Determination of the stress distributions in post-core restored endodontically treated teeth is challenging due to the fact that the post and core systems, the root and its canal, and the bony structures supporting the root have small dimensions and are structurally complex. In this research, a 3D finite element model was developed to evaluate the stress distributions in a post-core restored endodontically treated maxillary incisor under various static loads. The physical model includes dentin, PDL, bone, post, core, gutta percha and crown. All materials are assumed to be homogenous, isotropic, and linear elastic. The effects of various factors on the stress distributions are investigated through simulations. These factors include post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters. It has been found that the horizontal loading is the most dangerous, which causes the highest stresses in dentin and posts, followed by the oblique loading and the vertical loading. The above listed factors, such as post materials, post and core combinations, ferrule heights, post and dentin gaps at the coronal entrance of the canal, and canal diameters, do not change the stress distributions and magnitudes significantly under horizontal and oblique loading. However, the stresses are sensitive to the above factors under the vertical loading, and it has been found that the stress distributions in both dentin and the post are the most uniform without stress concentrations when the elastic modules of the post and the core are similar to that of dentin. Regarding the effects of the gaps at the cervical region on the stress distributions in dentin, the high stresses at the apical portion of the root and the bottom of the gaps decrease as the increase of the depth of the gap under vertical loading. Overall, the sharp angle and notch of the gap at the coronal entrance of the canal should be avoided in tooth restoration since they can cause stress concentrations. On the effects of the ferrule heights, the changes of the stress distributions in dentin and the post are insignificant except that higher ferrule shows lower stresses at the top of the ferrule. Regarding the effects of the diameters of the posts, the results show that although the posts with large diameters support more loads, they cause high stress concentrations at the apical portion of the root, which is not desirable. / October 2005

Finite-element model updating is the process of using measured data from a structure to update a numerical model representation of the structure. The measured data can represent either the static or dynamic properties of the structure. This document reviews and evaluates several methods of finite-element (FE) model updating, including direct, indirect, and control-based methods for the dynamic case. It is important to have a correct finite-element model obtained using model updating methods either to assess the current condition, or to modify the structure from its current state. In this study, three types of methods were evaluated; direct, indirect, and control based finite-element model updating methods. Each method was first used to update a simple example model for two separate cases. For the first case, the entire set of measured modal parameters were used; and for the second case, only a sub-set of the eigenvalues were used. These examples provide insights into the advantages and disadvantages of various methods. The model updating methods are also used to update a full-scale 42 degree of freedom model. Since it is not practical to measure all the degrees of freedom, the model was reduced using the SEREP model reduction method, down to 18 degrees of freedom. This was done to evaluate the effectiveness of the model updating methods on a real structure. Detailed methodologies and a comparison between the relative advantages and disadvantages between various model updating methods are highlighted in this thesis.

Finite-element model updating is the process of using measured data from a structure to update a numerical model representation of the structure. The measured data can represent either the static or dynamic properties of the structure. This document reviews and evaluates several methods of finite-element (FE) model updating, including direct, indirect, and control-based methods for the dynamic case. It is important to have a correct finite-element model obtained using model updating methods either to assess the current condition, or to modify the structure from its current state. In this study, three types of methods were evaluated; direct, indirect, and control based finite-element model updating methods. Each method was first used to update a simple example model for two separate cases. For the first case, the entire set of measured modal parameters were used; and for the second case, only a sub-set of the eigenvalues were used. These examples provide insights into the advantages and disadvantages of various methods. The model updating methods are also used to update a full-scale 42 degree of freedom model. Since it is not practical to measure all the degrees of freedom, the model was reduced using the SEREP model reduction method, down to 18 degrees of freedom. This was done to evaluate the effectiveness of the model updating methods on a real structure. Detailed methodologies and a comparison between the relative advantages and disadvantages between various model updating methods are highlighted in this thesis.

Soft tissue cervical spine (neck) injuries, known as ‘whiplash’, are a leading cause of injury in motor vehicle collisions. A detailed finite element (FE) model of the cervical spine that is able to predict local tissue injury is a vital tool to improve safety systems in cars, through understanding of injury mechanisms at the tissue level and evaluation of new safety systems. This is the motivation for the formation of the Global Human Body Models Consortium, which is a collective of major automotive manufacturers with the goal of producing a detailed FE human body model to predict occupant response in crash. This work builds on an existing detailed cervical spine model, with a focus on improved validation in terms of kinematics and tissue level response. The neck model used in this research represents a 50th percentile male and was developed at the University of Waterloo. The model includes both passive and active musculature, detailed nucleus and annulus models of the discs, rate dependent non-linear ligaments, facet capsules with a squeeze film model of the synovial fluid, and rigid vertebrae with the geometry derived from CT scans. The material properties were determined from published experimental testing and were not calibrated to improve the model response. The model was previously validated at the segment level. In this study, the model was validated for tension loading, local tissue response during both frontal and rear impacts, and head kinematic response during frontal and rear impact. The whole neck model without musculature was exposed to a tensile load up to 300N and the predicted response was within the experimental corridors throughout. The ligament strains and disc shear strains predicted by the model were compared to bench-top cadaver tests. In frontal impact, the ligament and disc strains were within a standard deviation of the experiments 26/30 and 12/15 times respectively. In rear impact, the strains were within a standard deviation of the experiments 9/10 and 12/15 times for the ligaments and discs respectively. All of the ligament strains were within two standard deviation of the experimental average and the disc strains were all within three standard deviations. The global kinematic response of the head for 4g and 7g rear impacts and 7g and 15g frontal impacts was generally a good fit to the experimental corridors. These impact loads are relevant to the low speed impacts that generally cause whiplash. In the global kinematic validation, the model was shown to oscillate more, which is likely due to the lack of soft-tissues such as the skin and fat or the lack of high-rate material data for the intervertebral discs. In rear impact, the head over extended by 17° and 6° for 4g and 7g impacts respectively; this is likely due to difficulties defining the facet gap or lack of uncovertebral joints. Even with these limitations the model response for these varied modes of loading was considered excellent. A review of organic causes of whiplash revealed the most likely sources of whiplash include the capsular ligament, other ligaments, and the vertebral discs. The model was exposed to frontal and rear impacts with increasing severities until the soft tissue strains reached damage thresholds. In frontal impact, these strains started to reach damage values at a 15g impact. The disc annulus fibres were likely injured at 10g in a rear impact, and the ligaments were likely injured at 14g in a rear impact. These impact severities agree with findings from real-life accidents where long term consequences were found in rear impacts from 9g to 15g. The model was used to show that bench-top cadaver impacts under predict strain because they lack active musculature. A number of recommendations have been proposed to improve the biofidelity of the model including perform in-vivo measurement of human facet gaps, incorporate the uncovertebral joints, measure rate-dependent properties for the annulus fibrosus of the disc, include non-structural soft tissues for increased damping, determine a muscle activation strategy that can maintain head posture in a gravity field, and continue to develop relationships between prolonged painful injury and strain in structures of the neck other than the capsular ligaments. Furthermore, it was recommended that the model should be developed further for whiplash injury prediction with out of position occupants.

In this thesis, numerical experiments are performed to test the numerical stability of the finite element method for analyzing incompressible materials from boundary displacements. The significance of the study relies on the fact that incompressibility, or density preservation during deformation, is an important property of materials such as rubber and soft tissue.<p>It is well known that the finite element analysis (FEA) of incompressible materials is less straightforward than for materials which are compressible. The FEA of incompressible materials using the usual displacement based finite element method results in an unstable solution for the stress field. Hence, a different formulation called the mixed u-p formulation (u displacement, p pressure) is used for the analysis. The u-p formulation results in a stable solution but only when the forces and/or stress tractions acting on the structure are known. There are, however, certain situations in the real world where the forces or stress tractions acting on the structure are unknown, but the deformation (i.e. displacements) due to the forces can be measured. One example is the stress analysis of soft tissues. High resolution images of initial and deformed states of a tissue can be used to obtain the displacements along the boundary. In such cases, the only inputs to the finite element method are the structural geometry, material properties, and boundary displacements. When finite element analysis of incompressible materials with displacement boundary conditions is performed, even the mixed u-p formulation results in highly unstable calculations of the stress field. Here, a hypothesis for solving this problem is developed and tested. Theories of linear and nonlinear stress analysis are reviewed to demonstrate that it may be possible to determine the von Mises stress uniquely in spite of the numerical instability inherent in the calculations.<p>To validate this concept, four different numerical examples representing different deformation processes are considered using ANSYS®: a plate in simple shear; expansion of a thick-walled cylinder; a plate in uniform strain; and Cooks membrane. Numerical results show that, unlike the normal stress components Sx, Sy, and Sz, the calculated values of the von Mises stress are reasonably accurate if measurement errors in the displacement data are small. As the measurement error increases, the error in the von Mises stress increases approximately linearly for linear problems, but can become unacceptably large in nonlinear cases, to the point where solution process encounter fatal errors. A quasi-Dirichlet patch test in association with this problem is also introduced.

This research focuses on the application of guided waves techniques to nondestructively characterize the structural integrity of bonded engineering components. Computational methods are used to examine the properties of multi-layered, adhesive bonded plates. This study quantifies the effect of the adhesive bond parameters (Young's modulus, Poisson's ration and bond thickness) on the dispersion curves. A commercial finite element (FE) code (ABAQUS/Explicit) is used for the numerical model while the global matrix method and the waveguide FE method are used to benchmark the resulting dispersion relationships in the form of a frequency-wavenumber or slowness-frequency relation. The postprocessing of FE data includes the two-dimensional Fourier transform (2D-FFT) and the short-time Fourier transform (STFT). Note that the 2D-FFT and STFT operate on multiple or just one transient output signals of the FE results respectively, while the waveguide FE method uses mass-, damping- and stiffness-matrices to generate the dispersion relations. In the dispersion relations, a set of bond parameter sensitive and FE-visible points is selected. The frequency locations of these points represent the solution criteria for the inversion procedure based on the global matrix method. The capabilities of the inversion process depend on the number of transient output signals from an FE simulation for the forward problem.

As electromagnetic launcher (EML) is an apparatus that uses the electromagnetic (EMAG) force to propel an armature along a rail. An applied electric current, coupled with the resulting magnetic field, creates an EMAG force capable of accelerating an armature to velocities up to several thousand meters per second. The high sliding velocity, coupled with the electric current density, creates extreme thermal conditions at the interface between the rail and the armature that can cause melting at the interface. This project considers a lab-scale EML which is pre-loaded to establish the initial contact between arils and armature. This contact area influences the flow of the electric current and, therefore, it affects the thermal conditions significantly. This work presents a finite-element analysis (FEA) of the aforementioned physical phenomena of the lab-scale EML. This work is aimed at improving the understanding of the armature-to-rail performance and the useful life of an EML by developing a computer simulation which can be used as a design tool to acquire conditiodecoup for the best performance. A two-dimensional structural FEA is used to determine the structural deformation, the contact area, the contact pressure, the von Mises stress, and the material properties of the structural compliance. The vibration characteristics of the lab-scale EML armature are studied using Modal analysis. A three-dimensional electromagnetic FEA is performed to determine the EMAG force. Frictional and Joule heating are determined from a two-dimensional thermal FEA. The commercial finite-element package, ANSYS, is used in the simulation.

This study used computer aided design software Solid Work to draw four models of pressure vessel, and to analyze the displacement and the stress by the finite element analysis software ANSYS. To carry on the main body of the pressure vessel and find the highest stress of the pressure vessels by finite element analysis. The stress analysis of the pressure vessel main body contains main nozzle, the skirt of the main body ban and the connected control line. And the stress analysis factor includes: the stress distribution situation by seismic force and the displacement change factor of the wind power and the stress distribution condition of the thermal load by expand with heat and contract with cold (normal temperature climb to high temperature). The researcher also discussed the difference of the stress distribution between individual analysis and the overall analysis. The present study used finite element analysis (contain main body, spray nozzle, skirt in view of the overall analysis ban) to carry on the shell individual analysis first, then using the boundary condition of the result displacements regarding connected spray nozzle, the pipeline by the shell analysis again carries on stress analysis of the spray nozzle and the pipeline. Based on the results of stress analysis by the finite element method, the researcher discussed the differences of stresses between overall analysis and the individual analysis results.

This dissertation presents the Generalized Finite Element Method (GFEM) for the scalar Helmholtz equation, which describes the time harmonic acoustic wave propagation problem. We introduce several handbook functions for the Helmholtz equation, namely the planewave, wave-band, and Vekua functions, and we use these handbook functions to enrich the Finite Element space via the Partition of Unity Method to create the GFEM space. The enrichment of the approximation space by these handbook functions reduces the pollution effect due to wave number and we are able to obtain a highly accurate solution with a much smaller number of degrees-of-freedom compared with the classical Finite Element Method. The q-convergence of the handbook functions is investigated, where q is the order of the handbook function, and it is shown that asymptotically the handbook functions exhibit the same rate of exponential convergence. Hence we can conclude that the selection of the handbook functions from an admissible set should be dictated only by the ease of implementation and computational costs. Another issue addressed in this dissertation is the error coming from the artificial truncation boundary condition, which is necessary to model the Helmholtz problem set in the unbounded domain. We observe that for high q, the most significant component of the error is the one due to the artificial truncation boundary condition. Here we propose a method to assess this error by performing an additional computation on the extended domain using GFEM with high q.

Smart materials are very important because of their potential applications in the biomedical, petroleum and aerospace industries. They can be used to build systems and structures that self-monitor to function and adapt to new operating conditions. In this study, we are mainly interested in developing a computational framework for the analysis of plate structures comprised of composite or functionally graded materials (FGM) with embedded or surface mounted piezoelectric sensors/actuators. These systems are characterized by thermo-electro-mechanical coupling, and therefore their understanding through theoretical models, numerical simulations, and physical experiments is fundamental for the design of such systems. Thus, the objective of this study was to perform a numerical study of smart material plate structures using a refined plate theory that is both accurate and computationally economical. To achieve this objective, an improved version of the Reddy third-order shear deformation theory of plates was formulated and its finite element model was developed. The theory and finite element model was evaluated in the context of static and dynamic responses without and with actuators. In the static part, the performance of the developed finite element model is compared with that of the existing models in determining the displacement and stress fields for composite laminates and FGM plates under mechanical and/or thermal loads. In the dynamic case, coupled and uncoupled electro-thermo-mechanical analysis were performed to see the difference in the evolution of the mechanical, electrical and thermal fields with time. Finally, to test how well the developed theory and finite element model simulates the smart structural system, two different control strategies were employed: the negative velocity feedback control and the Least Quadratic Regulator (LQR) control. It is found that the refined plate theory provides results that are in good agreement with the those of the 3-D layerwise theory of Reddy. The present theory and finite element model enables one to obtain very accurate response of most composite and FGM plate structures with considerably less computational resources.