This thesis presents a study of two basic modes of deformation of a thin sheet: wrinkling and crumpling, viewed primarily in the context of an elastic sheet confined by capillary forces on a drop of liquid. First, it provides a brief conceptual background in the relevant physics of thin sheet mechanics and capillarity and introduces the general principles of wrinkling and crumpling. The problem of confining a circular sheet on an increasingly curved spherical drop is presented as a vehicle to explore these principles. At finite curvature, the sheet is seen to wrinkle around its outer edge. At large confinement, characteristic features of crumpling gradually dominate the pattern. The experimental observations in both regimes are analyzed separately. Analysis of images of the sheet in the wrinkled regime yield data for the number and length of the wrinkled zone, as a function of the experimental control parameter, the pressure. The length of the wrinkles is correctly described by a far-from-threshold theory, which describes a limiting regime in thin-sheet mechanics, distinguished by high 'bendability'. The validity of this theory is verified by the data for highly bendable, ultrathin sheets for the first time. The theory is based on the assumption that the wrinkles completely relax compressive stresses and therefore preserve the cylindrical symmetry of the stress field. The emergence of crumpling from the wrinkled shape is explored via evolution of visible features in the sheet as well as gaussian curvature measurements obtained by analyzing height maps from optical profilometry. The emergence of several length scales, increasing asymmetry in curvature distribution, the failure of wrinkle extent prediction and formation of d-cones associated with crumpling are all measured to locate the transition to a crumpled state. The value of gaussian curvature at the center of the sheet appears to follow the cylindrically symmetric prediction over the whole range of the experiment, suggesting that the onset of crumpling events does not affect the global shape of the sheet. Finally, analogous wrinkling and crumpling behavior of particle-laden interfaces is discussed. The spontaneous formation of conical defects in a curved 2D crystal is compared to the crumpling of a sheet on a drop, and insight from thin sheet mechanics is applied to the mysterious wrinkling of particle rafts. Some future directions for measuring wrinkling of sheets on negative curvature surfaces and deformations of fluid interfaces are proposed.

A fairly general method for studying electromagnetic induction in cases where any lateral variations in conductivity are confined to the near-surface region is developed using the thin-sheet technique. The significant feature is that extended anomalies, subject only to the restriction that well-defined two-dimensional problems are approached at infinity, can be handled. The approximate boundary condition is that gradients parallel to the coordinate axes vanish at infinity. / Graduate

This study involves analyses and experiments of magnesium¡¦s hot extrusion of thin sheets and tubes. At first, hot compression tests are conducted to obtain the magnesium¡¦s plastic flow stresses in high tempearatures, which will be used in the finite element analysis. In the FE simulations of thin sheet extrusion, the flow pattern of the magnesium billet within the die, the temperature history at die exit and the elastic deformation of the die is analyzed. Sound and good thin sheets are obtained by appropriate die design, initial billet temperature and extrusion velocity¡¦s control. The goal of constant temperature extrusion is expected to achieved by controlling the extrusion velocity which will influences the billet temperature at die exit. In FE simulations of thin tube extrusion, the flow pattern of the magnesium billet within the port-holes, welding chamber and die bearing is analyzed. The elastic deformation of the die is dicussed. Extrusion of sound thin tubes is achieved by appropriate extrusion conditions. Finally, hot extrusion experiments are conducted and the experimental values of the extrusion load and dimensions of the products are compared with the analytical values to verify the validity of the analytical models.

In this study, a numerical model is used to investigate the evaporation and flow characteristics of heated liquid sheets and films. The liquid is modeled as water and as black liquor, a byproduct produced by paper mills. In the pulping process, black liquor is concentrated in an evaporator as a falling film. The effectiveness of the evaporator is reduced due to fouling on heat transfer surfaces. Two flow arrangements are studied: falling films, where the liquor and steam are separated by a heat transfer surface; and liquid curtains, which is a thin sheet of liquid falling due to gravity surrounded by steam. For the liquid curtain, the liquid and gas come into direct contact, therefore there is no place for fouling to occur allowing for a more consistent operation of the evaporator. This type of arrangement is not currently used in paper mills but is being investigated in this work to determine its feasibility. The fluid system is simulated using the finite volume method with a single-fluid field to capture the liquid-gas interface. This study investigates how the breakup of a liquid curtain is affected by flow parameters and how the breakup into droplets influences the evaporation characteristics of the liquid curtain. It is found that the falling film evaporator has a much higher liquid evaporation rate than evaporating as a liquid curtain. However the falling film evaporator has an entrance length with no evaporation, and liquid curtains allow for evaporation to start occurring very near the inlet. If reducing length of the evaporator is a priority, liquid curtain evaporators can obtain a higher evaporation rate than falling films within the same distance. Falling film evaporation has a higher steam efficiency than a liquid curtain evaporator. However, for short evaporator lengths the rate at which water is removed from a liquid curtain evaporator is much greater, but at the cost of a higher steam consumption rate.

A finite element analysis approach is used to determine the susceptibility to wrinkles for thin sheets with clamped ends when subjected to tensile loading. The model problem chosen to do this analysis is the stretching of a thin sheet with clamped-ends. In the preliminary analysis, a stress analysis of thin sheets is done to study the stresses that develop under these boundary conditions. The analysis shows that there is a stretch-induced compressive stress in the transverse direction to the applied load that causes wrinkles. Then, the parametric study is conducted to determine the effect of aspect ratio and strain on the compressive stress. Based on the results of the parametric study, a critical strain value for each aspect ratio is determined for which the corresponding compressive stress is zero. Further buckling analysis is performed to find the buckling modes of the model problem that shows a limit of aspect ratio below which buckling is not possible under given conditions. Finally, post-buckling analysis shows the nature of wrinkles observed in the model problem for different aspect ratios. / text

We work with two different mechanisms to generate geometric frustration on thin elastic sheets; isotropic differential growth and folding. We describe how controlled growth and prescribing folding patterns are useful tools for designing three-dimensional objects from information printed in two dimensions. The first mechanism is inspired by the possibility to control shapes by swelling polymer films, where we propose a solution for the problem of shape formation by asking the question, ``what 2D metric should be prescribed to achieve a given 3D shape?'', namely the reverse problem. We choose two different types of initial configurations of sheets, disk-like with one boundary and annular with two boundaries. We demonstrate our technique by choosing four examples of 3D axisymmetric shapes and finding the respective swelling factors to achieve the desired shape. Second, we present a mechanical model for a single curved fold that explains both the buckled shape of a closed fold and its mechanical stiffness. The buckling arises from the geometrical frustration between the prescribed crease angle and the bending energy of the sheet away from the crease. This frustration increases as the sheet's area increases. Stiff folds result in creases with constant space curvature while softer folds inherit the broken symmetry of the buckled shape. We extend the application of our numerical model to show the potential to study multiple fold structures.

Cette thèse se situe dans le domaine de l'électromagnétisme et plus particulièrement, celui de la compatibilité électromagnétique. L'objectif de cette thèse est de proposer une condition d'interface qui évite de mailler les plaques minces conductrices lors d’une modélisation tridimensionnelle. Cette condition permet de prendre en compte de manière précise la réflexion d'une onde ou sa transmission par une plaque conductrice. Elle permet aussi de tenir compte de l'effet de peau de l'effet de peau à l'intérieur de la plaque. Cette condition d'interface est intégrée dans une méthode Galerkin discontinue. La présence des termes de flux dans cette méthode rend facile l'implémentation de cette condition d'interface. Afin de montrer l'intérêt de cette condition dans le cadre de la compatibilité électromagnétique, des configurations d'interaction ondes-Structures sont traitées. Elles ont pour but d'étudier l'efficacité de blindage de diverses cavités bidimensionnelles et tridimensionnelles. / This thesis concerns electromagnetic fields and more particularly electromagnetic compatibility. The aim of this thesis is the modeling an interface condition to avoid the mesh of thin conductive sheets in 3D numerical methods. This interface condition allows to take in account the reflection or the transmission of an incident wave on a conductive sheet. It also takes into account the skin effect in this sheet. This interface condition is integrated in discontinuous Galerkin method. The presence of flux terms is this method makes easy to implement this interface condition. To demonstrate the advantage of this interface condition in electromagnetic compatibility problems, many configurations of interaction wave-Structure are treated. They aim to study the shielding effectiveness of different cavities in two and three dimensions.

Neste trabalho foram realizados experimentos de soldagem de chapas de Tântalo e Monel 400 com 100 m de espessura. Foram realizadas soldas em um laser de Nd:YAG operando em modo pulsado e em um Laser de Fibra operando em modo contínuo. Em seguida a microestrutura das amostras foram analisadas através de microscopia ótica e foram realizados ensaio de microdureza Vickers. As amostras que apresentaram melhores resultados foram submetidas a ensaios de tração e a ensaios de corrosão. Após análise dos resultados observou-se que a soldagem a laser apresenta muitos benefícios em relação a outros processos convencionais para chapas finas. A soldagem no modo pulsado apresentou maior relação de aspecto se comparado a soldagem em modo contínuo. A soldagem em modo contínuo apresentou uma velocidade de soldagem muito superior ao modo pulsado. Os resultados indicaram que a soldagem no modo pulsado apresenta maior aplicabilidade para chapas finas, devido à necessidade um controle preciso sobre a intensidade aplicada. / This work carried out welding experiments of Tantalum and Monel 400 plates with 100 mm thickness. Welds were made with an Nd: YAG laser operating in a pulsed mode and in a fiber laser operating in continuous mode. Then the microstructure of the samples were analyzed by optical microscopy and were performed Vickers microhardness test. Samples that showed better results were subjected to tensile tests and the corrosion tests. After analysis of the results showed that the laser welding offers many benefits over other conventional processes for thin sheets. The welding in pulsed mode presented in superior aspect ratio compared to welding in continuous mode. The welding in continuous mode showed a much higher welding speed to pulsed mode. The results indicated that the welding in pulsed mode shows more applicability for sheet metal, due the need of a precise control of applied intensity.

Neste trabalho foram realizados experimentos de soldagem de chapas de Tântalo e Monel 400 com 100 m de espessura. Foram realizadas soldas em um laser de Nd:YAG operando em modo pulsado e em um Laser de Fibra operando em modo contínuo. Em seguida a microestrutura das amostras foram analisadas através de microscopia ótica e foram realizados ensaio de microdureza Vickers. As amostras que apresentaram melhores resultados foram submetidas a ensaios de tração e a ensaios de corrosão. Após análise dos resultados observou-se que a soldagem a laser apresenta muitos benefícios em relação a outros processos convencionais para chapas finas. A soldagem no modo pulsado apresentou maior relação de aspecto se comparado a soldagem em modo contínuo. A soldagem em modo contínuo apresentou uma velocidade de soldagem muito superior ao modo pulsado. Os resultados indicaram que a soldagem no modo pulsado apresenta maior aplicabilidade para chapas finas, devido à necessidade um controle preciso sobre a intensidade aplicada. / This work carried out welding experiments of Tantalum and Monel 400 plates with 100 mm thickness. Welds were made with an Nd: YAG laser operating in a pulsed mode and in a fiber laser operating in continuous mode. Then the microstructure of the samples were analyzed by optical microscopy and were performed Vickers microhardness test. Samples that showed better results were subjected to tensile tests and the corrosion tests. After analysis of the results showed that the laser welding offers many benefits over other conventional processes for thin sheets. The welding in pulsed mode presented in superior aspect ratio compared to welding in continuous mode. The welding in continuous mode showed a much higher welding speed to pulsed mode. The results indicated that the welding in pulsed mode shows more applicability for sheet metal, due the need of a precise control of applied intensity.

Increasing mechanical, economic and environmental requirements lead to multi material designs, wherein different classes of materials and manufacturing processes are merged to realize lightweight components with a high level of functional integration. Particularly in automotive industry the use of corresponding technologies will rise in the near future, as they can provide a significant contribution to weight reduction, energy conservation and therefore to the protection of natural resources. Especially the use of continuous fiber reinforced polymers (FRP) with thermoplastic matrices offers advantages for automotive components, due to its good specific characteristics and its suitability for mass production. In conjunction with isotropic materials, such as steel or aluminum, optimized lightweight structures can be produced, whose properties can be easily adapted to the given component requirements. The present paper deals with the development of innovative hybrid laminates with low residual stresses, made of thin-walled steel sheets and glass fiber reinforced thermoplastic (GFRP) prepregs layers. Thereby the interlaminar shear strength (ILSS) was increased by an optimization of the FRP/metal-interfaces, carried out by examining the influence of several pre-operations like sanding, cleaning with organic solvents and applying primer systems. Based on these findings optimized compound samples were prepared and tested under realistic Cathodic dip paint conditions to determine the influence on the ILSS.