A suspended ionic solution of 1-butyl-3-methylimidazolium iron tetrachloride [BMIM][FeCl4] provides a novel medium for achieving Faraday rotation under small magnetic fields at pump wavelengths of 980nm. As verified with spectrophotometry, transmission at telecommunication wavelengths makes the solution applicable across multiple applications. A cryostation was used to measure the sample up to a 340K and under field at 600mT, the ionic sample shows the necessary temperature stability and enables compact formats suitable for potential industrial applications. With a rotation of linearly polarized light of 0.04° over a 450um path length, a full 45° rotation requires only a 50.6cm path length and with only a 0.000175°/K temperature dependence. The observation of polarization effects in real time using lock-in amplifiers, and a photo-elastic modulator demonstrates the scalability, responsiveness, and stability of the ionic liquids for photonic integration. The test set up provides a convenient way to expand the research on ionic liquid Faraday rotation materials and other Faraday liquids ideally leading to a compact in-line isolator solution.

We present new reconstruction results and methods for limited data problems in photoelastic tomography. We begin with a survey of the current state of x-ray tomography. Discussing the Radon transform and its inversion we also consider some stability results for reconstruction in Sobolev spaces. We describe certain limited data problems and ways to tackle these, in particular the Two Step Hilbert reconstruction method. We then move on to photoelastic tomography, where we make use of techniques from scalar tomography to develop new methods for photoelastic tomographic reconstruction. We present the main mathematical model used in photoelasticity, the Truncated Transverse Ray Transform (TTRT). After some initial numerical studies, we extend a recently presented reconstruction algorithm for the TTRT from the Schwartz class to certain Sobolev spaces. We also give some stability results for inversion in these spaces. Moving on from general reconstruction to focus on inversion of some special cases of tensors we consider solenoidal and potential tensor fields. We discuss existing reconstruction methods and present several novel reconstructions and discuss their advantages over using more general machinery. We also extend our new algorithms, as well as existing ones, to certain cases of data truncation. Finally, we present numerical studies of the general reconstruction method. We give the first published results of TTRT reconstruction and go into some detail describing the implementation before presenting our results.

[pt] O presente trabalho tem como objetivo o desenvolvimento de um material foto elástico, utilizando matéria-prima exclusivamente brasileira, para o emprego na análise das tensões em ensaio tridimensional. As experiências foram feitas com as resinas epóxi CY-205 e CY-175. Como endurecedores foram utulizados os produtos HY-901 (anidrido ftálico) e HT-906 (anidrido metilendometilene), todos da Ciba S/A, e ainda o endurecedor anidrido maleico produzido pela Ucebel S/A. Foram fundidos diferentes partes em peso desses componentes, resina epóxi-endurecedor e descritos o método de fundição como também o de tratamento térmico. Algumas propriedades foram inicialmente consideradas para a seleção da melhor composição. O material feito de epoxi CY-205 com a combinação dos endurecedores anidridos maleico e ftálico são apresentados como sendo o melhor. Os polímeros resultanes são feitos usando diferentes partes em peso desses endurecedores combinados e são traçados nomogramas de suas temperaturas críticas e módulos de elasticidade a essa temperatura, para determinar a composição ideal. Foi determinado o gelling time dos materiais selecionados. A aplicação desse material desenvolvido é adequada para análise tridimensional. Um modelo foi construído para ilustrar sua utilização, usando uma técnica especial de modelagem. / [en] The presentes work describes the development of the photoeslastical material for two and three-dimensional experiments. The model material hás been developed using the epoxy resin manufactured in BRAZIL. Two kinds of epoxy resins hás been used: CY-205 and CY-175, both produced by Ciba S/A, together with the hardeners HY-901 (phtalic anhydrid and HT-906 (metilendometylen anhydrid)) of Ciba S/A and maleic anhydrid, manufactured by Ucebel S/A. The different mixtures of epoxy resins and hardeners have been casted into samples and investigated with respect the properties essential in photoelasticity. The method of casting and heat treatment is also described. The misture of epoxy CY-205 with the combination of phtalic and maleic anhydrides hás been founs to have the Best photoelastical properties. The monogram indicating the mechanical proprieties as a functio of combination of hardeners hás been design. If casn be used for determination of proper combination of hardeners related to the desired mechanical properties or for determination of optimum composition. The application of the developed material in three-dimensional photoelasticity hás been illustrated by casting the complicated three-dimensional model.

Compression fracture specimens are ideally suited for miniaturization down to tens of microns. Fracture testing of thermal barrier coatings, ceramics and glasses are also best accomplished under compression or indentation. Compression fracture specimen of finite size with constant form factor was not available in the literature. The finite-sized specimen of edge cracked semicircular disk (ECSD) is designed which has the property of constant form factor. The novel ECSD specimen is explored further using weight function concept. This thesis, therefore, is mainly concerned with the design, development and geometric optimization of compression fracture specimen vis a vis their characterization of form factors, weight functions and isotropic points in the uncracked geometry. Inspired by the Brazilian disk geometry, a novel compression fracture specimen is designed in the form of a semicircular disk with an edge crack which opens up due to the bending moment caused by the compressive load applied along its straight edge. This new design evolved from a set of photoelastic experiments conducted on the Brazilian disk and its two extreme cases. Surprisingly, normalized mode-I stress intensity factor of the semicircular specimen loaded under a particular Hertzian way, is found constant for a wide range of relative crack lengths. This property of constant form factor leads to the development of weight function for ECSD for deeper analysis of the specimen. The weight function of a cracked geometry does not depend on loading configuration and it relates stress intensity factor to the stress distribution in the corresponding uncracked geometry through a weighted integral. The weight function for the disk specimen is synthesized in two different ways: using the conventional approach which requires crack opening displacement and the dual form factor method which is newly developed. Since stress distribution in the uncracked specimen is required in order to use weight function concept, analytical solution is attempted using linear elasticity theory. Since closed form solution for stresses in the uncracked semicircular disk is seldom possible with the available techniques, a new semi-analytical method called partial boundary collocation (PBC), is developed which may be used for solving any 2-D elasticity problem involving a semi-geometry. In the new method, part of the boundary conditions are identically satisfied and remaining conditions are satisfied at discrete boundary points. The classical stress concentration factor for a semi-in finite plate with a semicircular edge notch re-derived using PBC is found to be accurate to the eighth decimal. To enhance the form factor in order to test high-toughness materials, edge cracked semicircular ring (ECSR) specimen is designed in which bending moment at the crack-tip is increased significantly due to the ring geometry. ECSR is analyzed using nite element method and the corresponding uncracked problem is analyzed by PBC. Constant form factor is found possible for the ring specimen with tiny notch. In order to avoid varying semi-Hertzian angle during practice and thereby ensure consistent loading conditions, the designs are further modified by chopping at the loading zones and analyzed. Photoelastic isotropic points (IPs) which are a special case of zeroth order fringe (ZOF) are often found in uncracked and cracked specimens. An analytical technique based on Flamant solution is developed for solving any problem involving circular domain loaded at its boundary. Formation of IPs in a circular disk is studied. The coefficients of static friction between the surfaces of disk and loading fixtures, in photoelastic experiments of three-point and four-point loadings, are explored analytically to confirm with experimental results. The disk under multiple radial loads uniformly spaced on its periphery is found to give rise to one isolated IP at the center. Splitting of this IP into a number of IPs can be observed when the symmetry of normal loading is perturbed. Tangential loading is introduced along with normal loading to capture the effect of the composition on formation of IPs. Bernoulli's lemniscate is found to fit fringe order topology local to multiple IPs. Isotropic points along with other low fringe order zones including ZOF are ideal locations for material removal for weight reduction. Making a small hole in the prospective crack path at the IP location in the uncracked geometry might provide dual benefits: 1. Form factor enhancement; 2. Crack arrestor. Thus, this thesis describes experimental, theoretical and computational investigations for the design, development and calibration of novel compact compression fracture specimens.

O objetivo desta pesquisa foi avaliar in vitro as tensões transmitidas às estruturas de suporte, por meio da associação dos métodos fotoelásticos e elementos finitos, decorrentes da aplicação de forças sobre overdentures retidas em implantes com sistema de encaixe barraclipe, particularmente quando duas posições dos implantes são simuladas. Assim, dois modelos fotoelásticos de mandíbulas foram confeccionados, com dois implantes cada um, posicionados na região interforaminal a 22 mm de distância: modelo 1, denominado AFIP, modelo fotoelástico com implantes paralelos e orientados verticalmente; e modelo 2, denominado AFII, modelo fotoelástico com implantes angulados 10º em relação à linha média da mandíbula. Sobre os implantes, em cada modelo, foi posicionada uma prótese tipo overdenture, com sistema de retenção barra-clipe. Para simulação da mucosa, foi interposta entre a base da prótese e o rebordo residual uma camada de 2 mm de silicone. Este mesmo modelo foi representado para uma análise tridimensional (3D) de elementos finitos. As estruturas foram consideradas homogêneas, isotrópicas e lineares, além de serem atribuídas as correspondentes propriedades mecânicas para cada uma delas. Foram simuladas quatro mandíbulas de elementos finitos, sendo modelo 1, denominado EFRIP, com implantes paralelos; modelo 2, denominado EFRII, com implantes angulados em 10º, ambos modelos (1 e 2) simulando o modelo mandibular de resina fotoelástica; modelo 3, denominado EFOIP, com implantes paralelos; e modelo 4, denominado EFOII, com implantes angulados em 10º, ambos os modelos (3 e 4), simulando os ossos cortical e trabecular. Foram aplicadas cargas de 0,5; 1,0; 1,5; 2,0 e 3 bar no método fotoelástico e 0,1 MPa no método de elementos finitos e em seguida as imagens foram fotografadas e analisadas. Os resultados mostraram que: não houve semelhança entre as áreas de tensão dos modelos de resina fotoelástica, quando avaliada a angulação dos implantes (modelo 1 AFIP - e modelo 2 AFII). Houve semelhança entre as áreas de tensão nos modelos de elementos finitos com mandíbula em resina (modelo 1 EFRIP - e modelo 2 EFRII), tendo ocorrido o mesmo entre os modelos de elementos finitos com simulação de osso (modelo 3 - EFOIP - e modelo 4 EFOII) quando avaliada a inclinação dos implantes. Quando comparados os diferentes modelos com a mesma angulação de implante, observou-se que houve semelhança na distribuição das áreas de tensão entre os modelos 1 (AFIP e EFRIP), com uma alta concentração de tensão nos ápices dos implantes. Porém, não houve relação entre os modelos de implantes inclinados, modelos 2 (AFII e EFRII). Da mesma forma, não houve relação entre os modelos de análise fotoelástica e elementos finitos com simulação de mandíbula em resina, independentemente da angulação dos implantes, comparado os modelos de elementos finitos com simulação de osso. Frente às limitações do presente trabalho, concluiu-se que a associação dos métodos de análise fotoelástica e de elementos finitos é de grande valia para a obtenção de informação em relação à biomecânica referente a esse tipo de prótese e sistema de retenção. Além disso, houve semelhança nas áreas de concentração de tensão, quando comparado os modelos de análise fotoelástica e de elementos finitos, quando as propriedades mecânicas inseridas no modelo de elementos finitos foram compatíveis com o modelo fotoelástico, pois, quando o modelo de elementos finitos simulou uma mandíbula com diferenciação entre osso cortical e medular, as áreas de concentração de tensão sofreram alterações. / The objective of this study was to appraise in vitro the load transmission in bar-clip retention system for overdenture when two implant positions are simulated, using for this purpose the association of photoelastic analysis and finite elements techniques. Therefore, two photoelastic mandible were manufactured with two implants each one, positioned in interforaminal region within 22 mm of distance: (i) model 1, named AFIP, photoelastic model with parallel and vertically oriented implants; and (ii) model 2, named AFII, photoelastic model with 10º angled implants in relation to mandible midline. A bar-clip retention system and an overdenture were fixed over both implants. To simulate oral mucosa were added a 2 mm silicon layer between overdenture prosthesis and photoelastic mandible. This same model was submitted to finite elements analysis in 3D, being attributed the correspondent mechanic properties to each structure analyzed and also being considered homogenous, isotropic and linear characteristics. Four finite elements mandible were simulated, (i) one with parallel implants and (ii) other with 10º angled implants, simulating photoelastic resin in mandible (models 1 and 2, named EFRIP and EFRII respectively); and a another couple of mandibles also with (iii) parallel and (iv) 10º angled implants, simulating cortical and cancellous bones in mandible (models 3 and 4, named EFOIP and EFOII respectively). 0.5; 1.0; 1.5; 2.0 and 3.0 bars loads were applied and correspondent images were analyzed. Results evidenced that there is no similarity in loaded areas between photoelastic resin models, when the implant angle is appraised in models 1 and 2 (AFIP and AFII). Notwithstanding, there are similarity between loaded areas in finite elements model with resin mandible, models 1 and 2 (EFRIP and EFRII), and the same have occurred with finite elements models with bone simulation, models 3 and 4 (EFOIP and EFOII), when appraised implant inclination. When different models are compared with the same implant angulations, was noted that there was similarity in the distribution of loaded areas between models 1 (AFIP and EFRIP), with high concentration of tension forces at the implant apex. Nevertheless, there was no relation between inclined models 2 (AFII and EFRII). At the same direction, there was no relation between photoelastic analysis and finite elements with resin model, with no influence of implant angulations, with finite element models with bone simulation. Considering the limitations of this study, it was concluded that association of photoelastic analysis and finite elements has a high potential value for obtaining information concerning the biomechanics of this kind of prosthesis and retention system; furthermore, there was similarity in areas where loads were applied, when compared photoelastic and finite elements models, provided that finite elements mechanic properties are compatible with photoelastic model, since concentration areas of tension forces suffer changes when finite elements model simulates a mandible with cortical and cancellous bones differentiation.

Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2014-09-02T11:26:28Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação Joao Francisco Machado do Nascimento.pdf: 721039 bytes, checksum: 2a145e907cf0cfc7e15f26459ae30aff (MD5) / Made available in DSpace on 2014-09-02T11:26:28Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dissertação Joao Francisco Machado do Nascimento.pdf: 721039 bytes, checksum: 2a145e907cf0cfc7e15f26459ae30aff (MD5) Previous issue date: 2013-08-14 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / For patients poorly adapted to conventional dentures, the single-implant mandibular overdenture has been proposed as a simplified alternative for the two-implant treatment, together with the use of immediate loading of the implant. The aim of this in vitro study was to compare the photoelastic characteristics of stress transfer to the implant in a single-implant mandibular overdenture using different types of attachments. A photoelastic model of an edentulous mandible with a resilient edentulous ridge and a unique implant located at the symphyseal region was obtained to reproduce a single implant-retained mandibular overdenture. Six 2.0 mm height attachments were selected and inserted in the same photoelastic model in a random order. A universal material testing machine was used to induce axial vertical loads of 70 N applied in the central incisor and in the central region of the first right molar without contact on the contralateral side. The photoelastic analysis was performed using a polariscope integrated into the testing machine. Standard separate views were photographed and evaluated visually for stress-induced fringes, to comparatively rank the different attachment systems. All attachments showed a similar tension distribution concentrated in the apical third, and the highest stress concentration at the apical level. There was a low stress concentration at the coronal third of the implant, with no discernible stress in the first threads of the implants, except for Dalla Bona which showed low stress at the coronal part of the implant (one fringe). No identifiable fringes were observed when the load was applied in the molar region, which resulted from the low amount of stress transmitted by the implant for all attachments. It was concluded that the load transferred to a single mandibular implant is low and within the limits of functional loading, irrespective of the type of retention system. / Implantes osseointegrados vêm sendo utilizados com sucesso para restaurar a função e a estética de pacientes desdentados totais e parciais. No entanto há necessidade de tornar o tratamento de pessoas com necessidade de overdenture retida com implante menos oneroso e mais eficiente. O objetivo deste trabalho foi verificar pela técnica fotoelástica (Qualitativa) as tensões geradas ao redor do implante pela aplicação de carga sobre overdenture mandibular retida por um implante unitário na sínfise da mandibular. Foi confeccionado um modelo de resina fotoelástica Araldite, reproduzido de uma mandibular anatômica, onde foi fixado na região sínfise um implante 3.75x11mm (Titamax Ti Cortical, Neodent, Curitiba, Brasil). Com um modelo foi confeccionada uma prótese total e gingival artificial. Todos os pilares foram posicionados sobre o implante e apertado com 10 Ncm, a fêmea foi capturada de forma direta à prótese, com a réplica da mucosa em posição. Todos foram sucessivamente capturados e levados ‘à máquina de ensaio universal. Com uma carga axial de 70 Ncm na fossa central do 46 e incisal do 41. Foram fotografados em um polariscópio as franjas resultantes das tensões. Foram feitas análises qualitativa dos resultados das tensões sobre o attachment. De acordo com os resultados obtidos pode-se concluir que a carga transferida para o implante, é baixo, independente do sistema de retenção.

Granular materials are composed of solid, discrete particles and exhibit mechanical behavior that differs from those of fluids and solids. The rheology of granular flows is principal to a suite of natural hazards. Laboratory experiments and numerical models have adequately reproduced several features observed in terrestrial gravity driven geophysical flows; however, quantitative comparison to field observations exposes a failure to explain the high mobility and duration of many of these flows. The ability of a granular material to resist deformation is a function of the force chain network inherent to the material. This investigation addresses the evolutionary character of force chains in unconfined, two-dimensional, gravity driven granular flows. Our particular emphasis concerns the effects of stress localization on the substrate by dynamic force chain evolution and the implications for bed erosion in dense granular flows. Experimental systems employing photoelastic techniques provide an avenue for quantitative force analysis via image processing and provide dataset that can be used validate discrete element modeling approaches. We show that force chains cause extreme bed force localization throughout dynamic granular systems in spatial and temporal space; and that these localized forces can propagate extensively into the substrate, even ahead of the flow front.

Anisotropy in glass can lead to a transmitted double image due to birefringence. Stress-induced birefringence, the stress-optic effect, is undesirable for applications such as commercial imaging. The leading zero stress-optic glass exhibits dispersive effects near its absorbance edge and thus cannot be used in broadband applications. Finding zero stress-optic glasses with minimal dispersive effects over a broad band of the visible region requires a theory to predict which combinations of glass formers and modifiers could exhibit minimal dispersion. Two glass families known to have a zero stress-optic response using white light, tin phosphates and tin silicates, were studied as a function of composition and wavelength. Near the absorbance edge, dispersion varied considerably with composition for tin phosphate glasses, but remained constant for tin silicate glasses. The significant factor is the oxygen bonding influence near the band edge. This leads to composition rules for synthesis of broadband, zero stress-optic glasses.

O objetivo desta pesquisa foi avaliar in vitro as tensões transmitidas às estruturas de suporte, por meio da associação dos métodos fotoelásticos e elementos finitos, decorrentes da aplicação de forças sobre overdentures retidas em implantes com sistema de encaixe barraclipe, particularmente quando duas posições dos implantes são simuladas. Assim, dois modelos fotoelásticos de mandíbulas foram confeccionados, com dois implantes cada um, posicionados na região interforaminal a 22 mm de distância: modelo 1, denominado AFIP, modelo fotoelástico com implantes paralelos e orientados verticalmente; e modelo 2, denominado AFII, modelo fotoelástico com implantes angulados 10º em relação à linha média da mandíbula. Sobre os implantes, em cada modelo, foi posicionada uma prótese tipo overdenture, com sistema de retenção barra-clipe. Para simulação da mucosa, foi interposta entre a base da prótese e o rebordo residual uma camada de 2 mm de silicone. Este mesmo modelo foi representado para uma análise tridimensional (3D) de elementos finitos. As estruturas foram consideradas homogêneas, isotrópicas e lineares, além de serem atribuídas as correspondentes propriedades mecânicas para cada uma delas. Foram simuladas quatro mandíbulas de elementos finitos, sendo modelo 1, denominado EFRIP, com implantes paralelos; modelo 2, denominado EFRII, com implantes angulados em 10º, ambos modelos (1 e 2) simulando o modelo mandibular de resina fotoelástica; modelo 3, denominado EFOIP, com implantes paralelos; e modelo 4, denominado EFOII, com implantes angulados em 10º, ambos os modelos (3 e 4), simulando os ossos cortical e trabecular. Foram aplicadas cargas de 0,5; 1,0; 1,5; 2,0 e 3 bar no método fotoelástico e 0,1 MPa no método de elementos finitos e em seguida as imagens foram fotografadas e analisadas. Os resultados mostraram que: não houve semelhança entre as áreas de tensão dos modelos de resina fotoelástica, quando avaliada a angulação dos implantes (modelo 1 AFIP - e modelo 2 AFII). Houve semelhança entre as áreas de tensão nos modelos de elementos finitos com mandíbula em resina (modelo 1 EFRIP - e modelo 2 EFRII), tendo ocorrido o mesmo entre os modelos de elementos finitos com simulação de osso (modelo 3 - EFOIP - e modelo 4 EFOII) quando avaliada a inclinação dos implantes. Quando comparados os diferentes modelos com a mesma angulação de implante, observou-se que houve semelhança na distribuição das áreas de tensão entre os modelos 1 (AFIP e EFRIP), com uma alta concentração de tensão nos ápices dos implantes. Porém, não houve relação entre os modelos de implantes inclinados, modelos 2 (AFII e EFRII). Da mesma forma, não houve relação entre os modelos de análise fotoelástica e elementos finitos com simulação de mandíbula em resina, independentemente da angulação dos implantes, comparado os modelos de elementos finitos com simulação de osso. Frente às limitações do presente trabalho, concluiu-se que a associação dos métodos de análise fotoelástica e de elementos finitos é de grande valia para a obtenção de informação em relação à biomecânica referente a esse tipo de prótese e sistema de retenção. Além disso, houve semelhança nas áreas de concentração de tensão, quando comparado os modelos de análise fotoelástica e de elementos finitos, quando as propriedades mecânicas inseridas no modelo de elementos finitos foram compatíveis com o modelo fotoelástico, pois, quando o modelo de elementos finitos simulou uma mandíbula com diferenciação entre osso cortical e medular, as áreas de concentração de tensão sofreram alterações. / The objective of this study was to appraise in vitro the load transmission in bar-clip retention system for overdenture when two implant positions are simulated, using for this purpose the association of photoelastic analysis and finite elements techniques. Therefore, two photoelastic mandible were manufactured with two implants each one, positioned in interforaminal region within 22 mm of distance: (i) model 1, named AFIP, photoelastic model with parallel and vertically oriented implants; and (ii) model 2, named AFII, photoelastic model with 10º angled implants in relation to mandible midline. A bar-clip retention system and an overdenture were fixed over both implants. To simulate oral mucosa were added a 2 mm silicon layer between overdenture prosthesis and photoelastic mandible. This same model was submitted to finite elements analysis in 3D, being attributed the correspondent mechanic properties to each structure analyzed and also being considered homogenous, isotropic and linear characteristics. Four finite elements mandible were simulated, (i) one with parallel implants and (ii) other with 10º angled implants, simulating photoelastic resin in mandible (models 1 and 2, named EFRIP and EFRII respectively); and a another couple of mandibles also with (iii) parallel and (iv) 10º angled implants, simulating cortical and cancellous bones in mandible (models 3 and 4, named EFOIP and EFOII respectively). 0.5; 1.0; 1.5; 2.0 and 3.0 bars loads were applied and correspondent images were analyzed. Results evidenced that there is no similarity in loaded areas between photoelastic resin models, when the implant angle is appraised in models 1 and 2 (AFIP and AFII). Notwithstanding, there are similarity between loaded areas in finite elements model with resin mandible, models 1 and 2 (EFRIP and EFRII), and the same have occurred with finite elements models with bone simulation, models 3 and 4 (EFOIP and EFOII), when appraised implant inclination. When different models are compared with the same implant angulations, was noted that there was similarity in the distribution of loaded areas between models 1 (AFIP and EFRIP), with high concentration of tension forces at the implant apex. Nevertheless, there was no relation between inclined models 2 (AFII and EFRII). At the same direction, there was no relation between photoelastic analysis and finite elements with resin model, with no influence of implant angulations, with finite element models with bone simulation. Considering the limitations of this study, it was concluded that association of photoelastic analysis and finite elements has a high potential value for obtaining information concerning the biomechanics of this kind of prosthesis and retention system; furthermore, there was similarity in areas where loads were applied, when compared photoelastic and finite elements models, provided that finite elements mechanic properties are compatible with photoelastic model, since concentration areas of tension forces suffer changes when finite elements model simulates a mandible with cortical and cancellous bones differentiation.

<p> A three dimensional photoelastic method of analyzing the stresses in toroids, such as Bourdon Tubes, is proposed in this thesis, The experimental techniques and procedures developed are documented in detail, The experimental method is used to study a thick walled toroidal shell under a uniform internal pressure. </p> <p> The principal stresses on the inside and outside surfaces of the shell were determined and from these the maximum shear stresses calculated. The experimental results are compared to Lame's solution of a thick walled ring under iniform internal pressure, a thin walled toroidal shell subjected to uniform internal pressure, and a long, straight thin walled cylinder with closed ends loaded by internal pressure. </p> / Thesis / Master of Engineering (ME)