Browsing by Subject "finite element method"
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Item A finite element approach to the 3D CSEM modeling problem and applications to the study of the effect of target interaction andtopography(Texas A&M University, 2005-11-01) Stalnaker, Jack LeeThe solution of the secondary coupled-vector potential formulation of Maxwell??s equations governing the controlled-source electromagnetic (CSEM) response of an arbitrary, threedimensionalconductivitymodelmust be calculatednumerically.The finite elementmethod is attractive, because it allows the model to be discretized into an unstructured mesh, permitting the specification of realistic irregular conductor geometries, and permitting the mesh to be refined locally, where finer resolution is needed. The calculated results for a series ofsimple test problems, ranging from one-dimensionalscalar differentialequations to three-dimensional coupled vector equations match the known analytic solutions well, with error values several orders of magnitude smaller than the calculated values. The electromagnetic fields of a fully three-dimensional CSEM model, recovered from the potentials using the moving least squares interpolation numerical differentiation algorithm, compares well with published numerical modeling results, particularly when local refinement is applied. Multiple buried conductors in a conductive host interact via mutual induction and current flow through the host due to the dissipation of charge accumulated on the conductor boundary. The effect of this interaction varies with host conductivity, transmitter frequency, and conductor geometry, orientation, and conductivity. For three test models containingtwo highly conductive plate-like targets, oriented in various geometries (parallel, perpendicular, and horizontal), mutual coupling ranges as high as twenty times the total magnetic field. The effect of varying host conductivity is significant, especially at high frequencies. Numerical modeling also shows that the vorticity of the currents density induced in a vertically oriented plate-like conductor rotates from vertical at high frequencies, to horizontal at low frequencies, a phenomenon confirmed by comparison with time domain field data collected in Brazos County, Texas. Furthermore, the effect of the presence of a simple horst on the CSEM response of a homogeneous conductive earth is significant, even when the height of the horst is only a fraction of the skin depth of the model. When the transmitter is placedon topofthe horst, the currents inducedtherein account for nearly all of the total magnetic field of the model, indicating that topography, like mutual coupling must be accounted for when interpreting CSEM data.Item A Model for Nonlinear Electrokinetics in Electric Field Guided Assembly of Colloids(2011-02-22) Steuber, James G.Electric field guided assembly of colloids is a new area of research in colloidal science where sub-micrometer particles, or colloids, are assembled using patterned electrodes. The design of these devices is often limited by an inability to characterize accurately forces and fluxes with linearized electrokinetic theory. The research presented in this dissertation describes an application of the finite element method to the nonlinear electrokinetic equations. The finite element model thus developed is then used to describe the nonlinear electrophoretic mobility of a dilute colloidal dispersion, investigate hydrodynamic and electric particle-particle interactions, and characterize particle-surface interactions. The effect of Stern layer conduction on the electrophoretic mobility and dielectric response is included using the generalized dynamic Stern layer model. The electrokinetic force is calculated using the Maxwell stress tensor method rather than the effective dipole method as it is more consistent with nonlinear electrokinetic theory. Significant results of this dissertation demonstrate the effect of nonlinear electrokinetic phenomena and extend the present electrokinetic theory. The calculation of nonlinear electrophoretic mobility of a dilute colloidal dispersion, which is valid for arbitrary particle surface charge or zeta potential, applied (AC) electric field strength, and applied AC electric field frequency. Also, the adsorption isotherm used by the generalized dynamic Stern layer theory is extended to include non-equilibrium reaction kinetics. This results in a model for Stern layer conduction which is valid for frequencies above 1 MHz. The utilization of the Maxwell stress tensor method results in a finite element model which is valid for arbitrary electric field strength and includes the effects of traveling-wave dielectrophoresis a nonlinear electrokinetic phenomena resulting from non-uniform electric field phase.Item Endografts, Pressure, and the Abdominal Aortic Aneurysm(2010-07-14) Meyer, Clark A.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.Item Least-squares variational principles and the finite element method: theory, formulations, and models for solid and fluid mechanics(Texas A&M University, 2004-09-30) Pontaza, Juan PabloWe consider the application of least-squares variational principles and the finite element method to the numerical solution of boundary value problems arising in the fields of solidand fluidmechanics.For manyof these problems least-squares principles offer many theoretical and computational advantages in the implementation of the corresponding finite element model that are not present in the traditional weak form Galerkin finite element model.Most notably, the use of least-squares principles leads to a variational unconstrained minimization problem where stability conditions such as inf-sup conditions (typically arising in mixed methods using weak form Galerkin finite element formulations) never arise. In addition, the least-squares based finite elementmodelalways yields a discrete system ofequations witha symmetric positive definite coeffcientmatrix.These attributes, amongst manyothers highlightedand detailed in this work, allow the developmentofrobust andeffcient finite elementmodels for problems of practical importance. The research documented herein encompasses least-squares based formulations for incompressible and compressible viscous fluid flow, the bending of thin and thick plates, and for the analysis of shear-deformable shell structures.Item Modeling of Shape Memory Alloys Considering Rate-independent and Rate-dependent Irrecoverable Strains(2011-02-22) Hartl, Darren J.This dissertation addresses new developments in the constitutive modeling and structural analysis pertaining to rate-independent and rate-dependent irrecoverable inelasticity in Shape Memory Alloys (SMAs). A new model for fully recoverable SMA response is derived that accounts for material behaviors not previously addressed. Rate-independent and rate-dependent irrecoverable deformations (plasticity and viscoplasticity) are then considered. The three phenomenological models are based on continuum thermodynamics where the free energy potentials, evolution equations, and hardening functions are properly chosen. The simultaneous transformation-plastic model considers rate-independent irrecoverable strain generation and uses isotropic and kinematic plastic hardening to capture the interactions between irrecoverable plastic strain and recoverable transformation strain. The combination of theory and implementation is unique in its ability to capture the simultaneous evolution of recoverable transformation strains and irrecoverable plastic strains. The simultaneous transformation-viscoplastic model considers rate-dependent irrecoverable strain generation where the theoretical framework is modfii ed such that the evolution of the viscoplastic strain components are given explicitly. The numerical integration of the constitutive equations is formulated such that objectivity is maintained for SMA structures undergoing moderate strains and large displacements. Experimentally validated analysis results are provided for the fully recoverable model, the simultaneous transformation-plastic yield model, and the transformation-viscoplastic creep model.Item Numerical Modeling of Cased-hole Instability in High Pressure and High Temperature Wells(2012-11-12) Shen, Zheng 1983-Down-hole damages such as borehole collapse, circulation loss and rock tensile/compressive cracking in the open-hole system are well understood at drilling and well completion stages. However, less effort has been made to understand the instability of cemented sections in High Pressure High Temperature (HPHT) wells. The existing analysis shows that, in the perforation zones, casing/cement is subject to instability, particularly in the presence of cavities. This dissertation focuses on the instability mechanism of casing/cement in the non-perforated zones. We investigate the transient thermal behavior in the casing-cement-formation system resulting from the movement of wellbore fluid using finite element method. The critical value of down-hole stresses is identified in both wellbore heating and cooling effects. Differently with the heating effect, the strong cooling effect in a cased hole can produce significant tension inside casing/cement. The confining formation has an obvious influence on the stability of casing/cement. The proposed results reveal that the casing/cement system in the non-homogeneous formation behaves differently from that in homogeneous formation. With this in mind, a three-dimensional layered finite element model is developed to illustrate the casing/cement mechanical behavior in the non-homogeneous formation. The radial stress of cement sheath is found to be highly variable and affected by the contrast in Young?s moduli in the different formation layers. The maximum stress is predicted to concentrate in the casing-cement system confined by the sandstone. Casing wear in the cased-hole system causes significant casing strength reduction, possibly resulting in the casing-cement tangential collapse. In this study, an approach for calculating the stress concentration in the worn casing with considering temperature change is developed, based on boundary superposition. The numerical results indicate that the casing-cement system after casing wear will suffer from severe tangential instability due to the elevated compressive hoop stress. Gas migration during the cementing process results from the fluid cement?s inability to balance formation pore pressure. Past experience emphasized the application of chemical additives to reduce or control gas migration during the cementing process. This report presents the thermal and mechanical behaviors in a cased hole caused by created gas channels after gas migration. In conclusion, the size and the number of gas channels are two important factors in determining mechanical instability in a casing-cement system.Item Quantitative Modeling of Polymer Scratch Behavior(2013-12-02) Hossain, Mohammad MotaherScratch-induced surface deformation is a complex mechanical process due to high strain rate large-scale deformation, non-linear material response, heat dissipation and complex stress field evolved during the process. The rate, time, temperature and pressure dependent behavior of polymers, and the surface condition of the interacting surfaces also add to the complexity. In order to gain in-depth understanding of polymer scratch behavior; this dissertation focuses on numerical analysis and experimental study of scratch-induced deformation in polymers, leading to quantitative prediction of scratch behavior of model amorphous polymers. A comprehensive three-dimensional finite element method (FEM) parametric study has been performed by incorporating key characteristics of polymer constitutive behavior to investigate the effect of material parameters and surface properties on the evolution of scratch-induced deformation in polymers, along with relevant experimentation. The qualitative analyses using FEM simulation and experimental work suggest that indeed correlation between material and surface properties, and scratch-induced damage mechanisms can be established. To quantitatively predict the scratch behavior of polymers via FEM, PC and SAN model systems are chosen. A modification of Ree-Eyring theory is used to assess the rate dependent behavior of model polymers at high strain rates based on the experimental data obtained at low strain rates. By including the rate and pressure dependent mechanical behavior and pressure dependent frictional behavior in the FEM model, good agreement has been found between FEM simulation and experimental observations. The results suggest that, by including proper constitutive relationship and friction model in the numerical analysis, the scratch behavior of polymers can be quantitatively predicted with reasonable success.Item Stented Artery Biomechanics: A Computational and In Vivo Analysis of Stent Design and Pathobiological Response(2011-08-08) Timmins, Lucas HowardVascular stents have become a standard for treating atherosclerosis due to distinct advantages in trauma and cost with other surgical techniques. Unfortunately, the therapy is hindered by the risk of a new blockage (termed restenosis) developing in the treated artery. Clinical studies have indicated that stent design is a major risk factor for restenosis, with failure rates varying from 20 to 40% for bare metal stents. Subsequently, there has been a significant effort devoted to reducing failure rates by covering stents in polymer coatings in which anti-proliferative drugs are embedded, however complications have arisen (e.g. incomplete endothelization, lack of success in peripheral arteries, lack of long-term follow-up studies) that have limited the success of this technology. It has been thought that restenosis is directly related to the mechanical conditions that vascular stents create. Moreover, it has been hypothesized that stents that induce higher non-physiologic stresses result in a more aggressive pathobiological response that can lead to restenosis development. In this study, a combination of computational modeling and in vivo analysis were conducted to investigate the artery stent-induced wall stresses, and subsequent biological inflammatory response. In particular, variations in stent design were investigated as a means of examining specific stent design criteria that minimize the mechanical impact of stenting. Collectively, these data indicate that stent designs that subject the artery wall to higher stress values result in significantly more neointimal tissue proliferation, therefore, confirming the aforementioned hypothesis. Moreover, this work provides valuable insight into the role that biomechanics can play in improving the success rate of this percutaneous therapy and overall patient care.Item Support graph preconditioners for sparse linear systems(Texas A&M University, 2005-02-17) Gupta, RadhikaElliptic partial differential equations that are used to model physical phenomena give rise to large sparse linear systems. Such systems can be symmetric positive de?nite and can be solved by the preconditioned conjugate gradients method. In this thesis, we develop support graph preconditioners for symmetric positive de?nite matrices that arise from the ?nite element discretization of elliptic partial di?erential equations. An object oriented code is developed for the construction, integration and application of these preconditioners. Experimental results show that the advantages of support graph preconditioners are retained in the proposed extension to the ?nite element matrices.Item The piecewise linear discontinuous finite element method applied to the RZ and XYZ transport equations(Texas A&M University, 2008-10-10) Bailey, Teresa SIn 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.