SO(2)-invariantes. Também, caracterizamos as superfícies de ângulo constante do espaço Euclidiano tridimensional que possuem aplicação de Gauss bi-harmônica, provando que são cilindros de Hopf sobre uma clotóide. Além disto, caracterizamos as superfícies de ângulo contante de SL(2,R). Mais especificamente, damos uma descrição local explícita para estas superfícies em termos de uma determinada curva de SL(2,R) e de uma família a um parâmetro de isometrias do espaço ambiente. / In this work we mainly study some problems related to the concept of biharmonic curves and surfaces and to surfaces of constant angle. We characterize the biharmonic curves in the special linear group SL(2,R). In particular, we show that all proper biharmonic curves in SL(2,R) are helices and we give their explicit parametrizations as curves in the pseudo-Euclidean space R42</sub. We study the biconservative surfaces (which represent a large family including the biharmonic surfaces) in the Bianchi-Cartan-Vranceanu spaces, obtaining the characterization of those with constant angle and of those which are SO(2)-invariant. Furthermore, we characterize the constant angle surfaces of the three-dimensional Euclidean space which have bi-harmonic Gauss map, proving that they are Hopf cylinders over a clothoid. Also, we characterize the constant angle surfaces of SL(2,R). In particular, we give an explicit local description of these surfaces by means of a suitable curve of SL(2,R) and a 1-parameter family of isometries of SL(2,R).