ABSTRACT CONTACT MECHANICS OF GRADED MATERIALS WITH TWODIMENSIONAL MATERIAL PROPERTY VARIATIONS G&ouml / kay, Kemal M.S., Department of Mechanical Engineering Supervisor: Asst. Prof. Dr. Serkan Dag September 2005, 62 pages Ceramic layers used as protective coatings in tribological applications are known to be prone to cracking and debonding due to their brittle nature. Recent experiments with functionally graded ceramics however show that these material systems are particularly useful in enhancing the resistance of a surface to tribological damage. This improved behavior is attributed to the influence of the material property gradation on the stress distribution that develops at the contacting surfaces. The main interest in the present study is in the contact mechanics of a functionally graded surface with a two &ndash / dimensional spatial variation in the modulus of elasticity. Poisson&rsquo / s ratio is assumed to be constant due to its insignificant effect on the contact stress distribution [30]. In the formulation of the problem it is assumed that the functionally graded surface is in frictional sliding contact with a rigid flat stamp. Using elasticity theory and semi-infinite plane approximation for the graded medium, the problem is reduced to a singular integral equation of the second kind. Integral equation is solved numerically by expanding the unknown contact stress distribution into a series of Jacobi polynomials and using suitable collocation points. The developed method is validated by providing comparisons to a closed form solution derived for homogeneous materials. Main numerical results consist of the effects of the material nonhomogeneity parameters, coefficient of friction and stamp size and location on the contact stress distribution.

In this thesis, we consider real matrix functions that depend on two parameters and study the problem of how to detect and approximate parameters' values where the singular values coalesce. We prove several results connecting the existence of coalescing points to the periodic structure of the smooth singular values decomposition computed around the boundary of a domain enclosing the points. This is further used to develop algorithms for the detection and approximation of coalescing points in planar regions. Finally, we present techniques for continuing curves of coalescing singular values of matrices depending on three parameters, and illustrate how these techniques can be used to locate coalescing singular values of complex-valued matrices depending on three parameters.

The deep web contains a massive number of collections that are mostly invisible to search engines. These collections often contain high-quality, structured information that cannot be crawled using traditional methods. An important problem is selecting which of these collections to search. Automatic collection selection methods try to solve this problem by suggesting the best subset of deep web collections to search based on a query. A few methods for deep Web collection selection have proposed in Collection Retrieval Inference Network system and Glossary of Servers Server system. The drawback in these methods is that they require communication between the search broker and the collections, and need metadata about each collection. This thesis compares three different sampling methods that do not require communication with the broker or metadata about each collection. It also transforms some traditional information retrieval based techniques to this area. In addition, the thesis tests these techniques using INEX collection for total 18 collections (including 12232 XML documents) and total 36 queries. The experiment shows that the performance of sample-based technique is satisfactory in average.

Judgements of and sensitivity to style are ubiquitous. People become sensitive to the structural regularities of complex or “polymorphous” categories through exposure to individual examples, which allows them respond to new items that are of the same style as those previously experienced. This thesis investigates whether a dimension reduction mechanism could account for how people learn about the structure of complex categories. That is, whether through experience, people extract the primary dimensions of variation in a category and use these to analyse and categorise subsequent instances. We used Singular Value Decomposition (SVD) as the method of dimension reduction, which yields the main dimensions of variation of pixel-based stimuli (eigenvectors). We then tested whether a simple autoassociative network could learn to distinguish paintings by Picasso and Braque which were reconstructed from only these primary dimensions of variation. The network could correctly classify the stimuli, and its performance was optimal with reconstructions based on just the first few eigenvectors. Then we reconstructed the paintings using either just the first 10 (early reconstructions) or all 1,894 eigenvectors (full reconstructions), and asked human participants to categorise the images. We found that people could categorise the images with either the early or full reconstructions. Therefore, people could learn to distinguish category membership based on the reduced set of dimensions obtained from SVD. This suggests that a dimension reduction mechanism analogous to SVD may be operating when people learn about the structure and regularities in complex categories.

Judgements of and sensitivity to style are ubiquitous. People become sensitive to the structural regularities of complex or “polymorphous” categories through exposure to individual examples, which allows them respond to new items that are of the same style as those previously experienced. This thesis investigates whether a dimension reduction mechanism could account for how people learn about the structure of complex categories. That is, whether through experience, people extract the primary dimensions of variation in a category and use these to analyse and categorise subsequent instances. We used Singular Value Decomposition (SVD) as the method of dimension reduction, which yields the main dimensions of variation of pixel-based stimuli (eigenvectors). We then tested whether a simple autoassociative network could learn to distinguish paintings by Picasso and Braque which were reconstructed from only these primary dimensions of variation. The network could correctly classify the stimuli, and its performance was optimal with reconstructions based on just the first few eigenvectors. Then we reconstructed the paintings using either just the first 10 (early reconstructions) or all 1,894 eigenvectors (full reconstructions), and asked human participants to categorise the images. We found that people could categorise the images with either the early or full reconstructions. Therefore, people could learn to distinguish category membership based on the reduced set of dimensions obtained from SVD. This suggests that a dimension reduction mechanism analogous to SVD may be operating when people learn about the structure and regularities in complex categories.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (p. 97-104).

University, Diss., 2002--Kaiserslautern.

Este trabalho apresenta a formulação e implementação numérica do método dos elementos de contorno (MEC) para elasticidade linear tri-dimensional, com avaliação direta das integrais fracamente e fortemente singulares. A implementação segue a formulação tradicional do MEC direto, e a discretização do contorno das variáveis do problema é realizada com elementos descontínuos, permitindo o uso de malhas desconectadas ao longo das superfícies. O cálculo das integrais singulares é realizado através do uso de expansões assintóticas calculadas em torno de um ponto singular genérico. As expressões analíticas destas expansões são apresentadas no trabalho. Estas expansões serão subtraídas do núcleo original regularizando-o e a parte singular é integrada analiticamente, restando apenas uma integral regular, tornando ambas as integrais possíveis de serem calculadas com quadraturas de Gauss. É concluído que o presente método requer menos pontos de integração para o mesmo nível de erro quando comparado com outras técnicas. Alguns casos de elasticidade são resolvidos para ilustrar a eficiência e precisão do método. / This work presents the formulation and implementation of the boundary element method (BEM) to three dimensional linear elastostatics, with the direct evaluation of the strongly singular integral equations. The implementation follows the traditional direct BEM formulation, and the discretization of the boundary is carried out with discontinuous elements, enabling the use of disconnected meshes along the surfaces. The computation of the singular integral equations is accomplished by using the asymptotic expansions derived around a generic singular point. The analytical expressions for these expansions are presented in this work. The expansions are subtracted from the kernel to regularize it. This subtracted part is then added by computing a regular line integral along the boundary of the element. Both the integrals can be calculated with Gauss-type quadratures. It's observed that the present method needs less integration points for the same level of error when compared with other techniques. Several elasticity benchmarks are solved to demonstrate the eficiency and the accuracy of the present method.

O trabalho que aqui nos propusemos realizar tem como objetivo a análise de erros de escrita que apresentam um caráter singular, estatisticamente irrelevante, colocando em suspenso uma noção de língua enquanto uma ordem homogênea, estabilizada e constituída de fenômenos regulares. Chamamos esses erros de erros ortográficos singulares e analisamos aqueles presentes em 10 textos produzidos por alunos da 4º série do Ensino Fundamental de uma rede pública de Alagoas, em um teste de Português elaborado pelo Núcleo de Avaliação e Pesquisa Educacional da Universidade Federal de Pernambuco (NAPE-UFPE), no ano de 1997. O corpus é formado por 229 textos e, atualmente, pertence ao banco de dados do Projeto Integrado Práticas de Textualização na Escola , coordenado pelo professor Eduardo Calil, do Centro de Educação da Universidade Federal de Alagoas (CEDU-UFAL). De um ponto de vista diferenciado da noção psicológica de desenvolvimento tentamos mostrar como a singularidade desses erros aponta para um funcionamento que difere daquele suposto pelas habilidades cognitivas, na medida em que indicia uma ordem própria que escapa ao domínio do sujeito e que não mantém total relação entre o sistema de formas escritas e o sistema oral. Um funcionamento pautado na noção saussureana de valor lingüístico marcado pelas relações de diferença que mantém os significantes com outros significantes da língua, enquanto uma ordem simbólica habitada por uma subjetividade, operada pelos processos metafóricos e metonímicos (Jakobson 1966; Milner 1987; Lemos 1992). Assim, quando tomamos para análise os erros ortográficos singulares quisemos, na verdade, mostrar que o funcionamento lingüístico que rege o sistema ortográfico possui uma autonomia que nos obriga a relativizar as categorizações. Pela estrutura desse sistema, as ocorrências singulares não podem simplesmente ser descartadas ou consideradas irrelevantes para o processo de aquisição porque não são estatisticamente significativas. Elas estão inscritas num funcionamento próprio do sistema ortográfico e não podem ser apagadas pela busca do regular, do estabilizado, do categorizável. Elas nos revelam um sujeito sob os efeitos de um funcionamento de ordem lingüística.

A força hidrodinâmica em termos dos coeficientes de massa adicional e amortecimento, para obstáculos aproximadamente circulares, finos e submersos sob uma superfície livre aquática, é calculada numericamente usando um método espectral. Primeiramente, é apresentado um modelo matemático para ondas aquáticas de superfície e em seguida, o problema de difração de ondas devido à presença de um obstáculo é descrito. Quando o obstáculo é submerso e fino, o problema pode ser formulado em termos de uma equação integral hipersingular. Usando um mapeamento conforme sobre um disco circular, é mostrado que a solução pode ser obtida através de um método espectral onde a hipersingularidade é avaliada analiticamente em termos de polinômios ortogonais. Os coeficientes da força hidrodinâmica, em função do número de onda, são obtidos para obstáculos quase circulares. A ocorrência de frequências ressoantes ´e observada para submersões suficientemente pequenas e subpicos de ressonância aparecem para valores moderados da submersão, em comparação com o caso do disco circular. / The hydrodynamic force, in terms of the added mass and damping coefficients, for thin and submerged nearly circular obstacles below a water free surface is computed by a spectral method. Firstly, a mathematical model for surface water waves is presented. Next, the diffraction problem of waves due to the presence of an obstacle is described. When the body is thin and submerged, the problem can be formulated in terms of a hypersingular integral equation. Using a conformal mapping over a circular disc, it is shown that the solution can be obtained by means of a spectral method where the hipersingularity is analytically evaluated in terms of orthogonal polynomials. The hydrodynamics coefficients, in function of the wavenumber, are computed and shown for nearly circular obstacles. The occurrence of resonant frequencies is observed for sufficiently small submergences and subpeaks of resonances appear for moderate values of the submergence, in comparison with the case of a circular disc.