Smart materials are very important because of their potential applications in the biomedical, petroleum and aerospace industries. They can be used to build systems and structures that self-monitor to function and adapt to new operating conditions. In this study, we are mainly interested in developing a computational framework for the analysis of plate structures comprised of composite or functionally graded materials (FGM) with embedded or surface mounted piezoelectric sensors/actuators. These systems are characterized by thermo-electro-mechanical coupling, and therefore their understanding through theoretical models, numerical simulations, and physical experiments is fundamental for the design of such systems. Thus, the objective of this study was to perform a numerical study of smart material plate structures using a refined plate theory that is both accurate and computationally economical. To achieve this objective, an improved version of the Reddy third-order shear deformation theory of plates was formulated and its finite element model was developed. The theory and finite element model was evaluated in the context of static and dynamic responses without and with actuators. In the static part, the performance of the developed finite element model is compared with that of the existing models in determining the displacement and stress fields for composite laminates and FGM plates under mechanical and/or thermal loads. In the dynamic case, coupled and uncoupled electro-thermo-mechanical analysis were performed to see the difference in the evolution of the mechanical, electrical and thermal fields with time. Finally, to test how well the developed theory and finite element model simulates the smart structural system, two different control strategies were employed: the negative velocity feedback control and the Least Quadratic Regulator (LQR) control. It is found that the refined plate theory provides results that are in good agreement with the those of the 3-D layerwise theory of Reddy. The present theory and finite element model enables one to obtain very accurate response of most composite and FGM plate structures with considerably less computational resources.

A graphical preprocessor for Spectral Element Method (SEM) is developed with an emphasis on user friendly graphical interface and instructive element construction. The interface of the preprocessor helps users with every step during mesh generation, aiding their understanding of SEM. This preprocessor's Graphical User Interface (GUI) and help system are comparable to other commercial tools. Moreover, this preprocessor is designed for educational purposes, and prior knowledge of Spectral Element formulation is not required to use this tool. The information window in the preprocessor shows stepby- step instructions for the user. The preprocessor provides a graphical interface which enables visualization while the mesh is being constructed, so that the entire domain can be discretized easily. In addition, by following informative steps during the mesh construction, the user can gain knowledge about the intricate details of computational fluid dynamics. This preprocessor provides a convenient way to implement h/p type nonconforming interfaces between elements. This aids the user in learning advanced numerical discretization techniques, such as the h/p nonconforming SEM. Using the preprocessor facilitates enhanced understanding of SEM, isoparametric mapping, h and p type nonconforming interfaces, and spectral convergence. For advanced users, this preprocessor provides a proficient and convenient graphical interface independent of the solvers. Any spectral element solver can utilize this preprocessor, by reading the format of the output file from the preprocessor. Given these features, this preprocessor is useful both for novice and advanced users.

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.

In this paper¡Athe cable structures considering sag effect and flexural rigidity are used to the series of dynamic analysis.It dedatees on vibration of the cables by the harmonic force and win¡Ðrain induced vibration. Using the finite element method to analyze the effect of the sge and the effect of the sag and the flexural rigidity¡Aincluding frequencies of the cable and displacement of every nodes at arbitrarily time.

The roles of residual stresses distribution and creep deformation in the post-weld-shifts (PWS) of a laser model packaging are investigated in this dissertation. The temperature dependent material properties are employed to calculate the distribution of the residual stresses introduced in the solidification of soldering joints and lasering joints respectively. A power law proposed by Norton is applied to the creep deformation calculation. The post-weld-shifts of fiber-solder-ferrule (FSF) introduced in the aging and temperature cycling tests are simulation. A finite element package ¡V MARC is used to module the fiber-solder-ferrule joint and laser joint respectively. Experimental results of the PWS of a FSF joint are compared with the calculated shifts. Results indicate that the redistribution of residual stresses in joint and the creep deformation under high temperature load may affect the PWS significantly. A good agreement between the simulated and the measured results indicate the proposed model is feasible in the laser module packaging analysis.

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 are concerned with the analysis of the finite element method for the time-dependent Maxwell interface problem when Nedelec and Raviart-Thomas finite elements are employed and preconditioning of the resulting linear system when implicit time schemes are used. We first investigate the finite element method proposed by Makridakis and Monk in 1995. After studying the regularity of the solution to time dependent Maxwell's problem and providing approximation estimates for the Fortin operator, we are able to give the optimal error estimate for the semi-discrete scheme for Maxwell's equations. Then we study preconditioners for linear systems arising in the finite element method for time-dependent Maxwell's equations using implicit time-stepping. Such linear systems are usually very large but sparse and can only be solved iteratively. We consider overlapping Schwarz methods and multigrid methods and extend some existing theoretical convergence results. For overlapping Schwarz methods, we provide numerical experiments to confirm the theoretical analysis.

In this thesis, we discuss the development, implementation and testing of a piecewise linear (PWL) continuous Galerkin finite element method applied to the threedimensional diffusion equation. This discretization is particularly interesting because it discretizes the diffusion equation on an arbitrary polyhedral mesh. We implemented our method in the KULL software package being developed at Lawrence Livermore National Laboratory. This code previously utilized Palmer's method as its diffusion solver, which is a finite volume method that can produce an asymmetric coefficient matrix. We show that the PWL method produces a symmetric positive definite coefficient matrix that can be solved more efficiently, while retaining the accuracy and robustness of Palmer's method. Furthermore, we show that in most cases Palmer's method is actually a non-Galerkin PWL finite element method. Because the PWL method is a Galerkin finite element method, it has a firm theoretical background to draw from. We have shown that the PWL method is a well-posed discrete problem with a second-order convergence rate. We have also performed a simple mode analysis on the PWL method and Palmer's method to compare the accuracy of each method for a certain class of problems. Finally, we have run a series of numerical tests to uncover more properties of both the PWL method and Palmer's method. These numerical results indicate that the PWL method, partially due to its symmetric matrix, is able to solve large-scale diffusion problems very efficiently.

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.