This work is intended for high school and university students and their teachers who want to learn or improve their knowledge about affine transformations and perspective collineation. In this work the reader acquainted with the ideal elements, dividing ratio and cross ratio. The main part of the work is perspective collineation and affine transformations, their definitions, properties, specificity and finding other elements. This work also deals with the use of affine transformations and perspective collineation in descriptive geometry. The text is supplemented with illustrative images, applets and step-by-step images that are created with GeoGebra software. Keywords: affine transformations, perspective collineation, ideal elements, cuts of solids, dividing ratio, cross ratio

The axial map of a town is one of the key components of the space syntax method – a tool for analysing urban layout. It is derived by placing the longest and fewest lines, called axial lines, to cross the adjacencies between convex polygons in a convex map of a town. Previous research has shown that placing axial lines to cross the adjacencies between a collection of convex polygons is NP-complete, even when the convex polygons are restricted to rectangles and the axial lines to have orthogonal orientation. In this document, we show that placing orthogonal axial lines in orthogonal rectangles where the adjacencies between the rectangles are restricted to be crossed only once (ALPSC- OLOR) is NP-complete. As a result, we infer the single adjacency crossing version of the general axial line placement problem is NP-complete. The transformation of NPcompleteness of ALP-SC-OLOR is from vertex cover for biconnected planar graphs. A heuristic is then presented that gives a reasonable approximate solution to ALP-SC-OLOR based on a greedy method.

Estimativas de desempenho de compressores axiais através de métodos numéricos, entre eles o Método da Curvatura das Linhas de Corrente, são ferramentas utilizadas para reduzir o custo e o tempo de desenvolvimento de compressores axiais. A qualidade dos resultados está intimamente ligada às correlações que relacionam o escoamento à máquina, isto ée, correlações de incidência de mínima perda, de perda de pressão total e de desvio. O presente trabalho estuda as diferenças dos resultados obtidos com diferentes correlações de modo a definir a validade destas nos casos estudados e apontar as possibilidades de desenvolvimento do programa disponível no ITA. Pretende-se, desta forma, que as limitações do método, devido as simplificações necessárias, sejam totalmente exploradas. Foram simulados dois compressores: um estágio de "fan" de razão de pressão 1,35 (estágio NASA 53) e um estágio de compressor de alto desempenho construído com perfil MCA (estágio NASA 37).

Specific power output from a Low Pressure (LP) steam turbine can be enhanced by increasing the stage efficiency or raising its pressure ratio; both methods are interlinked and must be dealt with together. The latter is achieved by connecting to the exhaust diffuser; space and cost constraints often insist the use of an axial-radial diffuser with high levels of diffusion. The present study aims to investigate the interaction between the last-stage blade and the axial-radial diffuser, which can influence the diffuser performance and thus the total work output from the stage. This work is carried out using CFD simulations of a generic last stage low pressure (LP) turbine and axial-radial exhaust diffuser attached to it. In order to determine the validity of the computational method, the CFD predictions are first compared with data obtained from an experimental test facility. A computational study is then performed for different design configurations of the diffuser and rotor casing shapes. The study focuses on typical flow features such as effects of rotor tip leakage flows and subsequent changes in the rotor-diffuser interactions. The results suggest that the rotor casing shape and diffuser configurations influences the rotor work extraction capability and yields significant improvements in the static pressure recovery.

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Mecânica, 2018. / A busca por veículos seguros é uma necessidade atual dado o grande número de colisões veiculares, conforme mostrado por estatísticas de trânsito. Para o desenvolvimento de veículos mais seguros é necessário o entendimento do esmagamento axial de seus componentes estruturais durante colisões, pois a deformação de tais componentes absorve grande parte da energia cinética. Neste sentido, este trabalho apresenta um estudo acerca do esmagamento axial de tubos de seção quadrada usados como absorvedores de energia. Esses tubos constituem geometrias representativas do crash box, um absorvedor de energia posicionado entre o para-choque e as longarinas de muitos modelos de veículos. Para o desenvolvimento do trabalho, a influência de três parâmetros foi estudada: material da composição do absorvedor (alumínio e aço), espessura da parede e presença de furos laterais circulares nas paredes dos absorvedores. Os estudos foram realizados por meio de ensaios de esmagamento em baixa velocidade (solicitação quase-estática) e simulações numéricas foram executadas com o objetivo de analisar os modos de flambagem e a distribuição de tensão ao longo das paredes dos absorvedores de energia. Indicadores de desempenho foram estabelecidos e comparados com a finalidade de identificar os absorvedores mais eficientes. Verificou-se que a espessura da parede e o material influenciam significativamente os indicadores de desempenho estudados. Sobre a influência dos furos laterais, foi constatado que esses constituem concentradores de tensão e estabelecem um padrão de distribuição da tensão ao longo das paredes dos tubos, o que altera o processo de deformação dos absorvedores de energia e consequentemente influencia os indicadores de desempenho analisados. Em relação ao indicador de desempenho energia absorvida, verificou-se um aumento de 28% para os absorvedores fabricados em aço e de 67% para os absorvedores fabricados em alumínio quando a espessura da parede foi aumentada. Sobre o estudo da presença de furos, foi verificado um aumento de 15% da energia específica para o caso do aço e 9% para o alumínio quando o absorvedor de melhor desempenho foi comparado ao absorvedor sem furos laterais. Como inovação em relação aos trabalhos apresentados pela literatura estudada, apresenta-se o estudo da presença de várias camadas de furos laterais e o uso de simulações numéricas de distribuição de tensão como forma de entendimento do esmagamento axial de absorvedores de seção quadrada. / The search for safe vehicles is essential nowadays due to the large number of car crashes, as can be noted by the traffic statistcs. In order to design safer vehicles, it is necessary the understainment on how the structural components of the car behaves under axial crushing, since its deformation absorbes a large percentage of the kinetic energy. In this sense, this work presents a study on the axial crushing of square tubes used as energy absorbers. These tubes are representatives of crash box, which is an energy absorber placed between the bumper and the side members of many vehicles. In order to develop this work, three parameters were studied: material used on the absorber (aluminium and steel), wall thickness and the presence of circular holes on the tubes’ walls. The studies were conducted by means of low-speed crushing testes (quasi-static solicitation) and numerical simulations were conducted in order to analysis the buckling modes and the stress distribution along the absorbers’ walls. Performance indicators were stablished and compared for the purpose of finding the most efficient absorbers. It was found that the tube’s wall thickness and its material have a great influence on the performance indicators. Concerning to the influence of the lateral holes, it was verified that the holes work as stress concentrators and induce a pattern for the stress distribution along the tubes’ walls. This pattern changes the way the energy absorber deformates, and the performance indicators also change as a consequence. Concerning to the Absoved Energy, an increase of 28% was verified in the absorbers made with steel and 67% for the absorbers made with aluminum when the wall thickness was increased. About the study related to the presence of lateral holes, it was verified an increase of 15% for steel and 9% for aluminum when the best absorber was compared to its equivalent with no holes. As innovation, this work provides a study concernig to the presence of various layers of lateral holes and the use of numerical simulations to promote a better understanding about the crhusing behavior of tubes used as energy absorbers.

Plantar foot stress causing foot ulceration is a diabetic complication causing major economic burden throughout the world. It has long been thought that shear stresses on the plantar surface of the foot are a major contributing factor to the formation of these ulcers. Although there are many instruments available that measure the vertical foot pressure (vertical forces), there are currently no commercially available instruments to measure the horizontal or shear forces. It is the aim of this project to develop a platform instrument capable of measuring the three dimensional forces (i.e. vertical pressure and shear forces) across the plantar surface of the foot.

Tese de mestrado integrado. Engenharia Mecânica. Faculdade de Engenharia. Universidade do Porto. 2009

<p>This thesis investigates the effects of swashplate vibration and slipper surface geometry on the performance of the slipper-swashplate interface. The lubricating interfaces within a swashplate type axial piston machine are the most complicated part of the design process. These interfaces are supposed to provide support to the significant loads they experience during operation and to prevent continuous contact of the sliding surfaces. Therefore a proper slipper-swashplate interface design ensures full film lubrication during operation and provides sufficient load support while minimizing viscous and volumetric losses at the same time. The effects of two factors on the performance of the slipper-swashplate are examined during this work; swashplate vibration and slipper surface micro-geometry. An already existing model of the slipper-swashplate interface was used to carry out the results for this work however some modifications were made to the model to suit the needs of this research. Swashplate vibration is a phenomenon that has not been implemented in the model before, therefore its effects on the performance of the interface were analyzed. Thickness of the fluid film in the lubricating regime corresponds with its performance and is directly affected by the micro-geometry of the sliding interfaces. Therefore the effects of slipper surface micro-geometry is crucial to study in order to find the optimal slipper-swashplate interface design.</p>

This work is an investigation into the curvature related potential for flux to flow in the radial direction in the back-iron of laminated axial flux machine cores. Analytical and numerical models are presented. Analysis based on these models has shown that, in practical axial flux machines, the radial component of the flux density can be neglected with respect to the flux density distribution in the core back-iron. It has also been found that if the core permeability, core conductivity and number of poles are sufficiently high then power loss due to curvature related cross-lamination flux is negligible compared to normal eddy current losses. A closed form expression to predict losses due to curvature related radial flux is also presented. This expression allows axial flux machine designers to make quick assessment of the need to consider these losses when designing axial flux machines.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 291-304).