As part of a larger effort to understand the fundamental knowledge of polymer scratch behavior, this dissertation is focused on both experimental study and numerical analysis of scratch deformation of a broad range of polymers, with an emphasis on the mechanical understanding of how the scratch-induced damage is formed. An instrumented progressive load scratch method recommended by ASTM/ISO standards was adopted for the experimental work. The commercial finite element (FE) method package ABAQUS was employed as a numerical simulation tool to describe the stress-strain fields, and it analyzes the deformation mechanisms during the scratch process. A thorough parametric study has been performed to assess the influence of material parameters and surface properties, such as Young's modulus, yield strength, and friction coefficient, on the polymer scratch behavior. Upon investigation of the scratch behaviors of a broad range of polymer materials, various kinds of scratch damage features are identified and correlated with the mechanical characteristics of the polymers. A generalized scratch damage mechanism map for polymers is presented. Correlation between different material types and scratch damage mechanisms is made. It is found that both the material characteristics and the stress state exerted on the scratched surface are responsible for the observed scratch damage mechanisms. The phenomenological deduction of the scratch damage process based on the stick-slip mechanism is established. A more realistic material law for the scratch analysis is also provided. To evaluate the polymer resistance against scratch visibility quantitatively, an entirely new automated on-set scratch visibility determination methodology is developed based on typical visual characteristics of human eyes. Its application on the evaluation of mar and abrasion of polymer is also explored. This new methodology can quantify polymer scratch resistance consistently and reliably regardless of the sample surface characteristics and color.

We study approximation techniques for incompressible flows with heterogeneous properties. Speci cally, we study two types of phenomena. The first is the flow of a viscous incompressible fluid through a rigid porous medium, where the permeability of the medium depends on the pressure. The second is the ow of a viscous incompressible fluid with variable density. The heterogeneity is the permeability and the density, respectively. For the first problem, we propose a finite element discretization and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence is exponential, we propose a splitting scheme which involves solving only two linear systems. For the second problem, we introduce a fractional time-stepping scheme which, as opposed to other existing techniques, requires only the solution of a Poisson equation for the determination of the pressure. This simpli cation greatly reduces the computational cost. We prove the stability of first and second order schemes, and provide error estimates for first order schemes. For all the introduced discretization schemes we present numerical experiments, which illustrate their performance on model problems, as well as on realistic ones.

In this thesis, we survey some popular pricing methods of average options. They can be classified into three cateogries include approximation, Monte Carlo, and binomial tree approaches. We examine the accuracy of these methods by two cases, exchange rate and stock price. Numerical testing results show the accuracy of approximation and binomial tree are not stable. For the big-size feature of average option, their outputs are doubtful and damaging in pactice. Despite this, they are still valuable. This is because they own the other advantages. For example, the approximation approach can give us a quick formlas to calculate the Greek, and the binomial tree approach can price the American style options.

A theoretical model and numerical simulation of a direct methanol fuel cell (DMFC) is developed to simulate the reaction mechanisms and the cell voltage under several different designing parameters and operational conditions. The results of a numerical simulation include the distributions of the proton current density, the concentration of methanol, the electrochemical reaction rates, the overpotential losses, and the pressures within proton exchange membrane layer, catalyst layer and diffusion layer. In addition, the influence of aforementioned operational conditions on methanol crossover in a direct methanol fuel cell is also investigated. Finally, the results of the model are compared to the results from the experimental work. The results show that increasing of temperature, pressure and anode catalyst loading can enhance the performance of a direct methanol fuel cell, and the concentration of methanol plays an important role in its performance. The optimal concentration of methanol for a direct methanol fuel cell is about 2M. Methanol crossover can be suppressed by decreasing methanol concentration and increasing thickness of polymer electrolyte membrane (PEM). However, under operating condition of high current density, thick PEM and low methanol concentration will cause large concentration overpotential and ohmic losses, respectively.

With development and advancement of notebook, at the same time it brings its cooling problem, it is very important that use outside surface cooling except inside. The main in study is simulate of electronic cooling in Notebook outside surface, design force convection models and placed them under the Notebook, force convection has immediate effect on the surface and produce heat dissipation. The simulation uses software FLUENT 6.0 to analysis the result of heat dissipation, the models are constructed and described by use turbulent field of three dimensions. The study has two main parameters¡GThe form of force convection models and controlled airflow. The result of numerical analysis use Nusselt number to determine the effect of heat dissipation. According to the result of numerical analysis to increase effect of heat dissipation for the following methods¡G1. Increase airflow across the designed models, 2. Decrease the angle of elevation when using notebook, 3. Airflow enter the designed models by one entrance and leave by the side exports, 4. When airflow pass through the designed models smoothly, 5. Airflow can influence the notebook surface immediately.

In this thesis, a numerical simulation model is applied to investigate the long-term shoreline changes behind detached breakwaters. The model includes three components, namely a wave model, a current model, and a shoreline change model. In the numerical simulations, various combinations of wave conditions and the placement of detached breakwater are chosen to explore the effect of detached breakwaters on the shoreline change. The results of calculation show that with incident wave angles within 0~45, wave height in the range of 0.5~1.5m, or the offshore distance to the detached breakwaters being 60~120m, the larger in any one of these three parameters is, the bigger the erosion distance onshore from the original shoreline and the extent of salient offshore are behind detached breakwaters. When incident angle of the wave increases, shoreline plan form becomes skewed, and the time required to arrive at equilibrium also increases, in addition to the position of the top of salient moves downcoast. Within the wave periods of 7~10 seconds tested, waves with large period are found to show slight decrease of the erosion distance onshore and the extent of salient offshore behind detached breakwaters. The plan form of the salient is not affected by wave period. However, the larger the wave period is, the sooner the long-tern shoreline will result. Moreover, for a detached breakwater constructed in the range of offshore distances within 1.0¡ÕS/B¡Õ2.0, variable offshore distances do not produce much difference in the erosion distance onshore and the extent of salient offshore behind detached breakwaters, and salient only will form. In the case of the S/B =< 0.8, a tombolo will result. Finally, the results of shoreline plan form from the numerical modeling are verified by the empirical parabolic bay shape equation of Hsu and Evans (1989), a small-scale hydraulic model, and two numerical models based on GENESIS and LITPACK. Overall, the result are in good agreement with these four different approaches, and therefore, the present model is suitable for practical engineering applications.

The positions of high stress concentration in a bicycle frame structure made in composite materials and a way to strengthen them were investigated via SolidWorks and ANSYS, 3D picture plotting software, and numerical simulation software, respectively. The capability of productivity will be improved indirectly due to the shortening of the time in the process of customers¡¦ order, research, development and mass production. In experiment, prepreg tape (TOHO UT500 carbon fiber/AD. Group matrix) which were produced by AD. Group were made into laminates by hot-pressing machine. The material constants of the laminate and the stress-strain diagram were obtained according to the stander of ASTM D3039. The received material constants are E11 =151.55 GPa and E22 = 7.654 GPa, respectively. In simulation, the experimental data E11 and E22 were used in the numerical analysis, and obtained the stress and deformation fields of the bicycle frame structure and the front fork were plotted based on the standards provided by AD. Group. Reinforcements were made according to the positions of stress concentration in the diagrams. The results of improvements of the front fork after reinforcement include¡G the deformation of normal rigidity was improved to 9.45mm from 12.89mm, and the lateral deformation was significantly improved to 0.97mm from 13mm. Other improvements of the frame structure after reinforcement contain the deformation: dual-side rigidity was improved to 6.6mm from 11.7mm, and the deformation of single-side rigidity was improved to 12.5mm. The rigidity of the head lug was 0.46mm and there is no need to reinforce it because it was meets requirements. Keywords: Numerical analysis, bicycle frame, prepreg, stress concentration.

The present study aims to explore flow behavior in the mold during centrifugal casting process by numerical simulations. The theoretical model comprises two groups of steady conservation equations of mass and momentum and the governing equations are solved numerically with k-£` turbulence model and iterative SIMPLE(Semi-Implicit for Pressure-Linked Equations) algorithm to determine the flow property. The numerical results indicate that the melt liquids of titanium compound metal flow near the walls in the high rotation rate. With the high rotation rate, the outflow velocity is rapid. The products depend on the flow of the melt liquids. The flow is rapid, the filled process is quick, and the temperature is uniform. But if the flow is slow, the temperature is not uniform in the filled process. Therefore, the products may result in faults. When the rotation rate is up to 50 rpm, the melt liquids flow near the walls with the affect of centrifugal force. The velocity is larger than the velocity with zero rotation rate . Thus the flow with rotation rate can help to fill quickly, and reduce the temperature loss.

The purpose of thesis is aimed to predict the residual stiffness and residual strength of a composite laminate by adopting the method of cumulative damage theories numerically. In association with the experimental work the numerical result can be verified in comparison. The fatigue data in composites are well known more scattered than those in conventional metals, because the material properties are complicated due to nonhomogeneity and anisotropy. Until now there exists very few unified theories to model composite fatigue properties. Most of them are semi-empirical expressions fitted by selecting material characteristic values. This work tries to make a precise prediction with hopefully saving time, money and manpower in future experiments. On the aspect of numerical analysis, we employ finite element method incorporated with the software of ANSYS to generate 3-D finite element model and obtain the ultimate stress of cross-ply [0/90]4s and quasi-isotropic [0/+45/90/-45] laminates by Tsai-Wu failure criterion. It is assumed that the damage due to fatigue cycles is equal to the damage of stiffness and strength, in association with Miner¡¦s Rule and cumulative damage theories we obtain the residual stiffness and strength. The numerical result in comparison with the available empirical data is found acceptably well. Finally, this study can be concluded as follows. The error of ultimate stress is 3.84 % in cross-ply[0/90]4s , and 8.38 % in quasi-isotropic[0/45/90/-45]2s laminates. The error of ultimate stress in centrally notched cross-ply[0/90]4s is 0.4 %, and 22.4 % in centrally notched quasi-isotropic laminates. As the fatigue cycles increasing, the residual stiffness and residual strength of the laminates are all decreasing. The decreasing rate is very slight at first and intermediate stages, whilst it is much faster near the last stage. It is found that the prediction of residual strength is more accurate in the case of maximum stress of 60% ultimate stress than that of 80% ultimate stress.

Numerical dispersion resulting from using the second-order central-difference operation to approximate the differential operation is the main error source of the FDTD method. The effect of numerical dispersion can be minimized if the spatial grid size is small than£f/10. It is difficultly to analyze the modeling of electrically large structures since a huge amount of computer memory will be needed if using a very fine grid to discretize the structure. Using higher-order FDTD is the effective alternative to reduce the effect of numerical dispersion. In this paper will discuss the handling of the discontinuous PEC boundary condition in four-order FDTD and its applications to antenna pattern analysis. Using the fourth-order FDTD can enlarge the spatial grid size and reduce the requirement of computer¡¦s memory. The far field range of small size antenna operating at higher frequency is shorter enough to directly derive the far field pattern by enlarging the spatial size of fourth-order FDTD. It will compare the far field pattern derived by four-order FDTD with near-to-far field transformation and analyze their characteristic individually.