# Browsing by Subject "Finite element method"

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Item A comparison of simulation methods with finite-difference and finite element methods for solving Vlasov-Poisson systems(Texas Tech University, 1986-08) Ho, Wai HungShow more We consider the one dimensional periodic Vlasov-Poisson equation and discuss various approximations. These include the particle-in-cell method, the upstream-downstream method (a finite element method) and the Lax-Wendroff method (a finite-difference method). The model considered as a test problem numerically simulates electrons moving over a fixed, uniform positive background when, as an initial condition for the electron distribution, a Maxwellian beam is imposed. Landau damping phenomena are observed for all approximation methods. Good agreements on charge conservation have been observed for both finite element and finite-difference methods for up to 12.5 plasma periods. Numerical experiments show that for very short plasma periods (e.g., 2 plasma periods) the total energy of a Vlasov plasma system is conserved with finite element methods; however, it is not well conserved at all for longer plasma periods. Nevertheless, with finite - difference methods energy conservation of the system satisfactorily holds for up to 10 plasma periods. Modification of mesh sizes and time steps shows that fine mesh sizes and small time steps can be used for reducing numerical diffusion effects. Based on different numerical results, we make a comparative study of finite element and finite-difference methods with particle - in - cell methods.Show more Item A computational three field methodology for non-conforming finite elements over partitioned domains(Texas Tech University, 2005-05) Franklin, Scott R.Show more In this thesis, we describe a computational methodology to couple physical processes defined over independent sub-domains, that are partitions of a global domain in three-dimensions. The methodology presented helps to compute the numerical solution on the global domain by appropriately piecing the local solutions from each sub-domain. We discuss the mixed method formulation for the technique applied to a model problem and derive an error estimate for the finite element solution. We demonstrate through numerical experiments, that the method is robust and reliable in higher-dimensions. Additionally, this thesis is concerned with the application of non-conforming finite element methods to stochastic partial differential equations. We present a mixed formulation of a three-field finite element method applied to an elliptic model problem involving stochastic loads. We then derive the exact form for the expected value and variance of the solution. Additionally the rate of convergence for the stochastic error is presented. Finally, we demonstrate the reliability of the method by comparing our exact results with numerical experiments. The method is then extended for use in parabolic partial differential equations (e.g., time-dependent systems). After providing the derivation for the semi-discretization of the parabolic problem, we consider two classical full discretizations of a model problem: the backward Euler method and the Crank-Nicolson method. This method is implemented and used to model actual physical phenomena, namely, we consider the heat conduction/diffusion equation. Finally, we report on the specifics of the implementation of the method in various distributed computing environments, including a computational grid and a shared memory multi-processor.Show more Item A computational three-field methodology for non-conforming finite elements over partitioned domains(2005-05) Franklin, Scott R.; Smith, Philip W.; Seshaiyer, Padmanabhan; Allen, Edward J.Show more In this thesis, we describe a computational methodology to couple physical processes defined over independent sub-domains, that are partitions of a global domain in three-dimensions. The methodology presented helps to compute the numerical solution on the global domain by appropriately piecing the local solutions from each sub-domain. We discuss the mixed method formulation for the technique applied to a model problem and derive an error estimate for the finite element solution. We demonstrate through numerical experiments, that the method is robust and reliable in higher-dimensions. Additionally, this thesis is concerned with the application of non-conforming finite element methods to stochastic partial differential equations. We present a mixed formulation of a three-field finite element method applied to an elliptic model problem involving stochastic loads. We then derive the exact form for the expected value and variance of the solution. Additionally the rate of convergence for the stochastic error is presented. Finally, we demonstrate the reliability of the method by comparing our exact results with numerical experiments. The method is then extended for use in parabolic partial differential equations (e.g., time-dependent systems). After providing the derivation for the semi-discretization of the parabolic problem, we consider two classical full discretizations of a model problem: the backward Euler method and the Crank-Nicolson method. This method is implemented and used to model actual physical phenomena, namely, we consider the heat conduction/diffusion equation. Finally, we report on the specifics of the implementation of the method in various distributed computing environments, including a computational grid and a shared memory multi-processor.Show more Item A finite element analysis of the static and dynamic behavior of the automobile tire(Texas Tech University, 1977-05) Parikh, Prashant DShow more A mathematical model to represent a radial ply passenger car tire has been developed for axisymmetric and asymmetric static and dynamic eigenvalue analysis by the use of a direct stiffness finite element method. Linear analysis is performed. The tire is considered as a thin shell of revolution. The finite element chosen has a shape of a conical frustrum with five degrees of freedom at each node in the local coordinate system of the element. The tire properties have been derived by assuming the tire to be composed of thin layers of composite materials, linearly orthotropic in nature. Hamilton's principle has been applied to derive the equation of motion of the element. In the case of asymmetric static analysis, fifteen Fourier harmonic terms have been used to represent the as)TTimetric loading and deformation. The equation for the static case has been solved by employing the Gauss elimination method. Three different types of pressure distributions have been assumed to simulate the actual pressure distribution in the tire footprint area. The natural frequencies and the associated set of mode shapes have been evaluated by employing a method based on a modified version of Lanczos' n-step iteration procedure. The analysis predicts experimentally verifiable deformed shapes under static loading, and natural frequencies of vibration and associated mode shapes with good accuracy.Show more Item A finite element complementary energy formulation for plane elastoplastic stress analysis(Texas Tech University, 1979-05) Azene, MulunehShow more The m.ethod of analysis presented herein parallels that of Ref (8) with two added major distingushing features. First, the present model consists of an eighteen degree of freedom self-equilibrating finite element model wherein the stress function is expressed by means of a complete set of quintic Hermitian polynomials. The function used, while allowing for selfequilibrating stresses that are continuous within the element, also enables the admission of all the second derivatives of the function as nodal parameters, thereby permitting the determination of nodal stress values directly without the need of additional computation. Second, the present work introduces an additional force parameter that is essential to satisfy complete static equilibrium of external forces constistent with the assumed stress function.Show more Item A Finite Element-Multibody Dynamics Co-simulation Methodology Applied to FAST(2013-05-02) Suryakumar, Vishvas SamuelShow more A co-simulation methodology is explored whereby a finite element code and a multi-body dynamics code featuring flexible cantilevered beams can be coupled and interactively executed. The floating frame of reference formulation is used to develop the equations of motion. The floating frame is fixed at the blade root. Such a formulation results in ordinary differential equations without added algebraic constraints. A variety of loose coupling and tight coupling schemes are examined for this problem. To synchronize the coupling variables, a Gauss-Seidel type iterative algorithm is used. The resulting fixed-point iterations are accelerated using Aitken?s adaptive relaxation technique. The methodology is evaluated for FAST, a wind turbine aeroelastic simulation code developed by NREL. As with FAST, many multi-body codes which can model flexibility employ modal methods. A proposed addition for FAST to simulate flexible effects using a finite element method module offers a potential to include a variety of non-linearities and also provides possibilities for using a high-fidelity aerodynamics module. The coupling schemes are compared and their applicability and limitations for different scenarios are pointed out. Results validating the approach are provided.Show more Item A study into the application of piezoelectrics to modify ankle torques in active prosthetic feet using finite element analysis(2012-05) Powelson, Thomas; Yang, Jingzhou; Tate, Derrick; Ekwaro-Osire, StephenShow more Over the last fifty years there has been a steady advance in prosthetic foot technologies. These advances have primarily focused on more accurately mimicking the biologic foot for amputees. One eld of research currently being explored is active/powered prosthetic feet in which the movement of the foot is actively controlled through the use of electric motors. Some of these feet also seek to reproduce the ankle torques seen in the biologic foot. This thesis proposes to investigate the possibility of the integration of piezoelectrics into active prosthetic feet to more accurately reproduce these ankle torques. A general set of FEA models, simulations, and analysis tools have been developed for the design and testing of applications involving piezoelectric beam bending actuators. These tools were utilized to successfully replicate the ankle torques versus time pro les found in the literature through the application of a number of di erent con gurations of piezoelectric strips. It was found that while it was possible to replicate these toques with piezoelectrics alone, the required voltages were far too large to be practical.Show more Item Adaptive finite elements for nonlinear transport equations(2003-12) Carnes, Brian Ross; Carey, Graham F.Show more The a posteriori error analysis and estimation for conforming finite element approximation of stationary boundary value problems exhibiting certain classes of nonlinear reaction and nonlinear diffusion was investigated. Principal contributions were: (C1) Derivation of new rational local error indicators for both spatial and parameter error in parameterized nonlinear reaction–diffusion problems, (C2) New continuation algorithms for turning point prediction and calculation using adaptive mesh refinement (AMR), (C3) Improved linearization theory for nonlinear diffusion systems, (C4) A posteriori error analysis and new local error indicators for global error and error in output functionals for nonlinear diffusion systems, and (C5) A study of nonlinear diffusive mass transport in a PEM fuel cell cathode using AMR. For parameterized nonlinear reaction–diffusion problems, the solutions to a pair of local linear boundary value problems on each element were postprocessed to create local and global error indicators for both the spatial and parameter error, which were tested on representative problems, including the catalyst pellet problem from chemical engineering. The estimation of critical parameter values at simple turning points was demonstrated using AMR and the new local error indicator for the parameter error. The linearization theory for nondifferentiable, nonlinear diffusion operators with nonlinear solution–dependent diffusion coefficients was extended to systems, including the Stefan–Maxwell multicomponent diffusion operator. In addition, the application of the linearization arguments to the a posteriori error analysis of these operators was justified. Local error indicators for global error and error in output functionals were derived, based on solving local linear boundary value problems that approximate the primal and dual error. Numerical studies demonstrated the performance of the new indicators and confirmed the advantages of the linearization approach over simple estimates of the residuals. Finally, a study of nonlinear diffusive mass transport in the cathode of a PEM fuel cell was conducted, illustrating the use of AMR and the new local error indicators in an application problem of general interest. Calculation of an effectiveness factor that measures mass transport limitations in the cathode was also explored.Show more Item Analysis of linear elasticity and non-linearity due to plasticity and material damage in woven and biaxial braided composites(2009-05-15) Goyal, DeepakShow more Textile composites have a wide variety of applications in the aerospace, sports, automobile, marine and medical industries. Due to the availability of a variety of textile architectures and numerous parameters associated with each, optimal design through extensive experimental testing is not practical. Predictive tools are needed to perform virtual experiments of various options. The focus of this research is to develop a better understanding of linear elastic response, plasticity and material damage induced nonlinear behavior and mechanics of load flow in textile composites. Textile composites exhibit multiple scales of complexity. The various textile behaviors are analyzed using a two-scale finite element modeling. A framework to allow use of a wide variety of damage initiation and growth models is proposed. Plasticity induced non-linear behavior of 2x2 braided composites is investigated using a modeling approach based on Hill?s yield function for orthotropic materials. The mechanics of load flow in textile composites is demonstrated using special non-standard postprocessing techniques that not only highlight the important details, but also transform the extensive amount of output data into comprehensible modes of behavior. The investigations show that the damage models differ from each other in terms of amount of degradation as well as the properties to be degraded under a particular failure mode. When compared with experimental data, predictions of some models match well for glass/epoxy composite whereas other?s match well for carbon/epoxy composites. However, all the models predicted very similar response when damage factors were made similar, which shows that the magnitude of damage factors are very important. Full 3D as well as equivalent tape laminate predictions lie within the range of the experimental data for a wide variety of braided composites with different material systems, which validated the plasticity analysis. Conclusions about the effect of fiber type on the degree of plasticity induced non-linearity in a ?25? braid depend on the measure of non-linearity. Investigations about the mechanics of load flow in textile composites bring new insights about the textile behavior. For example, the reasons for existence of transverse shear stress under uni-axial loading and occurrence of stress concentrations at certain locations were explained.Show more Item Analysis of response of earth covered structures to earthquakes(Texas Tech University, 1983-05) Subbaraya, Anantha PrasadShow more Not availableShow more Item Analytical modeling of fully bonded and debonded pre-tensioned prestressed concrete members(2005) Baxi, Asit Nareshchandra, 1963-; Wood, Sharon L.; Burns, N. H. (Ned Hamilton), 1932-Show more Item Boundary/finite element meshing from volumetric data with applications(2005) Zhang, Yongjie; Bajaj, ChandrajitShow more The main research work during my Ph.D. study is to extract adaptive and quality 2D (triangular or quadrilateral) meshes over isosurfaces and 3D (tetrahedral or hexahedral) meshes with isosurfaces as boundaries directly from volumetric imaging data. The software named LBIE-Mesher (Level Set Boundary Interior and Exterior Mesher) is developed. LBIE-Mesher generates 3D meshes for the volume interior to an isosurface, the volume exterior to an isosurface, or the interval volume between two isosurfaces. An algorithm has been developed to extract adaptive and quality 3D meshes directly from volumetric imaging data. The extracted tetrahedral meshes are extensively used in the Finite Element Method (FEM). A top-down octree subdivision coupled with the dual contouring method is used to rapidly extract adaptive 3D finite element meshes with correct topology from volumetric imaging data. The edge contraction and smoothing methods are used to improve the mesh quality. The main contribution is extending the dual contouring method to crack-free interval volume 3D meshing with feature sensitive adaptation. Compared to other tetrahedral extraction methods from imaging data, our method generates adaptive and quality 3D meshes without introducing any hanging nodes. Furthermore, another algorithm has been developed to extract adaptive and quality quadrilateral or hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. An approach has been described to smooth the surface and improve the quality of surface/volume meshes with feature preserved using geometric flow. For triangular and quadrilateral surface meshes, the surface diffusion flow is selected to remove noise by relocating vertices in the normal direction, and the aspect ratio is improved with feature preserved by adjusting vertex positions in the tangent direction. For tetrahedral and hexahedral volume meshes, besides the surface vertex movement in the normal and tangent directions, interior vertices are relocated to improve the aspect ratio. Our method has the properties of noise removal, feature preservation and quality improvement of surface/volume meshes, and it is especially suitable for biomolecular meshes because the surface diffusion flow preserves sphere accurately if the initial surface is close to a sphere. A comprehensive approach has been proposed to construct quality meshes for imviii plicit solvation models of biomolecular structures starting from atomic resolution data in the Protein Data Bank (PDB). First, a smooth volumetric synthetic electron density map is constructed from parsed atomic location data of biomolecules in the PDB, using Gaussian isotropic kernels. An appropriate parameter selection is made for constructing an error bounded implicit solvation surface approximation to the Lee-Richards molecular surface. Next, a modified dual contouring method is used to extract triangular meshes for the molecular surface, and tetrahedral meshes for the volume inside or outside the molecule within a bounding sphere/box of influence. Finally, geometric flows are used to improve the mesh quality. Some of our generated meshes have been successfully used in finite element simulations. Techniques have been developed to generate an adaptive and quality tetrahedral finite element mesh of a human heart. An educational model and a patient-specific model are constructed. There are three main steps in our mesh generation: model acquisition, mesh extraction and boundary/material layer detection. (1) Model acquisition. Beginning from an educational polygonal model, we edit and convert it to volumetric gridded data. A component index for each cell edge and grid point is computed to assist the boundary and material layer detection. For the patient-specific model, some boundary points are selected from MRI images, and connected using cubic splines and lofting to segment the MRI data. Different components are identified. (2) Mesh extraction. We extract adaptive and quality tetrahedral meshes from the volumetric gridded data using our LBIE-Mesher. The mesh adaptivity is controlled by regions or using a feature sensitive error function. (3) Boundary/material layer detection. The boundary of each component and multiple material layers are identified and meshed. The extracted tetrahedral mesh of the educational model is being utilized in the analysis of cardiac fluid dynamics via immersed continuum method, and the generated patient-specific model will be used in simulating the electrical activity of the heart.Show more Item Computaional modeling of membrane mechanics(Texas Tech University, 2006-08) Kundomal, Chellaram A.; Seshaiyer, Padmanabhan; Martin, Clyde F.; Schovanec, LawrenceShow more In this work we analyze mechanics of thin membranes. After a brief review on the backgrounds and methods, this thesis develops a systematic approach to understanding membrane mechanics. The two essential mathematical tools employed include Principle of Virtual Work and the finite element method. More specifically after defining suitable measures of deformation of an arbitrary body, we describe how one can apply the Principle of Virtual Work for a fully dynamic application. We employ the finite element method to a quasi-static application which results in a system of nonlinear equations. These equations are solved by the Newton-Raphson procedure for systems. The computational methodology discussed in this work was implemented in Maple for two different membrane materials: neo-Hookean and Mooney-Rivlin.Show more Item Computational experiments using nonconforming finite elements(Texas Tech University, 2001-08) Mahood, Carrie LynnShow more Initially, the conforming finite element method is explained. The steps of the finite element method (begin with a second-order differential equation, multiply by a test function, put in integral form, produce a weak formulation by integrating by parts, reach a system of equations, and solve for unknowns) are discussed for a simple univariate case, general univariate case, and Poisson’s equation^1. A nonconforming finite element method is then used to solve the two-dimensional Poisson's equation. A matlab code, which may be found in the Appendix section A3 , solves the problem on Ù = [—1,1] x [0,1], where Ù1 = [—1.0] x [0,1] and Ù2 = [0,1] X [0,1]. The approximation on the boundary Ã12 =Ù1Ù2 is not truly continuous, but is “weakly" continuous. The result is a discontinuous approximation to a smooth function that demonstrates the feasibility of solving Poisson's equation by combining two separately meshed regions and enforcing "weak" continuity across the boundary.Show more Item Computational investigation of path instabilities in rising air bubbles(2002-05) Sreekantan, Venkatesh; Marder, Michael P., 1960-Show more This dissertation deals with a numerical investigation of path instabilities in rising air bubbles. This phenomenon has been looked at experimentally in a Hele{Shaw Geometry. The present work discusses a quasi-two dimensional Finite Element Method based simulation of the same experiment. The results validate the supercritical bifurcation nature of the instability. Reasons for disagreements between the experiment and simulation are presented.Show more Item A computational procedure for analysis of fractures in three dimensional anisotropic media(2004) Rungamornrat, Jaroon; Mear, Mark E.Show more A symmetric Galerkin boundary element method (SGBEM) is developed for analysis of fractures in three dimensional anisotropic, linearly elastic media, and the method is coupled with standard finite element procedures. Important features of the technique are that the formulation is applicable to general anisotropy, the kernels in the governing integral equations are only weakly-singular (of order 1/r) hence allowing the application of standard Co elements in the numerical treatment, and a special crack tip element is utilized which allows general mixed-mode fracture data (viz. the stress intensity factors) to be efficiently determined as a function of position along the crack front. The weakly-singular, weak-form displacement and traction integral equations which constitute a basis for the SGBEM are obtained via a regularization technique. The technique utilizes a particular decomposition for the stress fundamental solution and for the strongly-singular kernel in order to facilitate an integration by parts via Stokes’ theorem. The final integral equations contain only weakly-singular kernels (given explicitly in terms of a line integral) which are applicable to gen- eral anisotropic materials. These weakly-singular kernels are obtained by solving a system of partial differential equations via the Radon transform. A symmetric formulation is developed by a suitable use of the weakly-singular displacement and traction integral equations. As part of the numerical implemen- tation, a Galerkin approximation strategy is utilized to discretize the governing integral equations. Standard isoparametric Co elements are employed everywhere except along the crack front where a special crack-tip elements is used. To demon- strate the accuracy and versatility of the method, various examples for cracks in both unbounded and finite domains are considered. Finally, a symmetric coupling of the SGBEM and the standard finite element method is established. The coupling strategy exploits the versatility and capabil- ity of the finite element method to treat structures with complex geometry and loading, while employing the SGBEM to efficiently and accurately treat a (local) region containing the crack. In the numerical implementation, both conforming and nonconforming discretization along the interface of the two regions are treated. In addition, the coupling of the SGBEM with a commercial finite element code is ex- plored and successfully implemented. Several examples are presented to illustrate the capability and accuracy of the method.Show more Item Control of geometry error in hp finite element (FE) simulations of electromagnetic (EM) waves(2005) Xue, Dong, 1977-; Demkowicz, LeszekShow more The success of high accuracy Finite Element (FE) simulations for complex, curvilinear geometries depends greatly on a precise representation of the geometry and a proper mesh generation scheme. Sizable errors are introduced into the numerical predictions when the order of the geometric approximation is too low with respect to the polynomial order of the discretization. In hp finite element methods, preserving exponential convergence rates for problems over curved domains requires the use of either exact geometry elements or higher order (iso- or superparametric) geometry representations. Radiation of electromagnetic (EM) waves from various sources, including cell phones, and their absorption into the human body, has become a raising public concern. This has motivated us to select the problem of scattering and absorption of EM waves on the human head, as a driving application for the research on the geometry induced errors in FE simulations. Maxwell equations are discretized using H(curl)- conforming elements that turn out to be more sensitive to geometry induced errors than standard H1 - conforming (continuous) finite elements. In this dissertation, we review the theoretical framework for a general class of parametric H1 , H(curl) and H(div)- conforming elements, with both exact and isoparametric geometry description. A systematic way of computing H1− and H(curl)− discretization errors, accounting for the error in geometry approximation, is proposed. The technique is illustrated with numerical examples and compared with the customary error evaluation neglecting the geometry approximation error. Two general geometry representation schemes have been addressed: CADlike geometric modeling and geometry reconstruction from discrete data. A number of novel geometrical modeling techniques are explored and implemented in the presented Geometric Modeling Package (GMP). The package is used to generate an exact representation of complex objects, and provides a foundation for a multi-block hp mesh generator. The package allows for maintaining a continuous interface with adaptive codes to update the geometry information during mesh refinements. In addition, an approaches have been developed to accelerate preparation of geometry data by extracting topology information of a meshed model from existing mesh generation toolkits. The geometric model needs to be sufficiently smooth enough to produce a finite element mesh free of local geometric discontinuities which create numerical artifacts in the EM solutions. An efficient biquartic G1 surface reconstruction scheme is developed in this dissertation for general unstructured meshes. The polyvii nomial parameterizations are inexpensive to compute and guarantee high regularity of parametrization necessary in FE computations. The new geometric representation techniques have been incorporated into a 3D hp 1 coupled Finite Element/Infinite Element (FE/IE) codedeveloped in Dr. Demkowicz group at the Institute for Computational Engineering and Sciences (ICES). The new GMP and the coupled FE/IE hp code have been verified using the Mie series solution for the problem of scattering a plane EM wave on a dielectric sphere. The accuracy of FE/IE approximation has then been assessed using the precise definition of the solution error incorporating the effects of geometry approximation. Finally, an explicit a posteriori error estimator for time-harmonic Maxwell equations and arbitrary hp meshes on curvilinear geometries is implemented in the hp FE code. The estimator is used to drive an h-adaptive strategy to solve the head problem. The computed Spatial-peak and average Specific Absorption Rate (SAR) values have been compared with results obtained by other numerical methods.Show more Item Deformation Analysis of Sand Specimens using 3D Digital Image Correlation for the Calibration of an Elasto-Plastic Model(2012-10-19) Song, AhranShow more The use of Digital Image Correlation (DIC) technique has become increasingly popular for displacement measurements and for characterizing localized material deformation. In this study, a three-dimensional digital image correlation analysis (3D-DIC) was performed to investigate the displacements on the surface of isotropically consolidated and drained sand specimens during triaxial compression tests. The deformation of a representative volume of the material captured by 3D-DIC is used for the estimation of the kinematic and volumetric conditions of the specimen at different stages of deformation, combined with the readings of the global axial compression of the specimen. This allowed for the characterization of a Mohr-Coulomb plasticity model with hardening and softening laws. In addition, a two-dimensional axisymmetric finite element model was built to simulate the actual experimental conditions, including both the global and local kinematics effects captured by 3D digital image correlation analysis on the boundary of the specimen. A comparison between the axisymmetic model predictions and the experimental observations showed good agreement, for both the global and local behavior, in the case of different sand specimen configuration, including loose, dense and half-loose half-dense specimens.Show more Item Drill pipe fatigue analysis in offshore application(Texas Tech University, 1986-12) Majumdar, Barun KantiShow more It is well known that the ball joint in marine riser can cause fatigue damage in the drill pipe passing through it. Previous investigators have assessed the damage done for a lower ball joint angle of 3-5 degrees (drilling) and 1-3 degrees (running casing). This research extends that work to deepwater operations in which an upper ball joint is also present. Also, it is shown, via finite element models, that tool joint bending stiffness has a significant effect on fatigue life. Fatigue damage calculations including this heretofore unconsidered effect are presented for various ball joint angles and drill pipe tensions.Show more Item Effects of selected parameters on thermal performance of earth sheltered housing(Texas Tech University, 1983-08) Young, Ren-tsengShow more Not availableShow more

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