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Kung Kin Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 60-63). / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- 2-D Thermoelastic System --- p.5 / Chapter 2.1 --- Introduction to the thermo-elastic system --- p.5 / Chapter 2.2 --- Existing theoretical results on the system --- p.6 / Chapter 2.2.1 --- Well-posedness and energy decay phenomena of the thermoelastic system --- p.7 / Chapter 2.2.2 --- Reduction of the coupled thermoelastic sys- tem to a single heat equation --- p.8 / Chapter 2.3 --- Some existing numerical methods --- p.12 / Chapter 2.3.1 --- Explicit scheme --- p.12 / Chapter 2.3.2 --- Implicit scheme --- p.16 / Chapter 2.4 --- The formulation and transformation --- p.17 / Chapter 2.5 --- Finite element discretizations --- p.19 / Chapter 2.6 --- Existence of the discrete solution --- p.20 / Chapter 2.7 --- Numerical results --- p.23 / Chapter 2.7.1 --- Introduction to the FEM software --- p.23 / Chapter 2.7.2 --- Numerical experiments --- p.28 / Chapter 3 --- 3-D Elliptic Interface Problem --- p.35 / Chapter 3.1 --- Introduction to 2-D elliptic problems --- p.35 / Chapter 3.2 --- Finite element discretization --- p.36 / Chapter 3.3 --- Convergence of the numerical methods --- p.38 / Chapter 3.4 --- Numerical results --- p.43 / Chapter 3.4.1 --- Introduction --- p.43 / Chapter 3.4.2 --- Introduction to the FEM software --- p.45 / Chapter 3.4.3 --- Numerical experiments --- p.47 / Chapter 4 --- 2-D Parabolic Interface Problem --- p.53 / Chapter 4.1 --- Introduction to the 2-D parabolic problem --- p.53 / Chapter 4.2 --- Finite element discretization --- p.54 / Chapter 4.3 --- Existence and convergence analysis --- p.55 / Chapter 4.4 --- Numerical results --- p.57 / Chapter 4.4.1 --- Introduction --- p.57 / Chapter 4.4.2 --- Numerical experiments --- p.58 / Bibilography

The main portion of my thesis focuses on a 2-dimensional second order heat transmission problem in domains with pre-fractal interfaces. My focus is on the numerical approximation of the solutions. Precisely, I€™m concerned to develop a suitable mesh refinement algorithm that could be adapted to our situation, by taking into account the regularity of the solutions and the geometry of irregular pre-fractal interfaces. I obtain an error estimate between the weak solution and the discrete solution, which indicates an optimal rate of convergence as in the classical case when the solution has H^2-regularity. In addition, numerical simulations are also included, which demonstrates the features of our heat transmission model. Another portion of my thesis focuses on the asymptotic analysis of singular boundary value problems with highly conductive layers of pre-fractal type. My models illustrate the problems of a lower- dimensional highly conductive material intruding into a higher- dimensional material with lower conductivity. I consider a 2D model of Sierpinski pre-fractal layers and 3D models of hierarchical layers. The main results consist in the so-called Mosco-convergence of certain energy functionals, which implies the strong convergence of the solutions and of the spectral resolutions as a byproduct in real applications.

No description available.

No description available.

Thesis (M.Phil.)--University of Hong Kong, 1993. / Also available in print.

A new methodology is introduced where the natural hierarchical character of model descriptions and simulation results are exploited to expedite analysis of problems. The philosophy and the different concepts involved are illustrated by implementing the strategy to solve some practical problems. The end result was a mix of mechanics, well-designed data structures and software interfaces that forms a rapid analysis environment. This can be very advantageous for cases where a sequence of analyses is required because of safety concerns or cost. When designing a structure, it is common to make frequent modifications to the model during the process. In such cases, the ability to use data from different models within the same analysis environment becomes a major advantage. The proposed system's forte is its hierarchical framework that allows models to communicate with each other and share information with one another. This makes it ideal for global local analyses where solutions from a global model are used to derive the boundary conditions for the local model. The system was also used to conduct a micro mechanical analysis on unidirectional composites that have a non-uniform spatial distribution of the fibers. The hierarchical strategy is not tied to any specific methodology and can be adapted to solve problem using different technologies. This allows the strategy to be used across multiple length scales and governing equations.

Three 3D nonlinear finite-element (FE) models are developed to study the behavior of concrete beams and plates with and without externally reinforcement of fibre reinforced polymer (FRP). Ramtekkar’s mixed layer-wise 3 dimensional (3D) 18-node FE model (108 degrees-of-freedom, DOFs) is modified to accommodate the nonlinear concrete and elasto-plastic steel behaviour. Saenz’s stress-strain equation is used for material nonlinearity of concrete. As in any 3D mixed FE analysis, the run time using the model can be computationally expensive. Two additional layer-wise 18-node FE models: Displacement FE model (54 DOF) and transitional FE model (81 DOF) are developed. The displacement FE model is based on purely displacement field, i.e. only displacement components are enforced throughout the thickness of the structures. The transitional FE model has six DOF (three displacement components in the coordinate axis direction and three transverse stress components - where z is the thickness direction) per node in the upper surface and only three DOF (three displacement components in the coordinate axis direction) per node in the bottom surface.The analysis of reinforced concrete (RC) beam strengthened with FRP and composite plate using these models are verified against the experimental results and the results from the commercial software, ANSYS respectively. Several parametric studies are done on composite RC beam and composite plate. / May 2006

Tuned vibration absorbers (TVAs) are spring-mass-damper devices used to mini-mize energy in a vibrating body. TVAs decrease in efficiency when the vibrating body is subjected to variable, broadband, or random excitation. A state-switched absorber (SSA) can be used in these variable, broadband, or random excitation cases to more effectively reduce excitation. An SSA is a mass-spring-damper where one or more of these elements can instantaneously and discretely change. An SSA was designed, built and tested to fit the specifications for TVAs found on ATR 72 and 42 airplane fuselages. A magnetorheological elastomer (MRE), an elastomer with imbedded iron particles, was selected as a variable spring. Flux lines concentrated through all MREs in absorber configurations. MREs containing 35% iron by volume yielded the largest frequency shift. A 35% MRE based absorber had a frequency range of 45-183 Hz, which corresponds to a 360% frequency increase. Transient absorber behavior was observed by recording rise and drop times to step field intensity changes.The 35% MRE absorber yielded a 0.20 second rise time and a 0.03 second drop time. Future work will determine whether a modified input signal can generate an appropriate transient response.