From the results of the cases discussed, it can be concluded that the neglect of transverse-shear deformation and normal stress results in expressions for bending moments and deflection which may be seriously in error. / / Master of Science

The strength and behavior of gusset plates in buckling is evaluated herein based on data from the experimental investigations conducted by other researchers and the analytical work presented herein. A set of design guidelines has been recommended through the review of the current practice. Representative single and double brace gusset plates normally adopted for connections with compressive bracing/diagonal members in braced frames and trusses, were modeled and analyzed using linear and nonlinear finite element methods to determine the buckling loads. The buckling analysis data along with the test data indicated the occurrence of inelastic buckling of the gusset plates. Current design practice and a set of formulas for determination of gusset plate thickness have been reviewed. A set of guidelines has been recommended for the design and evaluating gusset plate buckling loads.

O presente trabalho é o início de um estudo da aplicação do método de otimização conhecido como adjunto em escoamentos incompressíveis, viscosos e periódicos, envolvendo um problema de bastante interesse: a análise da aplicação de splitter plates em cilindros de seção circular. Conhecido por sua simplicidade, o splitter plate, que consiste em uma placa plana alinhada ao escoamento e colocada a jusante do corpo, é um dispositivo efetivo na mudança de comportamento da esteira de vórtices de Von Kárman. A partir da revisão bibliográfica foi possível entender a dinâmica do escoamento, proporcionando uma calibração dos modelos numéricos. Complementando esta etapa, foi efetuada uma análise da qualidade das malhas computacionais. Através de uma geração de diversas malhas computacionais, o espaço de soluções foi explorado buscando encontrar o mínimo arrasto para diversos comprimentos de splitter plate e diferentes números de Reynolds (Re). Foi observada a influência da placa na formação da esteira de vórtices, obtendo uma redução dos coeficientes de força do cilindro. Com esses dados, foi possível desenvolver o método de otimização voltado para análise do gradiente de sensibilidade conhecido como método adjunto baseado nas equações de Navier Stokes utilizando o problema descrito como base para validação dos resultados. A abordagem do método adjunto caracteriza-se pela busca dos extremos de funções conhecidas como medidas de mérito. Essas funções podem ser integrais de sustentação e arrasto por exemplo. Na literatura, o método adjunto é apresentado como possuindo duas grandes vantagens: a primeira é a imposição das equações do escoamento como restrições do problema, o que sempre confinará as variações da medida de mérito dentro do universo de soluções realizáveis; já a segunda é conseqüência da primeira, pois as restrições permitem uma simplificação no cálculo do gradiente de sensibilidade, reduzindo o custo computacional. Para o cálculo do gradiente de sensibilidade, o objetivo é otimizar o arrasto do cilindro sob efeito do splitter plate variando os parâmetros de controle (comprimento e posicionamento do splitter plate). A direção de busca e o cálculo do passo da geometria são obtidos a partir da relação entre a solução numérica do escoamento e as variáveis adjuntas calculadas. Nesta dissertação, será apresentada a pesquisa bibliográfica, os resultados do método tentativa e erro, a formulação do método adjunto baseado nas equações de Navier Stokes e um exemplo de sua solução numérica, demonstrando sua existência. / The report is the beginning of a research about the application of the so called adjoint method in the optimization of incompressive, viscous and periodic flows. The study involves a problem of great interest: an analysis of the implementation of splitter plates in the flow around cylinders with circular section. Widely recognized for its simplicity, the splitter plate consists of a flat plate, which is placed in the wake of a cylinder, in the stream wise direction, and it works by changing the way the shear layers interact with one another. Based on a literature survey, it is possible to understand the physics of this class of flows. As a better result, one learns what to expect from the numerical solutions and hence, one can calibrate its parameters. Moreover, we study the best configuration of the computational mesh, thus reducing the computational cost. After the generation of meshes, the universe of solutions was explored to find the minimum drag for various lengths of splitter plate and Reynolds number (Re). The influence of the plate in the interaction of the shear layers was observed in the reduction of drag coefficient. These results form a the basis for comparison, upon one can develop the optimization by the adjoint method. The adjoint method can be used to search the extreme of objective functionals. These functionals can be the lift and drag integrals for example. The theory presents two advantages to the method: first, the imposing the equations that govern the flow as variational constraints one limits the variations to the universe of realizable solutions; second, these constrains simplify the computation of the sensitivity gradient, by reducing its computational cost. To compute the sensitivity gradient, the objective functional can be defined as the average drag coefficient of the circular cylinder with a splitter plate. The control parameters are the length of the plate and the distance between it and the body, which known as gap. The search direction and the variation of geometry can be obtained by the relationship between the solutions to the flow and the adjoint equations. This final report shows the literature survey, the results of trial and error method and the formulation and one result of adjoint equations based on the incompressible NavierStokes equations.

Annular gas seal clearances were simulated with closely spaced parallel plates using a Flat?Plate tester. The device is designed to measure the pressure gradient along the test specimen. The main function of the Flat?Plate tester is to provide friction factor data and measure dynamic pressure oscillations. A detailed description of the test facility is described, and a theory for determining the friction factor is reviewed. Three clearances were investigated: 0.635, 0.381, and 0.254 mm. Tests were conducted at three different inlet pressures (84, 70, and 55 bars), producing Reynolds numbers range from 50,000 to 700,000. Three surface configurations were tested including smooth?on-smooth, smooth?on?hole, and hole?on?hole. The Hole?pattern plates are identical with the exception of the hole depth. The results indicate that, for the smooth?on?smooth and smooth?on?hole configurations, the friction factor remains constant or increases slightly with increasing Reynolds numbers. Moreover, the friction factor increases as the clearance between the plates increases. However, the results from the hole?on-hole configurations are quite different. A "friction?factor jump" phenomenon was observed, and the Helmholtz frequency was detected on the frequency spectra.

Cette thèse concerne la géométrie asymptotique de variétés riemanniennes complètes non compactes, dont la courbure tend vers zéro à l'infini, assez vite. Afin de compléter des travaux déjà existants, on s'attache à comprendre le cas où la croissance du volume est non maximale, c'est-à-dire strictement moins rapide que dans l'espace euclidien de même dimension. Dans ce contexte, on prouve tout d'abord une inégalité de Sobolev à poids et une inégalité de Hardy, qui permettent de généraliser nombre de résultats établis quand la croissance du volume est maximale. On obtient en particulier des résultats de rigidité et de finitude de la topologie pour des variétés Ricci plates et asymptotiquement plates. On obtient ensuite un résultat de structure asymptotique pour une classe d'instantons gravitationnels : typiquement, ceux qui ont une croissance du volume cubique sont asymptotes à des fibrations en cercles au-dessus d'une variété asymptotiquement localement euclidienne .

Thesis (M. Eng.(Metallurgical engineering))--University of Pretoria, 2005. / Includes bibliographical references. Available on the Internet via the World Wide Web.

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O presente trabalho é o início de um estudo da aplicação do método de otimização conhecido como adjunto em escoamentos incompressíveis, viscosos e periódicos, envolvendo um problema de bastante interesse: a análise da aplicação de splitter plates em cilindros de seção circular. Conhecido por sua simplicidade, o splitter plate, que consiste em uma placa plana alinhada ao escoamento e colocada a jusante do corpo, é um dispositivo efetivo na mudança de comportamento da esteira de vórtices de Von Kárman. A partir da revisão bibliográfica foi possível entender a dinâmica do escoamento, proporcionando uma calibração dos modelos numéricos. Complementando esta etapa, foi efetuada uma análise da qualidade das malhas computacionais. Através de uma geração de diversas malhas computacionais, o espaço de soluções foi explorado buscando encontrar o mínimo arrasto para diversos comprimentos de splitter plate e diferentes números de Reynolds (Re). Foi observada a influência da placa na formação da esteira de vórtices, obtendo uma redução dos coeficientes de força do cilindro. Com esses dados, foi possível desenvolver o método de otimização voltado para análise do gradiente de sensibilidade conhecido como método adjunto baseado nas equações de Navier Stokes utilizando o problema descrito como base para validação dos resultados. A abordagem do método adjunto caracteriza-se pela busca dos extremos de funções conhecidas como medidas de mérito. Essas funções podem ser integrais de sustentação e arrasto por exemplo. Na literatura, o método adjunto é apresentado como possuindo duas grandes vantagens: a primeira é a imposição das equações do escoamento como restrições do problema, o que sempre confinará as variações da medida de mérito dentro do universo de soluções realizáveis; já a segunda é conseqüência da primeira, pois as restrições permitem uma simplificação no cálculo do gradiente de sensibilidade, reduzindo o custo computacional. Para o cálculo do gradiente de sensibilidade, o objetivo é otimizar o arrasto do cilindro sob efeito do splitter plate variando os parâmetros de controle (comprimento e posicionamento do splitter plate). A direção de busca e o cálculo do passo da geometria são obtidos a partir da relação entre a solução numérica do escoamento e as variáveis adjuntas calculadas. Nesta dissertação, será apresentada a pesquisa bibliográfica, os resultados do método tentativa e erro, a formulação do método adjunto baseado nas equações de Navier Stokes e um exemplo de sua solução numérica, demonstrando sua existência. / The report is the beginning of a research about the application of the so called adjoint method in the optimization of incompressive, viscous and periodic flows. The study involves a problem of great interest: an analysis of the implementation of splitter plates in the flow around cylinders with circular section. Widely recognized for its simplicity, the splitter plate consists of a flat plate, which is placed in the wake of a cylinder, in the stream wise direction, and it works by changing the way the shear layers interact with one another. Based on a literature survey, it is possible to understand the physics of this class of flows. As a better result, one learns what to expect from the numerical solutions and hence, one can calibrate its parameters. Moreover, we study the best configuration of the computational mesh, thus reducing the computational cost. After the generation of meshes, the universe of solutions was explored to find the minimum drag for various lengths of splitter plate and Reynolds number (Re). The influence of the plate in the interaction of the shear layers was observed in the reduction of drag coefficient. These results form a the basis for comparison, upon one can develop the optimization by the adjoint method. The adjoint method can be used to search the extreme of objective functionals. These functionals can be the lift and drag integrals for example. The theory presents two advantages to the method: first, the imposing the equations that govern the flow as variational constraints one limits the variations to the universe of realizable solutions; second, these constrains simplify the computation of the sensitivity gradient, by reducing its computational cost. To compute the sensitivity gradient, the objective functional can be defined as the average drag coefficient of the circular cylinder with a splitter plate. The control parameters are the length of the plate and the distance between it and the body, which known as gap. The search direction and the variation of geometry can be obtained by the relationship between the solutions to the flow and the adjoint equations. This final report shows the literature survey, the results of trial and error method and the formulation and one result of adjoint equations based on the incompressible NavierStokes equations.

There is no evidence in the literature of biomechanical stability characteristics comparing conventional rectangular screw placement with that of an angled mono-cortical screw plating system where standard 2mm diameter screws are applied at angles more acute than conventional 90° screws, through plate holes machined (cut) for a definite specific screw angle placement P. Angled screws will have an obvious clinical advantage of direct line of vision insertion, through an intra-oral route without the disadvantage of trans-buccal (cutaneous) approach required for conventional 90° rectangular screw application. Angled screw application will result in the prevention of possible, less post-operative swelling, nerve fall out (motor and/or sensory), haematoma, false aneurysm and scarring as unwanted clinical complications associated with trans-buccal extra-oral surgical technique. Intra-oral angled screw application will result in definitive cost saving due to less operating time required. Post-treatment removal of angled screws is uncomplicated, requiring only intra-oral surgical approach, without trochar use or skin incisions for screwdriver application. By determining angle displacement values at certain clinical relevant force values for both compression/tension and torsion, preference can be established for ideal angle(s) of screw application in a plating system. An own unique, designed and manufactured, jig and inclined screw insertion (ISI) plates were implemented during the biomechanical evaluation of stability at different screw angle applications in a Zwick machine. For the purpose of this biomechanical comparative investigation an inclined screw insertion (ISI) plate was manufactured with 90°, 75°, 60° and 45° angled plate holes orientated in line with the long-axis (quadrant 3) of the distal section of the plates and diagonal across (quadrant 1) in the proximal section of the plates. Screws with an ISI angle of 30° in any quadrant application resulted in lifting the plate from the bone surface and caused cortical bone destruction during pilot drilling. The results for mono-cortical 7mm screw placement proved superior in biomechanical stability during tension/compression - forces for screw insertion angles of 60° and 45°, when compared to conventional 90° rectangular screw placement. Screws inserted at an angle of 75° demonstrated no improvement in compression/tension stability when compared with 90°.Torsion force stability for all of the 75°, 60° and 45° inclined screw insertion (ISI) systems proved more stable compared to conventional 90° screw angle plates. It is concluded that angled monocortical screw placement between angles 60° and 45° has clinical significance as far as stability, intra-oral surgical technique and time-cost factor is concerned. The results of this biomechanical behaviour investigation of ISI, evolved new terminology such as screw-tip shifting, screw-tip travel, lag potential and clinical significance for the range of screw angle placement. Angled orientation to the plate design and plate geometry is also defined in terms of tension line distribution in the anatomical region for application in the mandible. An unique quadrant description for ISI is described for future communication. An international patent, based on the ISI principle, has been registered for monocortical six-hole plates of firstly different geometric designs to conform to specific anatomical topographic sites in the mandible and secondly specific screw plate-holes angled at 60° in different orientation to the plate (Patent:PCT/EP 2006/006365), (Addendum 6). A specific L-shaped, mandibular angle plate with screw holes at a 60° angle where orientation shifts from in-line with the long-axis of the plate in the distal three plate holes to diagonal orientation in the proximal section of the plate, is designed and manufactured by Stryker/Leibinger as an example of such a patent plate. It is recommended that a smart-lock plate with plate holes at 55° angles be manufactured to allow screw angle placements of 65° - 45° in different angle orientations. Pilot hole drilling and ISI can be performed without the use of a drill-guide. / Thesis (PhD)--University of Pretoria, 2009. / Maxillo-Facial and Oral Surgery / unrestricted