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.

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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

In this thesis, mixed finite element models of beams and plates bending are developed to include other variables (i.e., the membrane forces and shear forces) in addition to the bending moments and vertical deflection, and to see the effect of it on the nonlinear analysis. Models were developed based on the weighted residual method. The effect of inclusion of additional variables is compared with other mixed models to show the advantage of the one type of model over other models. For beam problems the Euler-Bernoulli beam theory and the Timoshenko beam theory are used. And for the plate problems the classical plate theory and the first-order shear deformation plate theory are used. Each newly developed model is examined and compared with other models to verify its performance under various boundary conditions. In the linear convergence study, solutions are compared with analytical solutions available and solutions of existing models. For non-linear equation solving direct method and Newton-Raphson method are used to find non-liner solutions. Then, converged solutions are compared with available solutions of the displacement models. Noticeable improvement in accuracy of force-like variables (i.e., shear resultant, membrane resultant and bending moments) at the boundary of elements can be achieved by using present mixed models in both linear and nonlinear analysis. Post processed data of newly developed mixed models show better accuracy than existing displacement based and mixed models in both of vertical displacement and force-like variables. Also present beam and plate finite element models allow use of relatively lower level of interpolation function without causing severe locking problems.

Free vibration of beam with moderate thickness is analyzed in the present study. Plane strain finite element is employed, which is based on 2-D elasticity. The conventional displacement-type variational principle is combined with Reissner¡¦s principle and a mixed-type variational formulation is derived. With such formulation, stresses, as well as displacements, are the primacy variables and both boundary conditions can be imposed exactly and simultaneously. Beams with various aspect ratios and boundary conditions are analyzed. Vibration frequencies and modes are obtained and compared to those by Euler¡¦s beam theory, Timoshenko beam theory, higher-order theory and displacement-type plane strain finite element method to see the effects of 2-D elasticity beam analysis compared to traditional 1-D theories, and the satisfying of stress boundary conditions, in addition to the displacement ones.

This paper uses a finite element code¡©DEFORM 3D¡ªto simulate the plastic deformation behavior in extrusion processes of heat sink for CPU. The relationships between the loading, strain, velocity distribution, and formability of the extruded product as well as the extrusion conditions are discussed. Furthermore, this research will propose a criterion for the die design of heat sink and to prove the validity of this proposed criterion by the experiments.

In the present study, the buckling behavior of beams is analyzed by a plane strain finite element. The displacement-type finite element formulation based on two-dimensional elasticity of a buckling beam leads to an eigenvalue problem and is transformed again into another type of eigenvalue problem to eliminate iterations and possible difficulty during iterations and to obtain the various critical loads simultaneously. Comparing with conventional beam theories, the present approach needs no approximations or assumptions except that the width-to thickness ratio should be large enough for the beam to be considered as a plane strain case. Theoretically the present method should be more accurate than conventional beam theories and attractive than iterative method if the same accuracy is obtained, due to the economy in computation of the present method. Buckling strength under different beam geometry, type of loading, and boundary condition by the present approach will be compared with those by iterative method and various beam theories to test its validation and accuracy.