This thesis presents numerical and experimental investigations into Electrochemical Machining (ECM). The aim is to develop a computer program to predict the shape of a workpiece machined by the ECM process. The program is able to simulate various applications of EC machining which are drilling, milling, turning and shaped tube electrochemical drilling (STED). The program has been developed in a MATLAB environment. In this present work, EC-drilling, EC-milling and EC-turning are analysed as three-dimensional problems whereas STED is simulated in two-dimensions. Experiments have been carried out to verify the accuracy of the predicted results in the cases of EC-milling and EC-turning. The ECM modeller is based on the boundary element method (BEM) and uses Laplace's equation to determine the current distribution at nodes on the workpiece surface. In 3D, the surfaces of the tool and the workpiece are discretised into continuous linear triangular element types whereas in 2D, the boundaries of the tool and workpiece are discretised into linear elements. The ECM modeller is completely self-contained, i.e. it does not rely on any other commercial package. The program contains modules to automatically discretize the surfaces/boundaries of the tool and workpiece. Since the simulation of the ECM process is a temporal problem, several time steps are required to obtain the final workpiece shape. At the end of each time step, the shape of the workpiece is calculated using Faraday's laws. However, the workpiece's shape changes with progressing time steps causing the elements to become stretched and distorted. Mesh refinement techniques are built in the ECM modeller, and these subdivide the mesh automatically when necessary.The effect of time step on the predicted 3D shape of a hole in EC-drilling is investigated. The effect of discontinuity in the slope between neighbouring elements is also studied. Results obtained from the ECM modeller are compared with 2D analytical results to verify the accuracy that can be obtained from the ECM modeller. Milling features ranging from a simple slot to a pocket with a complex protrusion were machined in order to determine the feasibility of the EC milling process. These features were machined on a 3-axes CNC machine converted to permit EC milling. The effect of tool geometry, tool feed rate, applied voltage and step-over distances on the dimensions, shape and surface finish of the machined features were investigated. A pocket with a human shape protrusion was machined using two different types of tool paths, namely contour-parallel and zig-zag. Both types resulted in the base surface of the pocket being concave and the final dimensions of the pockets are compared with the design drawing to determine the effect of tool path type on the accuracy of machining. The ECM modeller was used to simulate the machining of a thin-walled turned component. The machining parameters, i.e. initial gap, rotational speed, and applied voltage, were specified by the collaborating company. Since only a small amount of material had to be removed from the thin-walled component, the tool was held stationary i.e. a feed in the radial or longitudinal direction was not required. By taking advantage of the axi-symmetric nature of a turned component, only a sector of the component was analysed thereby reducing the computing time considerably. The accuracy of the modeller was verified by comparing the predicted time to machine the thin-walled component with the actual machining time. The initial investigations in STED were both experimental and numerical in nature and they studied the effect of applied voltage, tool feed rate and electrolyte pressure on the dimensions of the holes. Later investigations were numerical and an iterative methodology has been developed to calculate a set of feed rates which could machine a specified turbulator shape.

No description available.

A numerical method has been developed for computing the steady state flow about arbitrary shaped three dimensional bodies on or below the free surface using a Boundary Integral Element Method ( Panel Method). The method uses a singularity distribution over the body surface and the free surface. The method can solve for the potential distribution as well as the source density distribution. In this study a constant source distribution is assumed on each panel. The free surface boundary condition is linearized about the uniform undisturbed flow (Kelvin Free Surface condition). Upstream waves are prevented by the use of an one-sided upstream 4-point finite difference operator for the free surface condition. Wave elevations are computed using the linearized free surface condition. In this study two different bodies were considered: a submerged spheroid and a sphere. The wave resistance was computed for different Froude numbers and compares well with existing results. The study has also analyzed the effect of the number of panels on the body surface, the length of the free surface paneling behind the body and the aspect ratio of the free surface panels. / Master of Science

Spacecraft structures are subject to a series of load environments during their service life, with the most severe of these occurring during the spacecraft's launch and ascension through the atmosphere. In particular, acoustic loads imposed on stowed satellites within the launch vehicle fairing can result in high mechanical loads on sensitive spacecraft hardware. These acoustic loads have the potential to damage important components and as such it is necessary to accurately characterize and predict the acoustic launch environment for a given mission. This research investigates the Sound Pressure Level (SPL) that can be measured in and around spacecraft cavities resulting from a known excitation and the resultant structural responses. Linear finite element analysis (FEA) is coupled with the Boundary Element method (BEM) to analyze spacecraft acoustic environments and corresponding structural responses at low frequencies on the order of the structural modes. Analytical capability for predicting acoustic environments inside the launch vehicle has improved significantly in recent years; however, while it is easy to perform an analysis and obtain results, the modeling effort can become unnecessarily complicated and analytical data can be hard to interpret. This work seeks to alleviate unnecessary complexity in the low-frequency regime of acoustic modeling by examining the fundamentals of coupled BEM-FEM analysis and applying simplification to a spacecraft model where possible to achieve results verified against direct field acoustic testing (DFAT) methods. / Master of Science

No description available.

<p>In this thesis we study hybrid numerical methods to be usedin computational electromagnetics. We restrict the methods tospectral domain and scattering problems. The hybrids consist ofcombinations of Boundary Element Methods and Geometrical Theoryof Diffraction.</p><p>In the thesis three hybrid methods will be presented. Onemethod has been developped from a theoretical idea to anindustrial code. The two other methods will be presented mainlyfrom a theoretical perspective. We will also give shortintroductions to the Boundary Element Method and theGeometrical Theory of Diffraction from a theoretical andimplementational point of view.</p><p><b>Keywords:</b>Maxwell’s equations, Geometrical Theoryof Diffraction, Boundary Element Method, Hybrid methods,Electromagnetic Scattering</p>

Pitting corrosion is a form of highly localized corrosion that can lead to crack and failure of a structure. Study on pitting corrosion is necessary in order to predict and prevent the risk of failure of structure susceptible to corrosion. In this thesis, a combination of Cellular Automata (CA) and Boundary Element Method (BEM) was developed to simulate pitting corrosion growth under certain environment. It is assumed that pitting corrosion can be simplified to electrochemical corrosion cell. The distribution of potential around this corrosion cell can then be simulated by BEM. This distribution potential represents cathodic and anodic reactions around the corrosion cell. A CA model was developed that uses transition rules reflecting mechanism of pitting corrosion. The CA model has two types of cell states, one reflecting BEM simulation results and the other reflecting the status of corrosion cell (anode, cathode, and passive metal’s surface). For every CA iteration, the CA decides the state of the corrosion cells (the location and size of anode, cathode) while BEM simulate the level of electrochemical activity at discrete location on the surface (represented by potential distribution). In order to demonstrate the methodology, a simple case of rectangular corrosion cell with varied dimensions and under different polarization functions is considered. Results show certain shapes tend to grow at certain type environment and these pits are comparable to commonly observed pit shapes. In addition, stress analysis was carried out to investigate the severity of corrosion pits of varying shapes and sizes. Results show that certain pits induced highly varying stress concentration as it grows over time, while others have more steady increase of stress concentration.

Neste trabalho utiliza-se a formulação direta do Método dos Elementos de Contorno aplicada ao problema de flexão de placas com vinculação interna. Através da utilização da teoria baseada nas hipóteses de Reissner é possível atender em cada ponto, a três condições físicas de contorno. Admite-se a aplicação de cargas transversais distribuídas e concentradas, além de momentos distribuídos em linha. Os elementos de contorno apresentam geometria linear com aproximação quadrática para as variáveis de contorno. As equações integrais dos deslocamentos são escritas para pontos de colocação dispostos fora do domínio, evitando-se assim problemas de singularidades. O sistema de equações algébricas originado da análise de placas via MEC é modificado para incorporar o enrijecimento produzido pela vinculação interna. Primeiramente é analisado o enrijecimento produzido por apoios internos pontuais ou distribuídos em áreas pequenas e, em seguida, é estudada a associação da placa com uma estrutura qualquer, formada por barras. O enrijecimento produzido por esta estrutura é obtido utilizando-se o Método dos Elementos Finitos. Finalmente, são apresentados alguns exemplos simples que mostram a boa precisão da técnica utilizada. / The direct formulation of the Boundary Element Method is applied to the analysis of internally restrained plates in bending. By employing Reissner\'s theory, the three boundary conditions are satisfied at each point. Loading conditions include concentrated or uniformly distributed loads as well as linearly distributed moments. The boundary elements are geometrically linear with quadratic approximation for the boundary variables. The displacement integral equations are written for collocation points outside the domain thus avoiding any singularity problem. The resulting system of algebraic equations is modified to include the stiffening effects. Plates with internal point restraints and restrained over small areas are analyzed as well as plates connected to others structures made up of bars. In this last case, the stiffening effect is calculated through the Finite Element Method. The results obtained in simple problems indicate the accuracy of the procedure.

Based on the expression specifying the deformation of a multi-component object, a component-based condensation method is developed. This further reduces the size of the matrix to be inverted from the total number of unknown displacements to the number of unknown displacements with changing boundary condition. To speed up the construction of matrices, a maximal matrix technology is proposed. By categorizing the changes in boundary conditions, three fast update strategies on matrix inverse are introduced. Based on the maximal matrix technology and the matrix inverse update strategy, eight easily-formed characteristic matrices are defined to enhance the computation speed further. / In this thesis, an algorithm is developed for simulating the deformation of multiple objects with different material properties using the boundary element method. By tessellating the surface of a geometric model into elements, classifying all the element nodes into different groups with different attributes, and partitioning the stiffness matrix into several sub-matrices according to these attributes, a compact expression about the unknown variables is deduced. In this expression, the dimension of the system matrix has been effectively reduced compared with the traditional method. This expression shows that the deformation of a multi-component object can be simulated in a way similar to that of a single-component object. / Research on the real-time deformation of elastic models has captured wide attention and gained considerable achievement in the past two decades. Most related works focus on developing efficient ways to simulate the behavior of a single-component elastic object. However, objects are usually made up of multiple components with different material properties in practice. It is thus essential to develop efficient techniques for modeling objects which are composed of more than one material. / To make the proposed accelerated algorithm more applicable, a method for simulating the deformation of multi-component models with non-matching interfaces is developed. By applying the interpolation and extrapolation methods, the displacement data can be transferred between non-conforming interfaces. With the application of the energy conservation principle, a relationship between the internal forces on different surfaces can also be established. Together with the force equilibrium conditions and displacement compatibility conditions over the common faces of objects, the deformation of models composed of multi-material components with non-matching interfaces can be simulated. During the application of the linear interpolation method, when the mesh densities on the interfaces of the neighboring components are not the same, unexpected phenomena arise in the simulation process because of this disparity. A traction super-imposition method is adopted to enforce the force constraints on the interface. Experiments showed that this approach produces the correct results. / Zhou, Aifang. / "August 2007." / Adviser: Keh Chuen Hui. / Source: Dissertation Abstracts International, Volume: 69-02, Section: B, page: 1299. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 144-155). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract in English and Chinese. / School code: 1307.

In bubble dynamics, an underwater bubble may evolve from being singly-connected to being toroidal. Furthermore, two or more individual bubbles may merge to form a single large bubble. These dynamics involve significant topological changes such as merging and breaking, which may not be handled well by front-tracking boundary element methods. In the level set method, topological changes are handled naturally through a higher-dimensional level set function. This makes it an attractive method for bubble simulation. In this paper, we present a method that combines the level set method and the boundary element method for the simulation of bubble dynamics. We propose a formulation for the update of a potential function in the level set context. This potential function is non-physical off the bubble surface but consistent with the physics on the bubble surface. We consider only axisymmetric cavitation bubbles in this paper. Included in the paper are some preliminary results and findings. / Singapore-MIT Alliance (SMA)