O presente trabalho faz uma comparação entre resultados obtidos por um método prático e simplificado e o Método dos Elementos Finitos na determinação de esforços solicitantes em pontes celulares curvas em planta, submetidas à protensão. Na primeira parte, teórica, apresenta-se os conceitos fundamentais das vigas celulares curvas, mostrando-se principalmente as diferenças de seu comportamento em relação ao das vigas retas. Em seguida discute-se a protensão de peças de concreto com ênfase no seu efeito em vigas curvas. Finalmente, são apresentados os métodos a serem utilizados no cálculo, percorrendo as diversas situações de carregamento, mas sempre enfatizando o carregamento de protensão. Na segunda parte, prática, é elaborado um estudo comparativo, tomando-se como exemplo duas pontes rodoviárias em viga unicelular, sendo uma biapoiada e outra contínua, submetidas a protensão. Após a construção de modelos, tais vigas são processadas através de um programa comercial de elementos finitos. Alguns resultados são então comparados com aqueles obtidos através do método simplificado, elaborando-se assim observações práticas e que possam ser utilizadas nos projetos corriqueiros de engenharia. / This work compares the results from a practical and simplified method and the Finite Element Method to determinate section efforts in prestressed box-girder curved bridges. The first part, theoretical, introduces the basic principles of the cellular curved beams, showing the differences of its behavior comparing with straight beams. Next, prestressing of concrete members is discussed, emphasizing its effects in curved beams. Finally, calculation methods are presented, covering many loading situations, but always emphasizing the prestressing load. In the second part, practical, a comparative study is elaborated, taking two road unicellular bridges, one simply supported and another continuum, submitted to prestressing load. After models construction, such beams are calculated using a commercial software of Finite Element Method. Then, some results are compared with those calculated by simplified method, thus elaborating practical comments that can be used in the current designs of engineering.

Les structures pliées intéressent architectes et ingénieurs pour leurs qualités structurelles autant que spatiales et plastiques. En prenant comme point de départ la bande rectiligne pliée, ce travail de recherche aborde non pas la conception de surfaces plissées mais celle de structures réticulées. La conception de structures “à trous” à partir de bandes pliées constitue un angle d’approche original. La notion de continuité induite par le pli transforme la manière de concevoir la structure réticulée, habituellement caractérisée par des nœuds et barres dissociés. L’emploi de bandes continues rectilignes est une approche possible pour rationaliser la conception de formes complexes en minimisant la quantité de chutes de matière. Cette recherche explore de nouvelles méthodes de conception des formes courbes. Les objectifs de cette recherche sont :- la classification des différentes approches possibles dans la conception à partir de bandes rectilignes pliées- l'étude d'éléments modulaires pliés dont l’assemblage permet la génération de surfaces courbes variables: la géométrie de différentes configurations de bandes pliées sera décrite ainsi que les assemblages autorisés / Folded structures are attractive to architects and engineers for their structural qualities as well as spatial and plastic qualities. Taking as a starting point a linear folded stripe, this research does not address the design of pleated surfaces but that of reticular structures. The design of structures with "holes" from folded stripes is an original angle of approach. From a conceptual point of view, the continuity caused by folds transforms the usual conception by separated nodes and bars of reticular structures. The use of continuous linear stripes is one possible approach to make more efficient the design of complex shapes by minimizing the produced offcuts. This research investigates new methods of designing curved shapes. The aims of this research are:- A classification of different possible approaches encountered when conceiving from folded stripes.- The study a modular folded elements which assembly allows the generation of various curved surfaces : the geometry of different configurations of folded stripes and the assemblies allowed will be described

A proposta desse estudo in vitro foi avaliar a influência do pré-alargamento cervical no desgaste apical de canais simulados curvos preparados com instrumentos rotatórios de níquel-titânio. Foram confeccionados 30 blocos de resina com canais simulados de 20 graus de curvatura que foram divididos aleatoriamente em três grupos distintos (n=10) de acordo com o tipo de alargamento cervical realizado: Grupo I - sem alargamento cervical; Grupo II - alargamento cervical realizado com brocas CP Drill®; Grupo III - alargamento cervical realizado com brocas LA Axxess®. Previamente ao alargamento cervical os canais foram preenchidos com tinta nanquim em toda sua extensão e realizaram-se as fotografias iniciais com auxílio de máquina digital posicionada em estativa. Para o preparo apical utilizaram-se instrumentos rotatórios K3® na seqüência de 20.02 até 45.02, sendo que, entre o intervalo do uso de cada instrumento o canal foi preenchido, novamente, com tinta nanquim e realizada a fotografia final para cada instrumento. As fotografias pré e pós-operatórias foram sobrepostas e procedeu-se a mensuração do desgaste linear da parede interna e externa do canal simulado no ápice da curvatura e no ápice do canal proporcionado por cada instrumento, com auxílio do software Image Tool. A diferença entre esses valores, de acordo com cada área do canal avaliada, foi submetida à análise estatística. O teste de Regressão Linear permitiu estabelecer uma correlação entre o calibre do instrumento e o desgaste do canal, que pode ser traduzida em uma equação matemática, indicando que é diretamente proporcional. O teste de Kruskal-Wallis (complementado com pós-teste de Dunn) permitiu a comparação do desgaste entre os diferentes grupos experimentais. Por meio desses testes pode-se observar que grupo onde não foi realizado o pré-alargamento cervical apresentou padrões de desgastes diferentes daqueles onde o preparo foi executado. O grupo sem pré-alargamento provocou o desgaste acentuado do lado externo da curvatura, enquanto os grupos preparados com CP Drill® e LA Axxess® mostraram padrões de desgaste semelhantes, denotando a maior centralização do instrumento no canal em ambas as regiões analisadas (ápice da curva e ápice do canal). Pode-se concluir que o pré-alargamento cervical influenciou de forma positiva no preparo da região apical de canais simulados curvos, proporcionando preparos mais centralizados dessa região. / The purpose of this in vitro study was to evaluate the influence of cervical preflaring on prepared canal shape in simulated curved root canals prepared with nickel-titanium rotary systems. Thirty resin blocks with simulated canals with 20º curvature were fabricated and randomly assigned to three groups (n=10) according to the type of cervical preflaring: Group I - no cervical preflaring; Group II - cervical preflaring with CP Drill® burs; Group III - cervical preflaring with LA Axxess® burs. Previously cervical preflaring, the canals were thoroughly filled with India ink and the initial photographs were taken using a digital camera fixed in a static position. Right after, apical preparation was performed using 20.02 to 45.02 K3® rotary instruments. At each change of file, the canals were refilled with India ink and the final photographs were taken for each instrument. The initial and final photographs were superimposed and linear dentin removal produced by each type of rotary instrument was measured with specific software at the internal and external portions of the curvature apex and at the canal apex. The difference between the initial and final values was analyzed statistically, according to each canal region. Statistical analysis by linear regression established a correlation between instrument size and canal transportation, which can be expressed by a mathematical equation. This correlation is directly proportional, which means that the greater instrument, the more accentuated the canal transportation. Additionally, Kruskal- Wallis test (complemented by the Dunn\' post-test) allowed comparing dentin removal among the different experimental groups. These tests revealed that the non-flared group presented different dentin removal patterns, as compared to the groups where cervical preflaring was undertaken. The group without preflaring presented a significantly greater dentin removal on the external side of curvature, while the groups preflared with CP Drill® and LA Axxess® exhibited similar dentin removal patterns, demonstrating a greater centralization of the instrument inside the canal, for both analyzed regions (curvature apex and canal apex). It may be concluded that cervical preflaring influenced positively the apical preparation of simulated curved canals, producing more centralized preparations in this region.

Dos sistemas de pontes suspensas por cabos, as estaiadas tem sido largamente utilizadas devido a sua capacidade de vencer grandes vãos e, além dessa vantagem estrutural, são esteticamente bem aceitas pela sociedade, valorizando o espaço urbano e muitas vezes tornando-o ponto de referência. Atualmente, em que a otimização da infraestrutura viária é de extrema importância, as pontes estaiadas são bastante exploradas por suas vantagens construtivas, não demandando grandes áreas de apoio durante a construção que possam interferir no fluxo de veículos ou embarcações existente. Em conjunto a isso, a escolha do tipo de obra de arte se deve a diversos outros fatores, tais como as condições locais da fundação, o consumo de materiais e mão de obra, facilidades construtivas, etc. Muitas vezes é necessário estudar outras formas de utilização desse tipo de estruturas, como é o caso de pontes curvas, em que um traçado reto não bastaria para transpor um obstáculo e respeitar o traçado projetado ao viário. Para isso, o conhecimento das técnicas e teorias que fundamentam pontes estaiadas curvas é requisito para o estudo de uma concepção mais favorável e/ou otimizada, onde devem ser avaliados todos os fatores que influem em seu comportamento. Este trabalho apresenta a avaliação de esforços no tabuleiro e no mastro para diversos modelos estruturais. Na primeira etapa será discutida a forma de concepção dos modelos aplicados a um estudo de caso através de comparação dos esforços para avaliar a viabilidade de simular o tensionamento inicial nos cabos através da aplicação de uma queda de temperatura. Em seguida, serão avaliados os efeitos da posição do mastro e do posicionamento unilateral dos estais, permitindo obter a configuração que apresente um melhor desempenho geral. Por fim, as análises serão aplicadas a um estudo de caso com tabuleiro de maior largura. Dos resultados obtidos verificou-se que a configuração de tabuleiro suspenso pelo lado interno, única que não invade o gabarito de pedestres ou veículos, se mostrou viável sem, contudo, apresentar todas as vantagens estruturais, de modo que há torção significativa. Em compensação, a flexão se mostrou reduzida. / In systems of suspended cable bridges, the cable-stayed bridges had been widely used because of its capacity to overcome large spans and for being aesthetically well accepted by society, valuing the urban space and often making it a landmark. Currently, where the optimization of road infrastructure is of utmost importance, cable-stayed bridges are quite exploited by their constructive advantages, not requiring large areas of support during construction that may affect the existing traffic flow. In addition to this, the choice of the type of structure is due to several other factors such as local conditions of the foundation, the consumption of materials and labor, construction facilities, etc. It is necessary to study other forms of use of such structures, as in the case of curved bridges, where a straight path would not be enough to overcome an obstacle and respect the geometry of the road. For this, the knowledge of the techniques and theories behind curved cable-stayed bridges is a requisite for the study of a more favorable and/or optimized design, where all the factors that influence their behavior should be evaluated. This paper presents the assessment of forces on the deck and pylon for several structural models. In the first step, the models design will be discussed applied to a case by comparing the forces to evaluate the feasibility of simulating the initial tensioning in the cables through the application of a temperature drop. Next, the effects of the pylon position and the unilateral positioning of the cables will be evaluated, allowing to obtain the configuration that presents a better overall performance. Finally, the analyzes will be applied to a case with a wider deck. From the obtained results, it has been found that the configuration of deck suspended by the inner side, which does not invade the pedestrian or vehicle clearance, has proved to be feasible without, however, presenting all the structural advantages, so that there is significant torsion. In contrast, flexion was reduced.

Dos sistemas de pontes suspensas por cabos, as estaiadas tem sido largamente utilizadas devido a sua capacidade de vencer grandes vãos e, além dessa vantagem estrutural, são esteticamente bem aceitas pela sociedade, valorizando o espaço urbano e muitas vezes tornando-o ponto de referência. Atualmente, em que a otimização da infraestrutura viária é de extrema importância, as pontes estaiadas são bastante exploradas por suas vantagens construtivas, não demandando grandes áreas de apoio durante a construção que possam interferir no fluxo de veículos ou embarcações existente. Em conjunto a isso, a escolha do tipo de obra de arte se deve a diversos outros fatores, tais como as condições locais da fundação, o consumo de materiais e mão de obra, facilidades construtivas, etc. Muitas vezes é necessário estudar outras formas de utilização desse tipo de estruturas, como é o caso de pontes curvas, em que um traçado reto não bastaria para transpor um obstáculo e respeitar o traçado projetado ao viário. Para isso, o conhecimento das técnicas e teorias que fundamentam pontes estaiadas curvas é requisito para o estudo de uma concepção mais favorável e/ou otimizada, onde devem ser avaliados todos os fatores que influem em seu comportamento. Este trabalho apresenta a avaliação de esforços no tabuleiro e no mastro para diversos modelos estruturais. Na primeira etapa será discutida a forma de concepção dos modelos aplicados a um estudo de caso através de comparação dos esforços para avaliar a viabilidade de simular o tensionamento inicial nos cabos através da aplicação de uma queda de temperatura. Em seguida, serão avaliados os efeitos da posição do mastro e do posicionamento unilateral dos estais, permitindo obter a configuração que apresente um melhor desempenho geral. Por fim, as análises serão aplicadas a um estudo de caso com tabuleiro de maior largura. Dos resultados obtidos verificou-se que a configuração de tabuleiro suspenso pelo lado interno, única que não invade o gabarito de pedestres ou veículos, se mostrou viável sem, contudo, apresentar todas as vantagens estruturais, de modo que há torção significativa. Em compensação, a flexão se mostrou reduzida. / In systems of suspended cable bridges, the cable-stayed bridges had been widely used because of its capacity to overcome large spans and for being aesthetically well accepted by society, valuing the urban space and often making it a landmark. Currently, where the optimization of road infrastructure is of utmost importance, cable-stayed bridges are quite exploited by their constructive advantages, not requiring large areas of support during construction that may affect the existing traffic flow. In addition to this, the choice of the type of structure is due to several other factors such as local conditions of the foundation, the consumption of materials and labor, construction facilities, etc. It is necessary to study other forms of use of such structures, as in the case of curved bridges, where a straight path would not be enough to overcome an obstacle and respect the geometry of the road. For this, the knowledge of the techniques and theories behind curved cable-stayed bridges is a requisite for the study of a more favorable and/or optimized design, where all the factors that influence their behavior should be evaluated. This paper presents the assessment of forces on the deck and pylon for several structural models. In the first step, the models design will be discussed applied to a case by comparing the forces to evaluate the feasibility of simulating the initial tensioning in the cables through the application of a temperature drop. Next, the effects of the pylon position and the unilateral positioning of the cables will be evaluated, allowing to obtain the configuration that presents a better overall performance. Finally, the analyzes will be applied to a case with a wider deck. From the obtained results, it has been found that the configuration of deck suspended by the inner side, which does not invade the pedestrian or vehicle clearance, has proved to be feasible without, however, presenting all the structural advantages, so that there is significant torsion. In contrast, flexion was reduced.

Self-cleaning, anti-corrosion, anti-icing, dropwise-condensation, and drag-reduction are some applications in which superhydrophobic surfaces are implemented. To date, all the studies associated with superhydrophobic surfaces have been dedicated to understanding the liquid interaction with surfaces that are macroscopically smooth. The current study investigates the solid-liquid interaction of such surfaces which are fully decorated with macroscopic ridges (ribbed surfaces). In particular, the drop motion and impact on our newly designed non-wettable ribbed surface have been investigated in this work. Our experimental investigations have shown that liquid drops move faster on the ribbed surfaces due to lower friction induced by such a surface pattern. Moreover, an impacting droplet shows shorter contact time on ribbed surfaces. This concludes that ribbed surface pattern can be an efficient alternative design for the related applications. Besides the experimental studies, the theoretical analyses done in this work have led to, firstly a scaling model to predict descent velocity of a rolling viscous drops on an inclined non-wettable surface more accurately. Secondly, for curved superhydrophobic surfaces a scaling model which correlates the contact time of the impacting drop to its impact velocity has been developed. At the end, the knowledge obtained from this work has led to a special surface design which exhibits a contact time shorter than the inertial-capillary time scale, an unprecedented phenomenon.

Free energy techniques provide the basis for an analysis of aspects of the liquid-vapour interface undertaken in this study. The main focus of this work is an extensive theoretical investigation into properties of the surface tension, including curvature dependence and supersaturation effects, using Monte Carlo computer simulation techniques.

Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use in interactive simulation. Based on a three-dimensional beam model, a corotational approach is used for interactive simulation speeds in combination with adaptive mesh resolution to maintain accuracy. In the second paper we present a family of continuous piecewise linear finite elements for thin plate problems. Patchwise reconstruction of a discontinuous piecewise quadratic deflection field allows us touse a discontinuous Galerkin method for the plate problem. Assuming a criterion on the reconstructions is fulfilled we prove a priori error estimates in energy norm and L2-norm and provide numerical results to support our findings. The third paper deals with the biharmonic equation on a surface embedded in R3. We extend theory and formalism, developed for the approximation of solutions to the Laplace-Beltrami problem on an implicitly defined surface, to also cover the biharmonic problem. A priori error estimates for a continuous/discontinuous Galerkin method is proven in energy norm and L2-norm, and we support the theoretical results by numerical convergence studies for problems on a sphere and on a torus. In the fourth paper we consider finite element modeling of curved beams in R3. We let the geometry of the beam be implicitly defined by a vector distance function. Starting from the three-dimensional equations of linear elasticity, we derive a weak formulation for a linear curved beam expressed in global coordinates. Numerical results from a finite element implementation based on these equations are compared with classical results.

In this dissertation, a numerical method to design a curved surface for accurately flank milling with a general tool of revolution is presented. Instead of using the ruled surface as the design surface, the flank millable surface can better match the machined surface generated by flank milling techniques, and provide an effective tool to the designer to control the properties and the specifications of the design surface. A method using the least squares surface fitting to design the flank millable surface is first discussed. Grazing points on the envelope of the moving tool modeled by the grazing surface are used as the sample points and a NURBS surface is used to approximate the given grazing surface. The deviation between the grazing surface and the NURBS surface can be controlled by increasing the number of the control points. The computation process for this method is costly in time and effort. In engineering design, there is a need for fast and effortless methods to simplify the flank millable surface design procedure. A technique to approximate the grazing curve with NURBS at each tool position is developed. Based on the characteristics of the grazing surface and the geometries of the cutting tool, these NURBS representations at a few different tool positions, namely at the start, interior and end, are lofted to generate a NURBS surface. This NURBS surface represents the grazing surface and is treated as the design surface. Simulation results show that this design surface can accurately match the machined surface. The accuracy of the surface can be controlled by adding control points to the control net of the NURBS surface. A machining test on a 5-axis machine was done to verify the proposed flank millable surface design method. The machined surface was checked on a CMM and the obtained results were compared with the designed flank millable surface. The comparison results show that the machined surface closely matches the design surface. The proposed flank millable surface design method can be accurately used in the surface design.

This thesis develops strain and kinetic energy functions and a finite beam element useful for analyzing curved beams which go through large deflections, such as a hockey stick being swung and bent substantially as it hits the ice. The resulting beam model is demonstrated to be rotation invariant and capable of computing the correct strain energy and reaction forces for a specified deformation. A method is also described by which the model could be used to perform static or dynamic simulations of a beam.