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This thesis describes a new computer-based method for the generation of finite element meshes. It relies upon the Schwarz-Christoffel transformation, a conformal mapping from conplex variable theory. This mapping is defined and some examples of its use in classical fluid dynamics are given. A practical method for evaluating the parameters defining this transformation is described and emphasis is placed on the efficiency of the solution process in order that coirputer run times may be kept as short as possible. A theorem in Euclidean geometry is stated and proved which links the theory of the Schwarz-Christoffel mapping and the geometrical use to which it is put here. Two such Schwarz-Christoffel transformations are used to construct a mapping between any two polygons. The desirable properties of a finite element mesh are stated and a method is described which atteirpts to generate such a mesh in any sinply-connected two-dimensional region. Numbering of the nodes is an inherent part of the generation scheme, thus ensuring that the optimum bandwidth of the resulting system of linear equations in the analysis phase is obtained. In order to be able to present example meshes, a particular element type, the three-noded triangle, is used and a section describing the enumeration of hexagons, all of whose internal angles are 2n/3, is included. The thesis includes a brief survey of existing methods of two-dimensional mesh generation as well as several example meshes.

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Neste trabalho fazemos um estudo do conceito de soma torcida de F-espaços. Apresentamos algumas propriedades e simplificações na construção de somas torcidas de F-espaços localmente limitados. Em particular, estudamos uma condição suficiente para que uma soma torcida de espaços de Banach seja um espaço de Banach. Finalmente aplicamos esses conceitos para definir o espaço construído por N. J. Kalton, que é um exemplo de um espaço de Banach não isomorfo ao conjugado complexo. Este espaço X de Kalton corresponde a uma soma torcida de espaços de Hilbert, isto é, X possui um subespaço fechado E tal que E e X/E são isomorfos a espaços de Hilbert. / In this work we study the concept of twisted sum of F-spaces. We also study some properties and simplifications in the construction of twisted sums of locally bounded F-spaces. In particular, we study a sufficient condition for a twisted sum of Banach spaces to be a Banach space. Finally we apply these concepts to define the space constructed by N. J. Kalton, which is an example of a Banach space not isomorphic to its complex conjugate. The Kalton space X is a twisted sum of Hilbert spaces, i.e. X has a closed subspace E such that E and X/E are isomorphic to Hilbert spaces.

Étant donné une variété symplectique $(M,\omega)$, il existe toujours des structures presque complexes $\omega$-compatibles positives. La question qui nous intéresse est de trouver des méthodes de sélection de certaines de ces structures. Des réponses ont déjà été données par V. Apostolov et T.Draghici, J.G. Evans, et J. Keller et M. Lejmi. Nous nous intéressons ici principalement à des méthodes de sélection définies en termes du tenseur de Nijenhuis. De manière très générale, lorsqu'on veut sélectionner certaines données géométriques, on peut aborder le problème de différentes manières. L’une d’entre elles consiste à regarder la décomposition en composantes irréductibles de certains tenseurs naturellement associés à la structure considérée et poser des conditions sur certaines composantes. Nous avons montré que le tenseur de Nijenhuis est irréductible sous l'action du groupe unitaire. Cette irréductibilité ne nous permet pas d'imposer d'autre condition linéaire à ce tenseur que son annulation, qui correspond aux variétés de Kähler. Une autre méthode possible de sélection est d’imposer des conditions à certaines distributions liées au problème. Nous avons étudié des distributions liées au tenseur de Nijenhuis. Nous nous sommes intéressés ici aux dimensions et propriétés d’involutivité possibles de ces distributions. Nous donnons des exemples invariants sous l’action d’un groupe, construits sur des groupes symplectiques ou sur des fibrés de twisteurs sur une variété riemannienne. La dernière méthode envisagée dans ce travail est la considération de fonctionnelles définies à partir des données. Pour construire une fonctionnelle la plus simple possible en termes du tenseur de Nijenhuis, nous intégrons une fonction polynomiale du second degré en les composantes du tenseur de Nijenhuis. On montre qu’un tel polynôme est toujours un multiple de la norme au carré de ce tenseur. La fonctionnelle obtenue est celle étudiée par Evans. Elle est a priori peu intéressante pour notre problème de sélection car il a prouvé qu’on peut trouver des exemples de variétés symplectiques n’admettant aucune structure kählérienne mais telle que l’infimum de la fonctionnelle soit nul / Given a symplectic manifold $(M,\omega)$, there always exist almost complex $\omega,$-compatible positive structures. The problem studied in this thesis is to find methods to select some of these structures. Answers have already been suggested by V. Apostolov and T.Draghici, J. G. Evans, and J. Keller and M. Lejmi. We are mainly interested here in selection methods defined in terms of the Nijenhuis tensor. The problem of selecting geometric objects can be tackled in various ways. One of them is to decompose into irreducible components some tensors naturally associated with the structure, and to impose conditions on some of those components. We prove that the Nijenhuis tensor is irreducible under the action of the unitary group. This irreducibility does not allow to impose any linear condition on the Nijenhuis tensor, except the vanishing of it, which corresponds to Kähler manifolds. Another possible method of selection is to impose conditions on distributions related to the problem. We study distributions defined by the Nijenhuis tensor. Our results concern the possible dimensions and properties of involutivity of these distributions. We give examples which are invariant under the action of a group, on some symplectic groups and on twisted bundles over some Riemannian manifolds. The last method considered in this work consists in looking for extremals of functionals defined from the data. To construct the simplest functional defined in terms of the Nijenhuis tensor, we integrate a polynomial function of the second degree into the components of this tensor. All such polynomials are multiple of the square of the norm of this tensor. This functional is the one studied by Evans; the drawback for our selection problem is that there exist examples of compact symplectic manifolds which do not admit any K\"ahler structure but such that the infimum of the functional is zero

Neste trabalho fazemos um estudo do conceito de soma torcida de F-espaços. Apresentamos algumas propriedades e simplificações na construção de somas torcidas de F-espaços localmente limitados. Em particular, estudamos uma condição suficiente para que uma soma torcida de espaços de Banach seja um espaço de Banach. Finalmente aplicamos esses conceitos para definir o espaço construído por N. J. Kalton, que é um exemplo de um espaço de Banach não isomorfo ao conjugado complexo. Este espaço X de Kalton corresponde a uma soma torcida de espaços de Hilbert, isto é, X possui um subespaço fechado E tal que E e X/E são isomorfos a espaços de Hilbert. / In this work we study the concept of twisted sum of F-spaces. We also study some properties and simplifications in the construction of twisted sums of locally bounded F-spaces. In particular, we study a sufficient condition for a twisted sum of Banach spaces to be a Banach space. Finally we apply these concepts to define the space constructed by N. J. Kalton, which is an example of a Banach space not isomorphic to its complex conjugate. The Kalton space X is a twisted sum of Hilbert spaces, i.e. X has a closed subspace E such that E and X/E are isomorphic to Hilbert spaces.

Ce travail de recherche s’inscrit dans le cadre de l’analyse vibroacoustique des structures complexes. Il propose une nouvelle approche énergétique utilisant le champ de densité d’énergie afin de simplifier une telle analyse. Cette approche est basée sur un modèle numérique stochastique construit à l’aide de l’approche probabiliste non paramétrique des incertitudes de modélisation et de paramètres. L’approche énergétique stochastique développée correspond à une nouvelle représentation du système vibroacoustique en terme des grandeurs énergétiques aléatoires. Un modèle vibroacoustique énergétique moyen est alors construit en prenant la moyenne statistique des grandeurs énergétiques. On dispose alors d’un modèle énergétique moyen pour analyser la vibroacoustique des systèmes complexes dans la bande des basses et des moyennes fréquences alors que la méthode SEA ne permet pas d’analyser cette bande de fréquence. L’analyse des propriétés des grandeurs énergétiques moyennes utilisées pour la construction du modèle vibroacoustique énergétique permet de construire une version simplifiée conduisant à un modèle énergétique simplifié pour lequel une méthodologie de partition structurale par zone est établie. Une application de cette approche énergétique et de la méthodologie de partition structurale par zone est présentée pour une voiture constituée d’une structure automobile couplée avec sa cavité acoustique interne / This research lies in the domain of the vibroacoustic analysis of complex structures. It proposes a new energy approach using the energy-density field in order to simplify such an analysis. This approach is based on a stochastic computational model constructed using the nonparametric probabilistic approach of modeling and parameters uncertainties. The stochastic energy approach developed corresponds to a new representation of the vibroacoustic system in terms of random energy quantities. A mean vibroacoustic energy model is thus constructed using a statistical averaging of the random energy quantities. This mean energy model provides a tool to perform a vibroacoustic analysis of complex structures in the low and medium frequency range while the SEA is not adapted to this frequency band. The analysis of the properties of the mean energy quantities used for the construction of the vibroacoustic energy model allows the construction of a simplified model to be obtained and yields a simplified energy model for which a structural partitioning methodology is then established. An application of the energy approach ant of the structural partitioning methodology is done on an automotive vehicle structure coupled with its internal acoustic cavity

In this thesis we study the problem of determining the possible cobordism types of r-fold self-intersection manifolds associated to self-transverse immersions f: M^{n-k} -> \R^n for certain values of n, k, and r. Namely, we study the double-point self-intersection manifolds of immersions M^{n+2} -> \R^{2n+2} and M^{n+4} -> \R^{2n+4}, focusing on the case when $n$ is even. In the case of self-transverse immersions f : M^{n+2} -> \R^{2n+2}, we see that when n is even the double-point self-intersection manifold is a boundary, which is a result originally due to Szucs. In the case of self-transverse immersions f : M^{n+4} -> \R^{2n+4}, we show than when n is even the double-point self-intersection manifold is either a boundary or cobordant to RP^2 x RP^2, which is a new result. We then show that for even n such that the binary expansion of n+4 contains 5 or more 1s, the double-point self-intersection manifold of a self-transverse immersion M^{n+4} -> \R^{2n+4} is necessarily a boundary. We also survey the case when n is odd. We also set up and study the complex versions of the above problems: self-transverse immersions f : M^{2k+2} -> \R^{4k+2} and f : M^{2k+4} -> \R^{4k+4} of stably complex manifolds with a given complex structure on the normal bundle of f$. In these cases, the double-point self-intersection manifold L associated to the immersion inherits a stably complex structure, and we attempt to determine which complex cobordism classes of stably complex manifolds may arise in this way. This is all new work. In the case of self-transverse complex immersions f : M^{2k+2} -> \R^{4k+2}, we show that the first normal Chern number of the double-point self-intersection manifold is a multiple of 2^{\lambda_{k+1}} for some integer \lambda_{k+1}, and provide upper and lower bounds for the value of \lambda_{k+1}. We also determine the exact value of \lambda_{k+1} in certain cases. In the case of self-transverse complex immersions f : M^{2k+4} -> \R^{4k+4}, we identify a large class of stably complex manifolds that may arise as the double-point self-intersection manifold of such an immersion and also identify a class of manifolds that may not. Additionally, in both cases we identify a necessary (and sometimes sufficient) condition for a stably complex manifold of the appropriate dimension to admit a complex immersion of the appropriate codimension.

Yes / Despite the abundant use of polyethylene oxides (PEOs) and their integration as an excipient in numerous pharmaceutical products, there have been no previous reports of applying this important thermoplastic polymer species alone to fused deposition modelling (FDM) 3D printing. In this work, we have investigated the manufacture of oral doses via FDM 3D printing by employing PEOs as a backbone polymer in combination with polyethylene glycol (PEG). Blends of PEO (molecular weight 100 K, 200 K, 300 K, 600 K or 900 K) with PEG 6 K (plasticiser) and a model drug (theophylline) were hot-melt extruded. The resultant filaments were used as a feed for FDM 3D printer to fabricate oral dosage forms (ODFs) with innovative designs. ODFs were designed in a radiator-like geometry with connected paralleled plates and inter-plate spacing of either 0.5, 1, 1.5 or 2 mm. X-ray diffraction patterns of the filaments revealed the presence of two distinctive peaks at 2θ = 7° and 12°, which can be correlated to the diffraction pattern of theophylline crystals. Blends of PEO and PEG yielded filaments of variable mechanically resistance (maximum load at break of 357, 608, 649, 882, 781 N for filament produced with PEO 100 K, 200 K, 300 K, 600 K or 900 K, respectively). Filaments of PEO at a molecular weight of 200–600 K were compatible with FDM 3D printing process. Further increase in PEO molecular weight resulted in elevated shear viscosity (>104 Pa.S) at the printing temperature and hindered material flow during FDM 3D printing process. A minimal spacing (1 mm) between parallel plates of the radiator-like design deemed essential to boost drug release from the structure. This is the first report of utilising this widely used biodegradable polymer species (PEOs and PEG) in FDM 3D printing.

Orientador: Jose Maria Campos dos Santos / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-07-31T20:57:31Z (GMT). No. of bitstreams: 1 Ferraz_FabioGuilherme_M.pdf: 9315977 bytes, checksum: 2c619b06df862551ab474095f22421cc (MD5) Previous issue date: 2001 / Resumo: Este trabalho explora o uso de métodos de Síntese Modal dos Componentes (SMC), a Teoria da Perturbação por Mínimo Rank (MRPT) e o Algoritmo de Realização de vetores de Ritz (RRA) como uma ferramenta para a detecção de danos estruturais. A SMC consiste em modelar separadamente componentes individuais de uma estrutura e então acoplá-Ios num sistema único. Os métodos de SMC podem ser generalizados para se permitir o uso de outros vetores, tais como os vetores de Ritz em substituição aos modos normais. Os vetores de Ritz são obtidos a partir de relações de recorrência, e representam uma ótima base de vetores como alternativa aos modos naturais de vibrar dos componentes. O MRPT é um método de detecção de danos baseado em modelo, que usa o fato de que um dano discreto pode ser manifestado num modelo de elementos finitos (MEF) como uma pequena perturbação no rank das matrizes que compõe as propriedades da estrutura. O RRA converte as matrizes em tempo discreto identificadas pelo algoritmo ERA para o tempo contínuo, a partir das quais pode-se extrair os vetores de Ritz experimentais usados para se complementar a matriz de forças dinâmicas residuais na formulação do MRPT. Através do modelo sem danos sintetizado, e do modelo medido com danos, o MRPT com RRA é usado para se detectar a localização do dano e sua extensão, ou no mínimo o componente que contém o dano. Diferentes considerações de modelagem subestruturada são exploradas na detecção de danos usando exemplos numéricos. Em particular um MEF de vigas da estação espacial internacional é implementado e os efeitos de danos localizados em diferentes componentes são investigados / Abstract: This work explores the use of Component Mode Synthesis methods (CMS), Minimum Rank Perturbation Theory (MRPT), and Ritz Realization AIgorithm (RRA) as a structural damage detection tooI. The CMS consists in to modeling individual components of a structure separately and then to couple them to form an assembled system. CMS methods can be generalized to allow the use of other vectors, like Ritz vectors, rather than normal modes. The Ritz vectors are obtained from recurrence relations, and represent a suitable basis vectors as an alternative to component vibration modes. MRPT is a model-based damage detection method, which utilizes the fact that discrete damage is manifested in a structural finite element model (FEM) as a low rank perturbation to the structural property matrices. RRA converts the discrete time system matrices identified by Eigensystem Realization AIgorithm (ERA) to continuous time system matrices, from which one can extract the experimental Ritz vectors used to complement the matrix of dynamic residual forces in the MRPT formulation. With the coupled healthy model and the measured damaged model, the MRPT with RRA is used to detect the damage location and his extent, or at least the component that contains the damage. Different substructure modeling assumptions on damage detectability are explored using numerical examples. In particular a beam FEM of the international space station structure is implemented and the effects of different localized component damages are investigated. / Mestrado / Mecanica dos Sólidos e Projeto Mecanico / Mestre em Engenharia Mecânica