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Adult-Acquired Flatfoot is a degenerative condition in which the ligaments and tendons supporting the arch deteriorate eventually leading to arch collapse. This deterioration can occur at various locations along the arch creating a number of different patterns of collapse. Surgical treatment for adult acquired flatfoot consists of a combination of various osteotomies. Although general guidelines exist, there is no systematic way to determine which combination of osteotomies should be used to correct a given foot deformity. Computer simulation with finite element analysis might provide an analytical tool to optimize the choice of osteotomy location and size. By dividing a complex problem into simpler components, finite element analysis allows for the solution of complex problems by solving a large set of simple equations. Finite element analysis has previously been used to study effects of diabetes, shoe design, and gait analysis in the foot. These studies have oversimplified geometry and material properties of foot tissues which limits the true mechanical behavior. The goal of this study was to create an anatomically and physiologically correct finite element model of the foot and ankle. To create a healthy foot model, CT scans were collected from one cadaver foot to create a three-dimensional cortical bone model in 3D Slicer software. The cortical bone model was imported into SolidWorks to create the geometry for trabecular bone, cartilage, ligaments, and tendons. Journal articles, textbooks, and other resources were used in order to create realistic cartilage, ligament, and tendon models (Netter & Colacino, 1997; see also Boss & Hintermann, 2002; Campbell et al., Apr. 2014; Golanó et al., 2010; Mahadevan). Final approval of the model’s geometry was obtained from the orthopaedic surgeon supervising this study. After completing the anatomically correct geometry of the foot, it was imported into finite element software (ANSYS, http://www.ansys.com/). The model was meshed with solid elements only: tetrahedral elements for the foot and hexahedral elements for the ground support. Linear elastic material properties were assigned to all bodies. Boundary conditions and contacts were created including a fixed ground support and bonded and frictionless contacts. A body weight force was applied to the tibia and tendon forces were applied to simulate loading during midstance. The frictionless contacts created a nonlinear problem that caused the simulation to fail to converge to a solution. Abnormally high stresses and deformation were found in the results. The foot model failed to converge to realistic results because of the current model’s complexity. An anatomically correct foot model was successfully created, but simplifications need to be made to the model in the future for convergence. Recommendations for simplification include modeling ligaments as truss elements, adding spring elements to tendons, and adding soft tissue or fat pads to the model. After simplifications are completed and realistic results are obtained, Flatfoot conditions and surgeries can be simulated and analyzed.

The theme of the research is on the use of the hypersingular boundary element method for the modelling of surface waves. Surface waves in solids are known to be partially reflected & transmitted and mode converted into body waves at stress discontinuities, which suggests that a formulation continuous in stress and strain might prove beneficial for modelling purposes. Such continuity can be achieved with a subparametric approach where the geometry is approximated using linear elements and the field variables, displacement and traction, are approximated using cubic Hermitian and linear shape functions respectively. The higher order polynomial for approximating displacement is intended to be a more accurate representation of the physics relating to surface wave phenomena, especially at corners, and thus, is expected to capture this behaviour with greater accuracy than the standard isoparametric approach. The subparametric approach affords itself to continuity in stress and strain by imposing a smoothness in the elements, which is not available to the isoparametric approach. As the attention is focused primarily on the modelling of surface waves on the boundary of a medium rather than the interior, the boundary element method lends itself appropriately to this end.A 2D semi analytical integration scheme is employed to evaluate the integrals appearing in the hypersingular boundary integral formulation. The integration scheme is designed to reduce the errors incurred when integrals with singular integrands are evaluated numerically. The scheme involves the application of Taylor expansions to formulate the integrals into two parts. One part is regular and is evaluated numerically and the other part is singular but sufficiently simple to be evaluated analytically. The scheme makes use of the aforementioned subparametric approach and is applied to linear elements for the use in steady state elastodynamic boundary element method problems. The steady state problem is used as it is a simplified problem and is sufficient to permit the investigation of surface vibration at a constant motion. The 2D semi analytical integration scheme presented can be naturally extended to 3D.A particular focus and novelty of the work is the application of different limiting approaches to determine the free terms common to boundary integral methods. The accurate numerical solution of hypersingular boundary integral equations necessitates the precise evaluation of free terms, which are required to counter discontinuous and often unbounded behaviour of hypersingular integrals at a boundary. The common approach for the evaluation of free terms involves integration over a portion of a circular/spherical shaped surface centred at a singularity and allowing the radius of the circle/sphere to tend to zero. This approach is revisited in order to ascertain whether incorrect results are possible as a consequence of shape dependency, which is a recognised issue for hypersingular integrals.Two alternative methods, which are shape invariant, are proposed and investigated for the determination of free terms. The first approach, the point limiting method, involves moving a singularity towards a shrinking integration domain at a faster rate than the domain shrinks. Issues surrounding the choice of approach, shrinkage rates and path dependency are examined. A related and second approach, the boundary limiting method, involves moving an invariant, but shrinking, boundary toward the singularity, again at a faster rate than the shrinkage of the domain. The latter method can be viewed as a vanishing exclusion zone approach but the actual boundary shape is used for the boundary of the exclusion zone. Both these methods are shown to provide consistent answers and can be shown to be directly related to the result obtained by moving a singularity towards a boundary, that is, by comparison with the direct method. Unlike the circular/spherical approach the two methods involve integration over the actual boundary shape and consequently shape dependency is not an issue. A particular highlight of the point limiting approach is the ability to obtain free terms in mixed formulation, which is not available to the circular/spherical approach.There are three numerical problems considered in this research. The first problem considers the longitudinal vibration of a square plate. This is a problem for which a known analytical solution exists and is used to verify the equation formulation and integration scheme adopted for the isoparametric and subparametric formulations. Both formulations are as accurate as each other and produce results that are in keeping with the analytical solution, thus instilling confidence in their predictions.The second problem considers the simulation of surface waves on a square plate. Various boundaries of a square plate have displacement conditions imposed on them as a result of surface wave propagation. The results indicate that the surface wave behaviour is not captured. However, the analytical solution does not make any consideration for the effects from corners; the analytical solution is for a Rayleigh wave propagating upon a planar surface. It does not take into account the wave phenomena encountered at corners. Therefore, these results cannot be used to validate the predictions obtained on the boundary of the problem considered. The purpose of this problem is to illustrate the impact of corners on the surface wave propagation. Sensitivity studies are conducted to illustrate the effect of corners on the computed solution at the boundary.The final problem considers the simulation of surface waves on a circular plate. Various portions of the boundary of the circular plate have displacement conditions imposed on them as a result of surface wave propagation on curved surfaces. The results indicate that the isoparametric and subparametric predictions are similar to one another. However, both displacement profiles predict the presence of other waves. Given the multi faceted nature of the mesh, the computed solution is picking up mode conversion and partial reflection & transmission of surface waves. In reality, this is not expected as the surface of the boundary is smooth. However, due to the discretisation there are many corners in this problem.

D.Ing. (Mechanical Engineering) / The local buckling of axially loaded thin walled circular aluminium tubes is investigated in this work. Various buckling modes can be identified depending on certain geometrical ratios. Tubes with a thickness to diameter ratio of between 0,016 and 0,1 will buckle according to the so called axi-symmetric mode which is a very efficient collapse mechanism for energy absorbing purposes. Although there are numerous analytical solutions for this collapse mode the results are not fully descriptive. A finite-element model was developed and is described in this work. With this model it is possible to analyse the collapse mechanism in detail and the results obtained compare favourably with experimental values. When a relatively long thin walled tube is loaded axially it will undergo Euler buckling. This is not an effective collapse mechanism for energy absorbing purposes and a concept that overcomes this disadvantage is presented. With this energy absorber it is possible for axially loaded longthin walled circular tubes to collapse into a mode that resembles the axi-symmetric collapse mode. A finite element model was developed and successfully used to analyse the proposed concept. The results obtained correlate well with experimental values. A low speed impact test rig was designed, manufactured and commissioned. This rig was used to conduct dynamic tests on the proposed energy absorber and it was concluded that the proposed concept is viable for applications that require an inexpensive, reliable energy absorber with a long strokelength.

The energy convergence of mixed methods of approximate analysis for problems involving linear self-adjoint operators is investigated. A new energy product and the associated energy norm are defined for such indefinite systems and then used in establishing the strain energy convergence and estimation of error for problems in continuum mechanics. In the process, the completeness requirements are laid out for approximate solutions. Also established is the mean convergence of the basic variable e.g. displacements and stresses. After accomplishing a new mathematical framework for the mixed methods in continuum, the theory is then extended to the finite element method. The completeness requirements, convergence criteria and the effect of continuity requirements on convergence are established. The flexibility offered by the mixed methods in incorporating the boundary con ditions is also demonstrated. For stress singular problems, the strain energy convergence is established and an energy release method for determining the crack intensity factor K. is presented. A detailed eigenvalue-eigenvector analysis of the mixed finite element matrix is carried out for various combinations of interpolations for the plane stress linear elasticity and the linear part of the Navier-Stokes equations. Also discussed is its relation to the completeness requirements. Finally, numerical results are obtained from applying the mixed finite element method to several examples. These include beam bending, a plane stress square plate with parabolically varying end loads, a plane stress cantilever and plane strain stress concentration around a circular hole. A plane stress example of a square plate with symmetric edge cracks is also solved to study the strain energy convergence. Lastly, two rectangular plates, one with symmetric edge cracks and the other with a central crack are considered to determine the crack intensity factor K. In most of the examples, the strain energy convergence rates are predicted and compared with the numerical results, and excellent agreement is observed. / Applied Science, Faculty of / Civil Engineering, Department of / Graduate

archives@tulane.edu / This dissertation combines laboratory experiments with analysis of field samples and geochemical modeling to examine rare earth elements (REEs) geochemistry. The Mississippi River estuary, Louisiana and the Pettaquamscutt River estuary, Rhode Island provided ideal study sites to investigate the effects of salinity and redox gradients, respectively, on the cycling of the REEs in natural environments. Similar to the REE behavior in major estuaries such as the Amazon estuary, the REEs in the Mississippi River undergo salt-induced coagulation removal during mixing with the saline Gulf of Mexico seawater. However, unlike the Amazon estuary in which dissolved REE removal of up to 90% has been reported, only ca. 50% removal is observed in the Mississippi River estuary. The closed-system batch reaction experiment which followed showed that interactions with the Mississippi River particulate material substantially alter the dissolved REE concentrations of the Gulf of Mexico seawater. Combined effects of dissolution of the labile phases on the riverine particles and secondary mineral precipitation of likely REE phosphate phases result in a 24 ± 12 folds (mean ± 1σ) net increase in the REE concentrations of the seawater. Less than 1% of the REE contents in the operationally defined “exchangeable” phase of the sediments was mobilized at the maximum REE concentrations in the reacted seawater. The behavior of the REEs in the Pettaquamscutt River estuary is coupled with the cycling of Fe and Mn oxides/oxyhydroxides in the oxic surface waters and across the chemocline. Reaction path modeling suggests that the REE content of the oxic surface waters depicts a combined effect of mixing of 3 water masses and surface complexation with hydrous manganese oxides to achieve the cerium depleted pattern that characterizes the entire water column. / 1 / Segun Adebayo

Bibliography: pages 94-99. / This thesis describes work performed to establish and demonstrate a quantitative trace element microanalysis technique for geological material using protons accelerated by the Van de Graaff Accelerator at the National Accelerator Centre (NAC) in Faure near Cape Town. The method relies on the analysis of Proton Induced X-ray Emission (PIXE) spectra, interpreted with the help of the GeoPIXE software package. The use of the Si(Li) energy dispersive detector provides simultaneous multi-element detection at the parts-per-million (ppm) level, and a scanning beam facility permits trace element distributions to be studied at these levels. The calibration of the detector efficiency and the thicknesses of selectable X-ray attenuating filters was performed using pure elemental samples. This involved the accurate determination of the target to detector distance, the thickness of the active volume of the Si(Li) detector crystal, the thicknesses of all the absorbing layers between the sample and the detector crystal, and the assessment of the effects of incomplete charge collection in the detector.

Ports and waterways are vital to the economy of the United States. In the contiguous United States, there are some 25,000 miles of channels and over 300 ports. Together, this system carries 2 billion tons of freight with a value of over $700 billion annually. Ninety percent of all United States imports and exports travel through these ports and waterways. Dredging of these waterways in the United States costs over $1 billion annually. As ship draft increases, more dredging would be required to keep these ports and waterways open. Fine sediments are very common in these systems and have properties that can reduce dredging efficiency, including easy resuspension into the water column and cohesion among individual particles. Fluid mud is a high concentration aqueous solution of fine sediments that exhibits unique properties, including movement under gravity. A numerical model of fluid mud could be used to predict sediment fate as well as evaluating potential channel modifications to reduce dredging. The goal of this research is to test the flow of fluid mud under shear from the water column and develop a numerical model to simulate the transport of fluid mud. First, laboratory experiments are conducted to ascertain the effects of shear from the water column on the fluid mud layer. Next, a finite element numerical model is developed to simulate the physics of fluid mud, including any effects from shear over the mud layer. Results from the numerical model are compared to laboratory experiments, and the fluid mud model is developed for easy linkage to existing hydrodynamic models for forcing information.

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