Background: Osteoarthritis (OA) is a debilitating joint disease marked by cartilage and bone changes. Morphological and mechanical changes to bone, which are thought to increase overall bone stiffness, result in distorted joint mechanics and accelerated cartilage degeneration. Using a parametric finite element (FE) model of the proximal tibia, the primary objective of this study was to determine the relative and combined effects of OA-related osteophyte formation, and morphological and mechanical alterations to subchondral and epiphyseal bone on overall bone stiffness. The secondary objective was to assess how simulated bone changes affect load transmission in the OA joint. Methods: The overall geometry of the model was based on a segmented CT image of a cadaveric proximal tibia used to develop a 2D, symmetric, plane-strain, FE model. Simulated bone changes included osteophyte formation and varied thickness and stiffness (elastic modulus) in subchondral and epiphyseal bone layers. Normal and OA related values for these bone properties were based on the literature. “Effective Stiffness (K)” was defined as the overall stiffness of the proximal tibia, calculated using nodal displacement of the loaded area on the subchondral cortical bone surface and the load magnitude. Findings: Osteophyte formation and thickness or stiffness of the subchondral bone had little effect on overall bone stiffness. Epiphyseal bone stiffness had the most marked effect on overall bone stiffness. Load transmission did not differ between OA and normal bone. Interpretation: Results suggest that epiphyseal (trabecular) bone is a key site of interest in future analyses of OA and normal bone. Results also suggest that observed OA-related alterations in epiphyseal bone may result in OA bone being more flexible than normal bone.

The use of energy methods and variational principles is widespread in many fields of engineering of which structural mechanics and curve and surface design are two prominent examples. In principle many different types of function can be used as possible trial solutions to a given variational problem but where piecewise polynomial behaviour and user controlled cross segment continuity is either required or desirable, B-splines serve as a natural choice. Although there are many examples of the use of B-splines in such situations there is no common thread running through existing formulations that generalises from the one dimensional case through to two and three dimensions. We develop a unified approach to the representation of the minimisation equations for B-spline based functionals in tensor product form and apply these results to solving specific problems in geometric smoothing and finite element analysis using the Rayleigh-Ritz method. We focus on the development of algorithms for the exact computation of the minimisation matrices generated by finding stationary values of functionals involving integrals of squares and products of derivatives, and then use these to seek new variational based solutions to problems in the above fields. By using tensor notation we are able to generalise the methods and the algorithms from curves through to surfaces and volumes. The algorithms developed can be applied to other fields where a variational form of the problem exists and where such tensor product B-spline functions can be specified as potential solutions.

This thesis reports onreview and research work carried out on the numerical analysis of elastomers. The two numerical techniques investigated for this purpose are the finite and boundary element methods. The finite element method is studied so that existing theory is used to develop a finite element code both to review the finite element method as applied to the stress analysis of elastomers and to provide a comparison of results and numerical approach with the boundary element method. The research work supported on in this thesis covers the application of the boundary element method to the stress analysis of elastomers. To this end a simplified regularization approach is discussed for the removal of strong and hypersingularities generated in the system on non-linear boundary integral equations. The necessary programming details for the implementation of the boundary element method are discussed based on the code developed for this research. Both the finite and boundary element codes developed for this research use the Mooney-Rivlin material model as the strain energy based constitutive stress strain function. For validation purposes four test cases are investigated. These are the uni-axial patch test, pressurized thick wall cylinder, centrifugal loading of a rotating disk and the J-Integral evaluation for a centrally cracked plate. For the patch test and pressurized cylinder, both plane stress and strain have been investigated. For the centrifugal loading and centrally cracked plate test cases only plane stress has been investigated. For each test case the equivalent results for an equivalent FEM program mesh have been presented. The test results included in this thesis prove that the FE and BE derivations detailed in this work are correct. Specifically the simplified domain integral singular and hyper-singular regularization approach was shown to lead to accurate results for the test cases detailed. Various algorithm findings specific to the BEM implementation of the theory are also discussed.

No description available.

No description available.

No description available.

Motor vehicle accidents continue to be a leading cause of cervical spine injury despite a conscientious effort to improve occupant safety. Accurately predicting occupant head and neck response in numerical crash simulations is an essential part of the process for developing better safety solutions. <br /><br /> A biofidelic model of the human cervical spine was developed with a focus on accurate representation of the cervical spine at the local tissue level. These tissues were assembled to create a single segment model that was representative of <em>in vitro</em> spine in quasi-static loading. Finally, the single segment models were assembled to create a full cervical spine model that was simulated in dynamic loading and compared to human volunteer response. <br /><br /> Models of each segment were constructed from the basic building blocks of the cervical spine: the intervertebral disc, the vertebrae, the ligaments, and the facet joints. Each model was simulated in all modes of loading and at different levels of load. The results of the study indicate that the cervical spine segments performed very well in flexion, compression, and tension. Segment response to lateral bending and axial rotation was also good, while response in extension often proved too compliant compared to the experimental data. Furthermore, the single segment models did not fully agree with the experimental shear response, again being more compliant. <br /><br/> The full cervical spine model was assembled from the single segment models incorporating neck musculature. The model was simulated dynamically using a 15 G frontal impact test. Active muscles were used to simulate the response of the human volunteers used in the study. The response of the model was in reasonable agreement with the experimental data, and compared better than current finite element cervical spine models. Higher frequency oscillation caused most of the disagreement between the model and the experimental data, which was attributed to a lack of appropriate dynamic material properties of the soft tissues of the spine. In addition, a study into the active properties of muscle indicated that muscle response has a significant influence on the response of the head. <br /><br /> A number of recommendations were proposed that would improve the biofidelity of the model. Furthermore, it was recommended that the future goal of this model would be to implement injury-predicting capabilities through the development of advance material models.

Two efficiency-based grid refinement strategies are investigated for adaptive finite element solution of partial differential equations. In each refinement step, the elements are ordered in terms of decreasing local error, and the optimal fraction of elements to be refined is deter- mined based on e±ciency measures that take both error reduction and work into account. The goal is to reach a pre-specified bound on the global error with a minimal amount of work. Two efficiency measures are discussed, 'work times error' and 'accuracy per computational cost'. The resulting refinement strategies are first compared for a one-dimensional model problem that may have a singularity. Modified versions of the efficiency strategies are proposed for the singular case, and the resulting adaptive methods are compared with a threshold-based refinement strategy. Next, the efficiency strategies are applied to the case of hp-refinement for the one-dimensional model problem. The use of the efficiency-based refinement strategies is then explored for problems with spatial dimension greater than one. The work times error strategy is inefficient when the spatial dimension, d, is larger than the finite element order, p, but the accuracy per computational cost strategy provides an efficient refinement mechanism for any combination of d and p.

This thesis presents a numerical model for determining piezoelectric and non-linear elastic properties of piezoelectric composites consisting of nanotubes in a polymer matrix. Finite Element Analysis (FEA), in conjunction with the Embedded Fiber Method (EFM), is used, and variable nanotube geometry, alignment, and waviness are taken into account. First, a random morphology of a user-defined volume fraction of nanotubes is generated, and their properties are incorporated into the polymer matrix using the EFM. Next, the system is solved and the values are post-processed to determine the effective elastic and piezoelectric properties of the composite. Finally, incremental FEA approaches are used for the determination of the non-linear properties of the nanocomposite. Monte Carlo Analysis of five hundred random microstructures is performed to capture the stochastic nature of the fiber generation and to derive statistically reliable results. The models are validated by comparison with theoretical and experimental data reported in recent literature.

The project is a research on liquid methane. It is stored in a standing and static pressure vessel specially calculated for cryogenic purposes. All the simulations have been done using the finite element method.  The  finite  element  method  (FEM)  or  finite  element  analysis  (FEA)  is  a  numerical technique to find approximate solutions for partial differential equations and it is used to simulate the strength of materials. FEM allows the user to visualize the distribution of stresses and displacements. There is a wide range of software to do FEM simulations, the software chosen for the project is Pro/Engineer Wildfire 4.0.  Pro-Engineer  is  a  CAD/CAM/CAE  software  developed  by  Parametric  Technology Corporation (PTC).  It provides solid modeling, assembly modeling and finite element analysis.  The  results  obtained  in  the  mechanical  analysis  executed  with  the  application  Pro-mechanica show that the designed container holds the loads applied and stands stable.  The thermal analysis of the insulation verifies that the amount of heat exchanged with the environment is on acceptable levels. Finally, to protect the integrity of the structure the proper paints have been selected.