# Browsing by Subject "Finite element method"

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Item Acoustic radiation force and torque on a sphere or spheroid near a boundary(2023-08-15) Simon, Blake Elliott; Hamilton, Mark F.; Haberman, Michael R; Wilson, Preston S; Ling, Hao; Gunderson, Aaron MShow more This dissertation is a study of the acoustic radiation force and torque on a sphere or spheroid in an inviscid fluid near a planar boundary. First, a linear analytical solution for the acoustic scattering by the object and boundary is derived. The solution is based on expansion of the pressure field in spherical or spheroidal wave functions. The condition at the boundary is satisfied using the method of images, which is exact for rigid and pressure release boundaries. The analytical solution imposes no restriction on the structure of the incident field or size of the object. An approximation is introduced that extends the analytical solution to other types of boundaries, including a fluid-fluid interface. Next, the expansion coefficients in the linear solution are substituted into a known analytical expression for the acoustic radiation force and torque on the sphere or spheroid that follows from integration of the radiation stress tensor. The radiation force and torque are also modeled numerically using the finite element method, which is used to validate results from the analytical model. The finite element model is less computationally efficient than the analytical model, but it can be used for objects of any shape. Calculations based on both models illustrate the influence of multiple scattering effects between the object and the boundary on the radiation force and torque acting on the object. Radiation force on a polypropylene sphere in water was measured as a function of distance from a reflecting surface in the presence of an incident sound beam. The force was measured by forming a pendulum with the sphere and tracking its displacement. Measurements of the radiation force on the sphere are compared with the analytical model.Show more Item Adaptive finite element method for multiphase flow and poroelasticity(2022-09-12) Li, Hanyu; Wheeler, Mary F. (Mary Fanett); Foster, John T; Hughes, Thomas J; Arbogast, Todd J; Prodanovic, MasaShow more Numerical simulation of subsurface flow for applications such as carbon sequestration and nuclear waste deposit has always been a computational challenge. The main reason points to the strong nonlinearity inherited in the governing equations that describe the multiphysics phenomena. The enormous number of unknowns and small timesteps required for stable Newtonian convergence make this type of problems computationally exhaustive. To address this issue, we introduce adaptive finite element approaches guided by a posteriori error estimators to improve computational efficiency. A space-time discretization scheme with temporal and spatial mesh adaptivity is formulated for multiphase flow system. The solution algorithm adopts a geometric multigrid procedure that starts with solving the system in the coarsest resolution and locally refines the mesh in both space and time. Error estimators that measure the spatial and temporal discretization error are employed to guide such an adaptivity. These estimators provide a global upper bound on the dual norm of the residual and the non-conformity of the numerical solution. Results from two-phase immiscible and three-phase miscible flow are presented to confirm solution accuracy and computational efficiency as compared to the uniformly fine timestep and fine spatial discretization solution. We also resolve the common issue of high frequency residuals in multigrid methods by local residual minimization and dynamic advection-diffusion coupling to achieve additional computational speedup and stability. In addition to the multiphase flow models, we also study the Biot system that couples poromechanics with flow. A posteriori error estimators are derived with the flow and mechanics solved by mixed finite element formulation and continuous Galerkin respectively in a fixed-stress split algorithm. The effectivity of such estimators is validated by Mandel’s problem which enable us to compute the a priori error with its analytical solution. We demonstrate the efficiency of the estimators for adaptive mesh refinement using a fractured porous media example. The validity of the novel stopping criterion which balances the fixed-stress algorithm error with the discretization error is confirmed afterwards. We aim to ultimately provide efficient computations for high fidelity models from carbon sequestration and underground hydrogen storage scenarios.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 Algebraic coupling of 2D and 3D shallow water finite element models(2017-05) Choudhary, Gajanan Krishna; Dawson, Clinton N.Show more Baroclinicity in oceans may necessitate the use of 3D shallow water (SW) models for accurate description of physics. Particularly for baroclinic flows near coastal areas where frequent wetting and drying occurs due to tides and wind, we need a 3D SW model that can handle wetting and drying. Various methods for wetting and drying in 2D SW models are available, but for 3D SW models, wetting-drying remains a challenge. We propose using non-overlapping coupled 2D-3D models for taking advantage of well-tested 2D wetting-drying techniques and avoiding the complexities of 3D wetting and drying. We develop a theory for algebraic coupling of 2D and 3D SW models in a conforming, continuous Galerkin finite element framework, with mass and momentum conservation across the 2D-3D interface built into the coupling. This leads to a monolithic system of equations to be solved at each time step. The theory reduces to the usual finite element method when applied to 2D-2D or 3D-3D coupling. We verify 2D-3D coupling against two test cases with known analytical solutions. The results of 2D-3D coupled models for the test cases are in good agreement with the analytical solution and those of equivalent full-2D and full-3D SW models.Show more Item An evaluation of competing geoacoustic models and their applicability to sandy ocean sediments(2017-12-01) Bonomo, Anthony Lucas; Hamilton, Mark F.; Isakson, Marcia J.; Wilson, Preston S; Ghattas, Omar; Kallivokas, Loukas FShow more This dissertation studies five models that make up a cross section of the geoacoustic models that have been used to study sandy sediments: a simple fluid model, the effective density fluid model (EDFM) of Williams, the viscous grain-shearing (VGS[lambda]) model of Buckingham, the Biot-Stoll model, and the corrected and reparameterized extended Biot (CREB) model of Chotiros. The first objective is to use numerical experiments and model/data comparisons to determine the usefulness and assess the physical validity of these five models. The second objective is to ascertain the current state of knowledge of sandy sediments and describe what truths can be learned from model/data comparisons. To complete these objectives, the models' predictions of geoacoustic quantities such as wave speeds, attenuations, and bottom loss are compared with published measurements and to each other through Bayesian inference and computational studies. It is determined that while each model has its uses, no one model fully captures the wave physics of sandy sediments.Show 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 The research presented in this document is an in-depth analytical study of the bond behavior of strand in the end region of pre-tensioned prestressed concrete members, especially with respect to the transfer and development length of fully bonded and debonded strands. A detailed analytical investigation of several significant test specimens from Project 1210 and U-Beams from Project 9-580 was performed using the finite element method and other numerical methods. Additionally, an axi-symmetric finite element analysis of concrete cylinders containing fully bonded and debonded strands was performed to study the state of stress in the concrete surrounding the strands just after transfer of prestress. The current investigation involved developing a technique to model the transfer and flexural bond zone of a pre-tensioned member. The modeling approach developed for this research allowed for slip between the strand and the concrete in the transfer and flexural bond zone of the member. The FE analysis also allowed for modeling the cracking and crushing of the concrete, and modeling of the non-linear behavior of the strand. A typical analysis of a specimen involved comparing the external parameters such as the load-deflection relationship and the overall cracking response from the test and the analysis. Assuming a favorable comparison of the external parameters, which was usually obtained, the internal parameters such as the bond stress, steel stress and concrete stress profiles determined analytically were examined for the entire loading history of the test. This information could not be determined experimentally, and hence knowledge of the internal parameters provided an in-depth understanding of the actual behavior of each test specimen during the course of the test. The results from the analytical and experimental work were used to develop a simple behavioral model to determine the development length of 0.5-inch and 0.6- inch strand for any pre-tensioned member containing fully bonded and debonded strands. The model was tested against the different test series from Project 1210 and other relevant research studies. The research study concluded with a brief discussion on code implications and general recommendations for design.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 Characterization of Unbound Granular Layers in Flexible Pavements(2001-12) Adu-Osei, AlexShow more The mathematical characterization of unbound granular materials should ideally be based on the behavior of the individual constituent elements and their interaction. Until particulate mechanics are developed to a level where it can easily be applied to characterize unbound granular materials, a nonlinear and cross-anisotropic model must be used to characterize the behavior of granular materials in pavements. Existing pavement design and analysis methods have generally taken a very conservative view of the relative strength properties of granular materials used as base and subbase layers in conventional flexible pavements. The mechanical properties of unbound granular layers in flexible pavements are important to the overall structural integrity of the pavement structure. Linear elastic analysis can be used with reasonable confidence for pavements with full depth asphalt layers, but it is inappropriate for unsurfaced or thinly surfaced flexible pavements unless the nonlinear behavior of unbound granular materials are properly taken into account. Work done by several researchers suggest that incorporating a cross-anisotropic elastic model significantly improves isotropic models and drastically reduces the tensile stresses computed within granular layers. This is due to the fact that the behavior of granular materials depends on particle arrangement. The laboratory determination of cross-anisotropic properties of granular materials has been a difficult task for researchers. In this study, a new laboratory testing protocol has been developed based on the theories of elasticity to determine cross-anisotropic properties of granular materials. The testing protocol is efficient and precise. The test is also an excellent tool for comparative analysis of compacted materials. The behavior of four unbound granular materials was studied. The resilient responses of the materials obey the Uzan type nonlinear model. It was observed that under low stress levels accumulation of permanent strain could stabilize in granular layers. However, at high stress levels, permanent strain will continuously accumulate. A finite element program was modified to incorporate the cross-anisotropic material model. Pavement sections were analyzed with the finite element program. It was observed that cross-anisotropic modeling eliminates the presence of tension zones predicted by isotropic resilient models. Deflection bowls predicted by nonlinear resilient models agree with field deflection bowls.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 Earthquakes and slip transients through multi-dimensional and multi-physics thermomechanical modeling(2019-09-19) Tong, Xinyue; Lavier, Luc Louis; Choi, Eunseo; Gulick, Sean S; Ghattas, Omar N; Taylor, Frederick WShow more I study the physics and mechanics underlying seismic and aseismic slip. The slip behaviors are simulated by applying the rate and state friction formulation at steady state to 2D and 3D fault zones of finite thickness. The evolutionary frictional effect is modeled by the history-dependent stress and strain evolution in our model. The motivation of this research and summary of the rock friction laws’ development and application from a long-term tectonic (LTT) modeling point of view are covered in the first chapter. In the second chapter, I model fast and slow slip that have characteristics of earthquakes and slow slip events (SSEs) in which SSEs emerge at a critical friction-drop, ∆μ_c. The simulated earthquakes and SSEs have the same scaling as natural event for both stress and strain drop, as both type of events originate from shear failure. Co-seismic slip and moment release versus slip duration scale differently for earthquakes (cubic) and SSEs (linear), which indicate that energy is preferentially dissipated as kinetic energy for earthquakes. In my third chapter, I show that transients can arise spontaneously for mixed-brittle-ductile fault zones. Geological observations indicate that the core material composition in faults is highly heterogeneous. Brittle and ductile materials have velocity weakening and strengthening slip behaviors, respectively. Simulation results show that the semi-brittle shear zone forms complex fracture networks. Creeps and transients slip along few discrete fault surfaces. During earthquakes, both shear and tensile failures overwhelm the whole shear zone. This study confirms that fault core composition plays a critical role in determining slip behavior. In the last chapter, I investigate the effect of fault zone materials’ frictional properties on coseismic shallow slip deficit (SSD) at strike-slip faults. Our modeling approach generates coseismic slip profile that matches the SSD, the depth of peak slip, and the slip distribution below seismogenic zone that obtained from geodetic studies. Simulation results indicate that the frictional parameter distribution is the main factor controlling the fault zone coseismic slip profile. This study also shows that, contrary to the common belief, the shallow part of the strike-slip fault zone may have a velocity weakening slip behavior.Show more Item Electromechanical coupling behavior of dielectric elastomer composites(2016-12) Scurlock, Ryan Steven; Landis, Chad M.Show more Dielectric elastomers have gained substantial interest in the past few decades under research efforts aimed to improve electromechanical transducer technology. This material is often termed a “smart material” due to its intrinsic transduction properties, allowing the elastomer to deform in response to electric stimulation. High mechanical compliance, lightweight, low cost, and the ability to achieve enormous voltage induced strains make dielectric elastomers excellent candidates to serve as electromechanical transducers, both as high efficiency actuators and energy harvesters. This work is focused on increasing the transduction efficiency of dielectric elastomers, strengthening their potential effectiveness as a transducer. To enhance the electrostriction of the material, a composite concept is introduced where rigid conducting fibrous electrodes are embedded into the dielectric. A combined theoretical and numerical modeling framework is developed to analyze the electromechanical behavior of several different composite arrangements. In order to examine the large mechanical deformations of the elastomer, a finite deformation theory is required for the description of the material behavior. To describe the material free energy, a compressible Neo-Hookean model is utilized. The finite element method is used for the numerical solution technique to the boundary value problem.Show more Item Field Validation of the Cross-Anisotropic Behavior of Unbound Aggregate Bases(2001-03) Tutumluer, Erol; Adu-Osei, Alex; Little, Dallas N.; Lytton, Robert L.Show more The ICAR Research Project 502 has focused on determining structural considerations of unbound aggregate pavement layers for a proper representation in the new AASHTO Pavement Design Guide 2002. The research team developed models for the resilient and permanent deformation behavior from the results of triaxial tests conducted at the Texas Transportation Institute (TTI) and at the University of Illinois. The studies have mainly indicated that the unbound aggregate base (UAB) material should be modeled as nonlinear and cross-anisotropic to account for stress sensitivity and the significant differences between vertical and horizontal moduli and Poisson's ratios. UABs were constructed at the TTI Riverside research facility and tested for response and performance using the one-third scale model of the Texas Mobile Loading Simulator. The resilient responses of the test sections were modeled. The nonlinear cross-anisotropic material models used in the base layer predicted vertical deflections that are close to field deflections in the analyzed TTI pavements. Field validation data were also collected from a full-scale pavement test study conducted at Georgia Tech. The test sections had extensive instrumentation and the pavement response variables, such as stresses, strains, and deformations, were measured in all pavement layers including the UABs. The validation of the anisotropic modeling approach was accomplished by analyzing these test sections using GT-PAVE finite element program, predicting UAB responses, and comparing them to the measured ones. Laboratory testing of the aggregate samples was conducted at the University of Illinois and the characterization models were developed for the stress sensitive, cross-anisotropic aggregate behavior. With nonlinear anisotropic modeling of the UAB, the resilient behavior of pavement test sections was successfully predicted at the same time for a number of response variables. In addition, the stress sensitive, cross-anisotropic representation of the base was shown to greatly reduce the horizontal tension computed in the granular base when compared to a linear isotropic representation.Show more Item Finite element investigation of tunable and non-reciprocal elastic wave metamaterials(2019-05-08) Goldsberry, Benjamin Michael; Haberman, Michael R. (Michael Richard), 1977-; Hamilton, Mark F; Seepersad, Carolyn C; Kallivokas, Loukas F; Norris, Andrew NShow more This dissertation studies elastic wave propagation in metamaterials subjected to an externally-applied static or spatiotemporally-varying pre-strain. Elastic metamaterials are media with subwavelength structure that behave as effective materials displaying atypical effective dynamic properties that are used to directly control the propagation of macroscopic waves. One major design limitation of most metamaterial structures is that the dynamic response cannot be altered once the microstructure is manufactured. However, the ability to modify, or tune, wave propagation in the metamaterial with an external pre-strain that induces geometric nonlinearity is highly desirable for numerous applications. Acoustic and elastic metamaterials with time- and space-dependent effective material properties have also recently received significant attention as a means to induce non-reciprocal wave propagation. However, the modulation of effective material properties in space and time using mechanical deformation has been unexplored. Tunable elastic metamaterials that exhibit large effective material property changes under a varying external pre-strain are therefore strong candidates for a non-reciprocal medium. The complex geometry present in unit cells that exhibit large geometric nonlinearity necessitates the development of a numerical technique. In this dissertation, a finite element approach is derived and implemented to study elastic wave propagation in a static pre-strained metamaterial, then generalized to include the effects of a spatiotemporally-varying pre-strain. A honeycomb structure composed of a doubly-periodic array of curved beams, known as a negative stiffness honeycomb (NSH), is analyzed as a tunable and non-reciprocal elastic metamaterial. It is shown that NSH exhibits significant tunability and a high degree of anisotropic wave behavior when a static pre-strain is imposed. This behavior can be used to guide wave energy in different directions depending on static pre-strain levels. In addition, it is shown that partial band gaps exist where only longitudinal waves propagate. The NSH therefore behaves as a meta-fluid, or pentamode metamaterial, which may be of use for applications of transformation elastodynamics such as cloaking and gradient index lens devices. A negative stiffness chain, a quasi-one-dimensional representation of NSH, is also shown as a case example of a non-reciprocal medium. It is shown in this work that this structure displays a high degree of non-reciprocity for a small amount of modulation pre-strain. The utility of the finite element approach is further demonstrated by investigating the effects of chiral geometric asymmetry to enhance the non-reciprocal behavior of elastic wave propagation in NSH.Show more Item Finite element modeling of the stability of single wellbores and multilateral junctions(2003) López Manríquez, Alberto; Podio, A. L.; Sepehrnoori, Kamy, 1951-Show more This dissertation describes investigation of the stability of single holes and multilateral junctions in order to optimize their design. The investigation is based on finite element three-dimensional modeling using the commercial software ABAQUS. The stability of single holes and multilateral junctions was analyzed at different orientations in a three-dimensional in-situ stress field. Traditional stressdisplacement analysis in steady-state was coupled with transient phenomena to compute strain and stress behaviors and changes in pore pressure due to disturbances created by drilling. This coupled analysis allowed for the inclusion of time dependent processes and the non-linear processes that influence the behavior of the system compounded by rock, fluids contained in the rock, and insitu stresses. The three-dimensional wellbore stability modeling presented here overcomes the limitations of common assumptions in wellbore stability analysis, such as linear poroelasticity, homogeneous and isotropic formations, and isotropic in-situ stress field, because this modeling accounts for the sources of non-linearity affecting the strain and stress responses of rock. This study showed that precise knowledge of the in-situ stress field is an important geomechanical parameter needed to optimize the orientation of a single wellbore and the orientation of the lateral at the junction in a multilateral scenario regarding stability. In addition, performing stress-displacement analysis of multilateral junctions identified critical areas regarding failure in the junction area. Geometry, placement, and orientation of the junction were analyzed, and the results provided a real insight to propose strategies to optimize drilling and completion design of multilateral wells. Comparisons of the predictions of this numerical approach with experimental data recently published showed that this numerical approach is reliable for simulating the steady-state phenomena and some transient phenomena encountered in wellbore stability analysis of both single holes and multilateral junctions.Show more Item Finite element study of a heated thin fluid layer including surfactant effect(2002) Wang, Xiaowen; Carey, Graham F.Show more This investigation deals with modeling and numerical approximation of thermocapillary and surfactant effects in long wavelength evolution of thin liquid layers. We consider several aspects including: model development, scaling and perturbation analysis, variational formulations, finite element approximation and solution strategies for these problems. Issues related to treating the fluid volume constraint within this variational finite element setting are also considered. A linear stability analysis of the nonlinear thermocapillary problem is developed and its implications are explored numerically over the related parameter space. In the inclined plane case for the thermocapillary problem, it is observed in the time dependent finite element solutions that a slight inclination of the system may give rise to premature onset of instability. We also extend the treatment of the physical problem to include an insoluble surfactant monolayer and develop a supporting perturbation analysis. The resulting more complex model involves coupling to an additional transport equation for surfactant concentration on the surface. We develop the variational formulation, finite element implementation and stability analysis of this coupled system. We characterize the stability behavior into four parametric regions based on linear stability analysis and verify the behavior using finite element approximation of time dependent solutions on one and two-dimensional spatial domains.Show more Item Fully automatic hp-adaptivity for acoustic and electromagnetic scattering in three dimensions(2007-05) Kurtz, Jason Patrick, 1979-; Demkowicz, LeszekShow more We present an algorithm for fully automatic hp-adaptivity for finite element approximations of elliptic and Maxwell boundary value problems in three dimensions. The algorithm automatically generates a sequence of coarse grids, and a corresponding sequence of fine grids, such that the energy norm of error decreases exponentially with respect to the number of degrees of freedom in either sequence. At each step, we employ a discrete optimization algorithm to determine the refinements for the current coarse grid such that the projection-based interpolation error for the current fine grid solution decreases with an optimal rate with respect to the number of degrees of freedom added by the refinement. The refinements are restricted only by the requirement that the resulting mesh is at most 1-irregular, but they may be anisotropic in both element size h and order of approximation p. While we cannot prove that our method converges at all, we present numerical evidence of exponential convergence for a diverse suite of model problems from acoustic and electromagnetic scattering. In particular we show that our method is well suited to the automatic resolution of exterior problems truncated by the introduction of a perfectly matched layer. To enable and accelerate the solution of these problems on commodity hardware, we include a detailed account of three critical aspects of our implementations, namely an efficient implementations of sum factorization, several interfaces to the direct multi-frontal solver MUMPS, and some fast direct solvers for the computation of a sequence of nested projections.Show more Item Hamilton's equations with Euler parameters for hybrid particle-finite element simulation of hypervelocity impact(2002) Shivarama, Ravishankar Ajjanagadde; Fahrenthold, Eric P.Show more Hypervelocity impact studies (impact velocities > 1 km/sec) encompass a wide range of applications including development of anti-terrorist defense and orbital debris shield for the International Space Station (ISS). The focus of this work is on the development of a hybrid particle-finite element method for orbital debris shield simulations. The problem is characterized by finite strain kinematics, strong energy domain coupling, contact-impact, shock wave propagation and history dependent material damage effects. A novel hybrid particle finite element method based on Hamilton’s equations is presented. The model discretizes the continuum of interest simultaneously (but not redundantly) into particles and finite elements. The particles are ellipsoidal in shape and can translate and rotate in three dimensional space. Rotation is described using Euler parameters. Volumetric and contact impact effects are modeled using particles, while strength is modeled using conventional Lagrangian finite elements. The model is general enough to accommodate a wide range of material models and equations of state.Show more Item A hybrid-stress finite element approach for stress and vibration analysis in linear anisotropic elasticity(1987) Mahadevan, L. (Lakshminarayanan); Oden, J. Tinsley (John Tinsley), 1936-Show more A hybrid-stress finite element method is developed for accurate stress and vibration analysis of problems in linear anisotropic elasticity. A modified form of the Hellinger-Reissner principle is formulated for dynamic analysis and an algorithm for the determination of the anisotropic elastic and compliance constants from experimental data is developed. These schemes have been implemented in a finite element program for static and dynamic analysis of linear anisotropic two-dimensional elasticity problems. Specific numerical examples are considered to verify the accuracy of the hybrid-stress approach and compare it with that of the standard displacement method, especially for highly anisotropic materials. It is that the hybrid-stress approach gives significantly better results than the displacement method. Preliminary work on extensions of this method to three-dimensional elasticity is discussed, and the stress shape functions necessary for this extension are includedShow more

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