Thesis (Ph. D.)--University of Hong Kong, 2006. / Title proper from title frame. Also available in printed format.

In this thesis, numerical experiments are performed to test the numerical stability of the finite element method for analyzing incompressible materials from boundary displacements. The significance of the study relies on the fact that incompressibility, or density preservation during deformation, is an important property of materials such as rubber and soft tissue.<p>It is well known that the finite element analysis (FEA) of incompressible materials is less straightforward than for materials which are compressible. The FEA of incompressible materials using the usual displacement based finite element method results in an unstable solution for the stress field. Hence, a different formulation called the mixed u-p formulation (u displacement, p pressure) is used for the analysis. The u-p formulation results in a stable solution but only when the forces and/or stress tractions acting on the structure are known. There are, however, certain situations in the real world where the forces or stress tractions acting on the structure are unknown, but the deformation (i.e. displacements) due to the forces can be measured. One example is the stress analysis of soft tissues. High resolution images of initial and deformed states of a tissue can be used to obtain the displacements along the boundary. In such cases, the only inputs to the finite element method are the structural geometry, material properties, and boundary displacements. When finite element analysis of incompressible materials with displacement boundary conditions is performed, even the mixed u-p formulation results in highly unstable calculations of the stress field. Here, a hypothesis for solving this problem is developed and tested. Theories of linear and nonlinear stress analysis are reviewed to demonstrate that it may be possible to determine the von Mises stress uniquely in spite of the numerical instability inherent in the calculations.<p>To validate this concept, four different numerical examples representing different deformation processes are considered using ANSYS®: a plate in simple shear; expansion of a thick-walled cylinder; a plate in uniform strain; and Cooks membrane. Numerical results show that, unlike the normal stress components Sx, Sy, and Sz, the calculated values of the von Mises stress are reasonably accurate if measurement errors in the displacement data are small. As the measurement error increases, the error in the von Mises stress increases approximately linearly for linear problems, but can become unacceptably large in nonlinear cases, to the point where solution process encounter fatal errors. A quasi-Dirichlet patch test in association with this problem is also introduced.

Determination of the stress distributions in post-core restored endodontically treated teeth is challenging due to the fact that the post and core systems, the root and its canal, and the bony structures supporting the root have small dimensions and are structurally complex. In this research, a 3D finite element model was developed to evaluate the stress distributions in a post-core restored endodontically treated maxillary incisor under various static loads. The physical model includes dentin, PDL, bone, post, core, gutta percha and crown. All materials are assumed to be homogenous, isotropic, and linear elastic. The effects of various factors on the stress distributions are investigated through simulations. These factors include post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters. It has been found that the horizontal loading is the most dangerous, which causes the highest stresses in dentin and posts, followed by the oblique loading and the vertical loading. The above listed factors, such as post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters, do not change the stress distributions and magnitudes significantly under horizontal and oblique loading. However, the stresses are sensitive to the above factors under the vertical loading, and it has been found that the stress distributions in both dentin and the post are the most uniform without stress concentrations when the elastic modules of the post and the core are similar to that of dentin. Regarding the effects of the gaps at the cervical region on the stress distributions in dentin, the high stresses at the apical portion of the root and the bottom of the gaps decrease as the increase of the depth of the gap under vertical loading. Overall, the sharp angle and notch of the gap at the coronal entrance of the canal should be avoided in tooth restoration since they can cause stress concentrations. On the effects of the ferrule heights, the changes of the stress distributions in dentin and the post are insignificant except that higher ferrule shows lower stresses at the top of the ferrule. Regarding the effects of the diameters of the posts, the results show that although the posts with large diameters support more loads, they cause high stress concentrations at the apical portion of the root, which is not desirable. / October 2005

In this thesis, numerical experiments are performed to test the numerical stability of the finite element method for analyzing incompressible materials from boundary displacements. The significance of the study relies on the fact that incompressibility, or density preservation during deformation, is an important property of materials such as rubber and soft tissue.<p>It is well known that the finite element analysis (FEA) of incompressible materials is less straightforward than for materials which are compressible. The FEA of incompressible materials using the usual displacement based finite element method results in an unstable solution for the stress field. Hence, a different formulation called the mixed u-p formulation (u displacement, p pressure) is used for the analysis. The u-p formulation results in a stable solution but only when the forces and/or stress tractions acting on the structure are known. There are, however, certain situations in the real world where the forces or stress tractions acting on the structure are unknown, but the deformation (i.e. displacements) due to the forces can be measured. One example is the stress analysis of soft tissues. High resolution images of initial and deformed states of a tissue can be used to obtain the displacements along the boundary. In such cases, the only inputs to the finite element method are the structural geometry, material properties, and boundary displacements. When finite element analysis of incompressible materials with displacement boundary conditions is performed, even the mixed u-p formulation results in highly unstable calculations of the stress field. Here, a hypothesis for solving this problem is developed and tested. Theories of linear and nonlinear stress analysis are reviewed to demonstrate that it may be possible to determine the von Mises stress uniquely in spite of the numerical instability inherent in the calculations.<p>To validate this concept, four different numerical examples representing different deformation processes are considered using ANSYS®: a plate in simple shear; expansion of a thick-walled cylinder; a plate in uniform strain; and Cooks membrane. Numerical results show that, unlike the normal stress components Sx, Sy, and Sz, the calculated values of the von Mises stress are reasonably accurate if measurement errors in the displacement data are small. As the measurement error increases, the error in the von Mises stress increases approximately linearly for linear problems, but can become unacceptably large in nonlinear cases, to the point where solution process encounter fatal errors. A quasi-Dirichlet patch test in association with this problem is also introduced.

This study used computer aided design software Solid Work to draw four models of pressure vessel, and to analyze the displacement and the stress by the finite element analysis software ANSYS. To carry on the main body of the pressure vessel and find the highest stress of the pressure vessels by finite element analysis. The stress analysis of the pressure vessel main body contains main nozzle, the skirt of the main body ban and the connected control line. And the stress analysis factor includes: the stress distribution situation by seismic force and the displacement change factor of the wind power and the stress distribution condition of the thermal load by expand with heat and contract with cold (normal temperature climb to high temperature). The researcher also discussed the difference of the stress distribution between individual analysis and the overall analysis. The present study used finite element analysis (contain main body, spray nozzle, skirt in view of the overall analysis ban) to carry on the shell individual analysis first, then using the boundary condition of the result displacements regarding connected spray nozzle, the pipeline by the shell analysis again carries on stress analysis of the spray nozzle and the pipeline. Based on the results of stress analysis by the finite element method, the researcher discussed the differences of stresses between overall analysis and the individual analysis results.

Abdominal aortic aneurysms (AAA) are an expansion in diameter of the abdominal aorta and their rupture is a leading cause of mortality. One of the treatments for AAA is the implantation of an endograft (also called a stent graft), a combination of fabric and metal stents, to provide a new conduit for blood and shield the aneurysm sac from direct pressurization. After implantation of the stent graft, the aneurysm may shrink, grow, or stabilize in diameter ? even in the absence of apparent flow into the sac ? in some cases resulting in graft failure through component separation, kinking, or loss of seal at its ends. Greater understanding of AAA and treated AAA could provide insight on how treatment might be modified to improve treatment methods and/or design devices to be more effective in a wider range of patients. Computational models provide a means to investigate the biomechanics of endografts treating AAA through analysis of the endografts, the AAA, and the combination of them. Axisymmetric models of endograft-treated AAA showed that peak von Mises stress within the wall varied between 533 kPa and 1200 kPa when different material properties for the endograft were used. The patient-specific models, built from time series of patient CT scans with similar patient history but different outcomes, show that wall shrinkage and stability can be related to the level of stresses within the vessel wall, with the shrinking AAA showing a greater reduction by endograft treatment and a lower final value of average von Mises stress. The reduction in pressure felt by the wall is local to the central sac region. The inclusion of thrombus is also essential to accurate stress estimation. The combination of axisymmetric and patient-specific computational models explains in further detail the biomechanics of endograft treatment. The patient-specific reconstruction models show that when effectively deployed and reducing the pressure felt in the AAA wall, the graft is under tension in the sac region and compression at its ends.

The purpose of this study is to investigate the impact effect of varied structure of golf ball. The researcher applied finite element analysis software LS-DYNA to do nonlinear impact analysis of different golf ball models. It was hoped that this study could design a better golf ball for golfer. The researcher had developed ten stress versus strain curves of two-piece golf balls (including a core and a cover) and three-piece golf balls (including a core, an inner cover and a cover) and four different thicknesses of inner cover of three-piece golf balls. The simulation also adjust the density of inner cover to analyze the impact procedure under the definite weight. With the special design of two-piece balls and three-piece balls, the impact models extract the ball velocities, and angular velocities for the calculation of the ball flight. Finally, the researcher made suggestions for some combination of material property and thickness of the core and the inner cover of the golf ball for the designer to develop a suitable golf ball.

Abstract This study aims to investigate the impact effect of varied thickness of the hitting surface and different shapes of the golf club head. The researcher integrated the computer-aided design software Pro/ENGINEER and finite element analysis software LS-DYNA to do the club head design and impact analysis. The researcher had developed five different shapes and eight different thicknesses of hitting surface of the club head model to compare the ball speed and the sweet spot of the hitting surface. He found that ball speed had increased as the hitting surface is enlarged, both laterally and vertically. He also found that thicker center surface and decreasing thickness to the rim of the thickness of the hitting surface is a better design club head. Finally, he made suggestions about the scientific information of the shape and the surface thickness of the golf club head for the designer to develop a suitable club head.

In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A&M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiativetransfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.

In the past ten years, various sewage treatment technologies have got extensive and profound studying in the field of water pollution control in Taiwan. In each unit apparatus of the sewage disposal system, a lamella separator as the sewage treatment facility, is an important link in the structure, has irreplaceable functions. This research investigated the lamella separator structure by means of the static analysis, add factors of earthquake, and typhoon. To achieve the purpose, the researcher used the computer-aided design software Solidworks to set up this structure model. After that, he used finite element analysis software, ANSYS, to analyze the structure. This research simulated in three situations. In static, earthquake, and typhoon analysis, the researcher found the stress of the original modal is over the yielding stress of materials. So, the researcher modified the support of a model to reduce the stress. Generally, the researcher hoped that this study could provide helpful references for designers¡¦ relevant studies on lamella separator structure in the future.