Wong Chak-fu. / "September 2004." / Thesis (Ph.D.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (p. 451-475). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese.

In the first part, an efficient and reliable a posteriori error estimate is derived for solving three-dimensional static Maxwell's equations based on the lowest order edge elements of the first family. We propose an adaptive finite element method and establish convergence of the adaptive scheme in energy norm under a restriction on the initial mesh size. Any prescribed error tolerance is thus achieved in a finite number of steps. For discretization based on the lowest order edge elements of the second family, a similar adaptive method is designed which guarantees convergence without any initial mesh size restriction. The proofs rely mainly on error and oscillation reduction estimates as well as the Galerkin orthogonality of the edge element approximation. For time-dependent Maxwell's equations, we deduce an efficient and reliable a posteriori error estimate, upon which an adaptive finite element method is built. / In this thesis, we will address three typical problems with discontinuous coefficients in a general Lipschitz polyhedral domain, which are often encountered in numerical simulation of electromagnetism. / The second part deals with a saddle point problem arising from Maxwell's equations. We present an adaptive finite element method on the basis of the lowest order edge elements of the first family and prove its convergence. The main ingredients of the proof are a novel quasi-orthogonality, which replaces the usual Pythagoras relation, which fails in this case, all error reduction depending on an efficient and reliable a posteriori error estimate and an oscillation reduction. We show that this adaptive scheme is a contraction for the sum of some energy error plus the oscillation. Likewise, the above result is generalized to the discretization by the lowest order edge elements of the second family. / We introduce in the third part an adaptive finite element method for solving the eigenvalue problem of the Maxwell system based on an inverse iterative method. By modifying the exact inverse iteration algorithm involving an inner saddle point solver, we construct an adaptive inverse iteration finite element algorithm, which consists of an inexact inner adaptive procedure for a discrete mixed formulation in place of the original saddle point problem. An efficient and reliable a posteriori error estimate is obtained and the convergence of the inner adaptive method is proved. In addition, the important convergence property of the algorithm is studied, which ensures the errors between true solutions (eigenfunction and eigenvalue) and iterative ones to fall below any given tolerance within a finite number of iterations. / Xu, Yifeng. / "June 2007." / Adviser: Jun Zou. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 166-175). / 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. / Abstracts in English and Chinese. / School code: 1307.

A finite element (FE) based level set method is proposed for structural topology optimization problems in this thesis. The level set method has become a popular tool for structural topology optimization in recent years because of its ability to describe smooth structure boundaries and handle topological changes. There are commonly two stages in the optimization process: the stress analysis stage and the boundary evolution stage. The first stage is usually performed with the finite element method (FEM) while the second is often realized by solving the level set equation with the finite difference method (FDM). The first motivation for developing the proposed method is the desire to unify the techniques of both stages within a uniform framework. In addition, there are many problems involving irregular design domains in practice, the FEM is more powerful than the FDM in dealing with these problems. This is the second motivation for this study. / Numerical examples are involved in this thesis to illustrate the reliability of the proposed method. Problems on both regular and irregular design domains are considered and different meshes are tested and compared. / Solving the level set equation with the standard Galerkin FEM might produce unstable results because of the hyperbolic characteristic of this equation. Therefore, the streamline diffusion finite element method (SDFEM), a stabilized method, is employed to solve the level set equation. In addition to the advantage of simplicity, this method generates a system of equations with a constant, symmetric, and positive defined coefficient matrix. Furthermore, this matrix can be diagonalized by virtue of the lumping technique in structural dynamics. This makes the cost in solving and storing quite low. It is more important that the lumped coefficient matrix may help to improve the stability under some circumstance. / The accuracy of the finite element based level set method (FELSM) is compared with that of the finite difference based level set method (FDLSM). The FELSM is a first-order accurate algorithm but we prove that its accuracy is enough for structural optimization problems considered in this study. Even higher-order accurate FDLSM schemes are used, the numerical results are still the same as those obtained by FELSM. It is also shown that if the Courant-Friedreichs-Lewy (CFL) number is large, the FELSM is more robust and accurate than FDLSM. / The reinitialization equation is also solved with the SDFEM and an extra diffusion term is added to improve the stability near the boundary. We propose a criterion to select the factor of the diffusion term. Due to numerical errors and the diffusion term, boundary will drift during the process of reinitialization. To constrain the boundary from moving, a Dirichlet boundary condition is enforced. Within the framework of FEM, this enforcement can be conveniently preformed with the Lagrangian multiplier method or the penalty method. / Velocity extension is discussed in this thesis. A natural extension method and a partial differential equation (PDE)-based extension method are introduced. Some related topics, such as the "ersatz" material approach and the recovery of stresses, are discussed as well. / Xing, Xianghua. / Adviser: Michael Yu Wang. / Source: Dissertation Abstracts International, Volume: 71-01, Section: B, page: 0628. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 102-113). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese.

by Chong Man Yuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 125-128). / Dedication / Acknowledgements / List of Figure / List of Table / List of Appendix / Chapter 1. --- Introduction / Chapter 1.1 --- Background / Chapter 1.2 --- Ultra-Wide Band Antenna / Chapter 1.3 --- Finite Element Method (FEM) / Chapter 1.3.1 --- Domain Discretization / Chapter 1.3.2 --- Formulation of Variational Method / Chapter 2 --- Theory / Chapter 2.1 --- Variational principles for electromagnetics / Chapter 2.1.1 --- Construction of Functional / Chapter 2.2 --- Artificial Boundary / Chapter 2.2.1 --- Absorbing Boundary Conditions / Chapter 2.2.2 --- Perfectly Matched Layer (PML) / Chapter 2.3 --- Edge Basis Function / Chapter 2.4 --- Slotline Analysis / Chapter 3 --- Implementation of FEM / Chapter 3.1 --- Formulation of Element matrix / Chapter 3.2 --- Mesh Generation / Chapter 3.3 --- Assembly / Chapter 3.4 --- Incorporation of Boundary Conditions / Chapter 3.5 --- Code Implementation / Chapter 4 --- Finite Element Simulations / Chapter 4.1 --- Slotline / Chapter 4.2 --- Artificial Boundary of the domain / Chapter 4.3 --- Slotline Taper Junction / Chapter 4.4 --- Slotline Bowtie Junction / Chapter 5 --- Conclusion / Appendix A1 / Appendix A2 / Appendix A3 / Bibliography

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A ideia de realizar este trabalho surgiu durante do curso de pós-graduação, ministrado pelo Prof. M. Drigas, \"Tópicos especiais sobre máquinas elétricas\", realizado no 2º semestre de 1980 na EPUSP, onde foi observada a necessidade do conhecimento das distribuições de campos magnéticos em dispositivos eletromecânicos com o objetivo de se prever seu desempenho na fase de projeto. Nesta época, já havia sido apresentada a tese do Prof. Janiszewski, o primeiro trabalho, de nosso conhecimento realizado no Brasil nesta área, onde foi desenvolvida a técnica de resolução de problemas de Campos Magnéticos em Regime Estacionário, que, evidentemente, não pode ser aplicada na resolução de problemas onde a variável tempo está envolvida; baseado neste tese, em 1982 o Prof. Luiz Lebensztajn, reproduziu o trabalho do Dr. Janiszewski o qual foi aplicado para verificar a consistência dos resultados práticos na tese de Livre Docência do Prof.. Dr. Aurio Gilberto Falcone. As formulações mais frequentes do Método dos Elementos Finitos (MEF), publicada nos periódicos internacionais, são baseadas no Cálculo Variacional, onde o sistema de equações algébricas não linear resultante, é derivado a partir da obtenção do extremo de uma funcional que em algumas situações não pode ser obtida, limitando assim sua aplicação. Em decorrência deste fato, o primeiro objetivo deste trabalho foi organizar os procedimentos para obtenção do sistema de equações de MEF aplicado à resolução de problemas de campo descritos por equações diferenciais não lineares, sem a necessidade. Algumas contribuições interessantes são encontradas no Capítulo II, referente à formulação do MEF para problemas de campo descrito por operadores diferenciais não auto-adjuntos.No Capítulo III são apresentadas as técnicas de montagem das matrizes, bem como aquelas de introdução das condições de contorno, originárias deste método, que muito embora sejam técnicas de aplicação corriqueiras, ajudarão em muito o pesquisador iniciante nesta área, sem a necessidade de recorrer a outro texto. No Capítulo VI são apresentadas as formulações necessárias para a solução de problemas de campos eletromagnéticos estáticos, para elementos de quatro lados retos (e curvos) assim como a técnica utilizada na obtenção da relutividade em meios não lineares. No Capítulo V são tratados os problemas de campo, onde a variável tempo está envolvida, permitindo assim a resolução de uma série enorme de problemas referentes aos campos de natureza eletromagnética, tais como os fenômenos transitórios e o Regime Permanente Senoidal. Os aspectos computacionais ligados ao trabalho estão expostos no Capítulo VI, onde são apresentadas as rotinas de resolução do sistema de equações resultante adaptadas às particularidades do problema, e as rotinas de integração numérica de problemas descrito por equações diferenciais dependentes do tempo de primeira e segunda ordem. Algumas técnicas apresentadas nestes Capítulos, são aplicadas espe3cificamente para a obtenção da distribuição de campo magnético no Capitulo VII deste trabalho, com o objetivo de analisar o desempenho de um transformador em regime transitório, onde é confirmada a consistência do método. / The idea of making this work came during a graduation course, \" Special topics on electric machines\", lectured by Prof. Dr. M. Drigas during the 2nd semester of 1980 at EPUSP, when the need of knowing the distribution of magnetic fields in electromechanics devices was notices, in order to foresse its performance during design. At that time, the first work about this subject realized made in Brazil was presented in prof. Janiszewski\'s thesis, where a technique was developed to solve Steady-State Magnetic Fields. However, it is clear that when the time variable is considered, this technique cannot be applied. The usual formulations of the Finite Element Method, published in international journals, was based on Variational Calculations, where the resulting non-linear algebraic equations system is derived from the extreme of a functional, which sometimes cannot be obtained, limiting in this way its application. Consequently, the first aim of this work is to organize procedures to obtain the Finite Method equations system, in order solve non-linear differential equations of fields, without the need of a previous functional for the problem. In Chapter II, one will find some interesting contributions referred to the Finite Element Method formulation, in the description of field problems by the use of non self-adjacent differentials operations.Matrix building techniques are presented in Chapter III, as well as the introduction of boundary conditions in this method. In spite of being an ordinary technique, it will help the beginners a lot, eliminating the need of other sources. Chapter IV presents the necessary formulations, which solve static electromagnetic fields for elements of four square (and curved) sides, and the technique used in the determination of non-linear media reluctivity. In Chapter V, the time variable of electromagnetic fields is treated, making possible the solution of problems of this nature, such as transient phenomena and sinusoidal steady-state. Computer aspects of the work are shown in Chapter VI, presenting resolution routines of the equation system fitted to the problem, and numeric integration routines described by first and second order differential equations, which depend on the time. Some techniques showed in those previous Chapters are specifically used in Chapter VII to obtain the magnetic field distribution, which analyses transformer performance during transients. The coherence of the method is also confirmed.

Composite materials are becoming popular in almost all industries. Carbon-fiber and glass-fiber composites are used in aircraft, sports equipment, boats, prosthetics, and wind turbine blades. In all these applications, the composites are subjected to different loads. Loads can take the form of impact or cyclic/fatigue loading, both of which decrease the strength of composites as micro-cracks grow through the composite. Composite laminates are made up of fiber plies (thin layers of fiber) and the fibers are surrounded by a resin like epoxy. It is common for laminates to fail because of delamination growth (plies peeling apart). Small delaminations do not fail a composite, but as delaminations grow, the composite weakens and eventually fails. Composites behave differently than metals do, and failure analysis is more complicated because of the various directions of fibers. Numerical methods (specifically Finite Element Analysis) exist for predicting when failure will occur, but improvements are needed to make these numerical methods more accurate and efficient. The method created, for this thesis, is computationally efficient because it doesn’t require the analyst or computer to adjust the simulation based on where the delamination is (or what kind of shape it is). Energy values are extracted directly from the delamination front and not averaged from nearby locations.

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This thesis provides a contribution towards a general procedure for solving robustly and efficiently limit and shakedown analyses of engineering structures within the static approach which has been chosen for its simplicity of implementation. Throughout the thesis, attempts at improving the robustness and efficiency of the computations are presented. Beginning with efforts to prevent volumetric locking, which is a severe shortcoming of traditional low order h-type displacement elements, the investigation proposes the use of the high order p-version of the finite element method. It is shown theoretically and confirmed numerically that this p-method is not only robust in preventing locking, but also provides very accurate results. However, the use of uniformly distributed high order p-elements may be computationally demanding when the size of the problem becomes large. This difficulty is tackled by two main approaches: use of a p-adaptive procedure at the elastic computation stage and use of approximate piecewise linear yield functions. The p-adaptive scheme produces a non-uniform p-distribution and helps to greatly reduce the number of degrees of freedom needed while still guaranteeing the required level of accuracy. The overall gain is that the sizes of the models are reduced significantly and hence also the computational effort. The adoption of piecewise linear yield surfaces helps to further increase the efficiency at the expense of possibly slightly less accurate, but still very acceptable, results. State-of-the-art linear programming solvers based on the very efficient interior point methodology are used. Significant gains in efficiency are achieved. A heuristic, semi-adaptive scheme to piecewise linearize the yield surfaces is then developed to further reduce the size of the underlying optimization problems. The results show additional gains in efficiency. Finally, major conclusions are summarized, and various aspects suitable for further research are highlighted.

This PhD thesis presents research aims to improving the dynamic modelling of coupled plate structures across a wide frequency range by using analytical, statistical and experimental methods. The analytical waveguide method is used to model the flexural displacement of coupled plate structures which are simply supported along two parallel edges. A method of quickly predicting the average energy level in a plate from details of the waveguide model is described, and used for comparison with SEA models. The Poynting and Impedance methods of predicting the energy flow in coupled plate structures are investigated. Transmission coefficients for coupled plate structures are evaluated using the analytical waveguide method for both semi-infinite and finite coupled plate structures. Finite transmission coefficients have traditionally been more difficult to evaluate due to the presence of a reverberant field, but in this work a novel method of separating the reverberant field using a scattering matrix method is presented. The transmission coefficients for semi-infinite and finite structures are then compared for L-shaped plates. A modal transmission coefficient is also defined and for the cases considered, and is used to develop an alternative method of deriving the transmission coefficient in a finite structure. Frequency averaged transmission coefficients are also considered, and the transmission coefficients derived for finite and semi-infinite structures are found to be very similar after frequency averaging. Statistical Energy Analysis models of coupled plates are evaluated using transmission coefficients derived from waveguide models. The results of the SEA models are compared to those predicted by the analytical waveguide method. A modal transmission coefficient based SEA model is also investigated. In an attempt to validate the numerical work presented in this thesis, experiments have been conducted. Using a wave extraction technique, both the wave amplitudes and plate properties have been evaluated from experimental data, and are subsequently used to experimentally measure the transmission coefficient for two plates coupled at different angles.