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In this study, a laminated glass unit which consists of two glass sheets bonded together by PVB is analyzed as a curved beam and as a cylindrical shell. Laminated glass curved beams and shells are used in architecture, aerospace, automobile and aircraft industries. Curved beam and shell structures differ from straight structures because of their initial curvature. Because of mathematical complexity most of the studies are about linear behavior rather than nonlinear behavior of curved beam and shell units. Therefore it is necessary to develop a mathematical model considering large deflection theory to analyze the behavior of curved beams and shells. Mechanical behavior of laminated glass structures are complicated because they can easily perform large displacement since they are very thin and the materials with the elastic modulus have order difference. To be more precise modulus of elasticity of glass is about 7*104 times greater than the modulus of elasticity of PVB interlayer. Because of the nonlinearity, analysis of the laminated glass has to be performed by considering large deflection effects. The mathematical model is developed for curved beams and shells by applying both the variational and the minimum potential energy principles to obtain nonlinear governing differential equations. The iterative technique is employed to obtain the deflections. Computer programs are developed to analyze the behavior of cylindrical shell and curved beam. For the verification of the results obtained from the developed model, the results from finite element models and experiments are used. Results used for verification of the model and the explanation of the bahavior of the laminated glass curved beams and shells are presented in figures.

This thesis improves a previous kinematic analysis and develops the elastic portion of the analysis of a curved compliant beam. This analysis is used to develop a Pseudo-Rigid-Body Model for the curved compliant beam. The Pseudo-Rigid-Body Model consist of kinematic and elastic parameters which can be used to simplify the computation of the large deflections of the beam as it undergoes spherical motion. The kinematic parameters that are developed are the characteristic radius, Gamma*length, the parametric angle coefficient, c_theta, and the kinematic parametrization limit, Capital_theta_max(Gamma). The elastic parameters developed are the stiffness coefficient, K_theta, and the elastic parameterization limit, Capital_theta_max(K). Additionally, curve fit parameters are developed which enable the calculation of the stress in curved beam as it deflects.

[pt] No presente trabalho é feito um apanhado de teorias de estruturas unidimensionais que não se utilizam da teoria tridimensional como ponto de partida. São discutidos alguns modelos sob a mesma ótica, ressaltando-se seus pontos comuns e suas diferenças. Posteriormente é desenvolvido um modelo exato para estruturas unidimensionais. São discutidos em profundidade medidas de deformação e esforços internos. É tomado um modelo constitutivo elasto-plástico. A modelagem utilizada não faz restrições quanto ao tamanho das deformações e considera a extensibilidade da estrutura. Através de técnicas numéricas simples, conhecidas como métodos do Tiro, são resolvidos alguns problemas de estruturas unidimensionais modelados pela teoria desenvolvida neste trabalho. Dentro destes casos estuda-se o problema da instabilidade, o efeito do cisalhamento para vigas e o comportamento não linear de materiais (plasticidade). Os resultados são apresentados graficamente. Por fim são indicados novos caminhos que dão continuidade a este trabalho. / [en] A survey of rod’s models which are not based in the three-dimensional theory is presented. One of the models is picked out and discussed in details (kinematics, efforts and balance laws). An elasto-plastic constitutive model is considered. This model takes into account large deformations and the extensibility of the tods. A series of numerical simulations of rod’s problems which utilize the shooting methods are considered. These applications study the non linear behavior of rods, in cases which shear. Geometric instability and plasticity are treated. At the end, suggestions for the continuity of this work are presented.

This thesis presents a novel compliant mechanism with adjustable force output. The force comes from the bending of a rectangular cross section beam within the mechanism. By rotating this beam with a stepper motor, the force output of the mechanism changes. A model was made to simulate this mechanism, and a prototype was made based off of this data. A test apparatus was constructed around this mechanism, and a series of tests were performed. These tests adjusted parameters such as beam rotation speed and weight in order to characterize the system. Adjustments were made based on this information and the mechanism was refined. The results suggest the following. The speed has a negligible effect on the behavior of the system, while the weight, length of top link r3, and position of bottom stop have a significant effect. Also, there is a large, consistent amount of hysteresis in the system. This is likely caused by the beam storing torsion or friction from the slider.

[pt] Nesta dissertação são estudados a flambagem e o comportamento pós-crítico de colunas esbeltas sob a ação do peso próprio. Primeiramente, é realizada uma análise linear para a determinação das cargas críticas e modos críticos para colunas com diferentes condições de contorno e para a determinação da relação carga-frequência. Para estudar o comportamento pós-crítico da coluna, uma formulação geometricamente exata para a análise não-linear de elementos estruturais unidimensionais foi desenvolvida, considerando uma distribuição arbitrária da carga e condições de contorno. A partir desta formulação obtém-se um conjunto de equações não-lineares de primeira ordem, as quais,juntamente com as condições de contorno dos extremos da coluna, formam o problema de valor de contorno. Este problema é resolvido pelo uso simultâneo do método de integração numérica de Runge-Kutta e pelo método de Newton- Raphson. Devido a um algorítmo de continuação, soluções precisas podem ser obtidas para uma variedade de problemas de estabilidade apresentando pontos limite ou de bifurcação. Com o uso desta formulação, é feita uma análise paramétrica detalhada a fim de possibilitar o estudo da flambagem e do comportamento pós-crítico de colunas esbeltas sujeitas a ação do peso próprio, incluindo a influência das condições de contorno na estabilidade, a distribuição dos esforços internos e o comportamento não- linear geométrico da coluna. Com o objetivo de verificar a qualidade e a precisão dos resultados, foi conduzida uma análise experimental para o caso de uma coluna esbelta engastada e livre. Os resultados experimentais obtidos para a flambagem, freqüências naturais e para o comportamento pós-crítico foram comparados de forma favorável com os resultados teóricos e numéricos. / [en] In this thesis the buckling and post-buckling behavior of slenders columns under self-weight are studied. First a linear analysis is conducted to determine the critical loads for different boundary conditions and the load-frequency relation. In order to study the post-buckling behavior of the column, a geometrically exact formulation for the non- linear analysis of uni-dimentional structural elements has been derived, considering arbitrary load distribution and boundary conditions. From this formulation one obtains a set of first-order coupled non-linear equations which, together with the boundary conditions at the column ends, form a two-point boundary value problem. This problem is solved by the simultaneous use of the Runge-Kutta integration scheme and the Newton-Raphson method. By virtue of a continuation algorithm, accurate solutions can be obtained for a variety of stability problems exhibiting either limit point or bifurcational-type buckling. Using this formulation, a detailed parametric analysis is conducted in order to study the buckling and post-buckling behavior of slender columns under self-weight, including the influence of boundary conditions on the stability, internal forces distribution and large deflection behavior of the column. To verify the quality and accuracy of the results, an experimental analysis was conducted considering a clamped-free thin-walled metal column. The buckling and post-buckling behavior as well as the load-frequency relation were obtained and compared favorably with the theoretical and numerical results. / [es] En esta disertación se estudian el flameo el comportamiento postcrítico de columnas esbeltas bajo la acción del peso proprio. Primeramente, se realiza un análisis lineal para la determinación de las cargas críticas y modos críticos para columnas con diferentes condiciones de contorno y para la determinación de la relación carga frecuencia. Para estudiar el comportamiento postcrítico de la columna, fue desarrollada una formulación geométricamente exacta para el análisis no lineal de elementos extructurales unidimensionales, considerando una distribuición arbitraria de la carga y condiciones de contorno. A partir de esta formulación se obtiene un conjunto de ecuaciones no lineales de primer orden, las cuales, juntamente con las condiciones de contorno de los extremos de la columna, forman el problema de valor de contorno. Este problema se resuelve usando simultáneamente el método de integración numérica de Runge Kutta y el método de Newton Raphson. A través de un algorítmo de continuación, pueden ser obtenidas soluciones precisas para una variedad de problemas de estabilidad presentando puntos límite o de bifurcación. Utilizando esta formulación, se realiza análisis paramétrico detallado a fin de hacer posible el estudio del flameo y del comportamiento postcrítico de columnas esbeltas sujetas a la acción del proprio peso, inclyendo la influencia de las condiciones de contorno en la estabilidad, la distribuición de los esfuerzos internos y el comportamiento no lineal geométrico de la columna. Con el objetivo de verificar la calidad y la precisión de los resultados, se ejecutó un análisis experimental para el caso de una columna esbelta y libre. Los resultados experimentales obtenidos para el flameo, frecuencias naturales y para el comportamiento postcrítico fueron comparados de forma favorable con los resultados teóricos y numéricos.

Carbon fabric-reinforced polymer (CFRP) composites are widely used in aerospace, automotive and construction structures thanks to their high specific strength and stiffness. They can also be used in various products in sports industry. Such products can be exposed to different in-service conditions such as large bending deformations caused by quasi-static and dynamic loading. Composite materials subjected to such bending loads can demonstrate various damage modes - matrix cracking, delamination and, ultimately, fabric fracture. Damage evolution in composites affects both their in-service properties and performance that can deteriorate with time. Such damage modes need adequate means of analysis and investigation, the major approaches being experimental characterisation and numerical simulations. This work deals with a deformation behaviour and damage in carbon fabric-reinforced polymer (CFRP) laminates caused by quasi-static and dynamic bending. Experimental tests are carried out first to characterise the behaviour of a CFRP material under tension, in-plane shear and large-deflection bending in quasi-static conditions. The dynamic behaviour of these materials under large-deflection bending is characterised by Izod-type impact tests employing a pendulum-type impactor. A series of impact tests is performed on the material at various impact energy levels up to its fracture, to obtain a transient response of the woven CFRP laminate. Microstructural examination of damage is carried out by optical microscopy and X-ray micro computed tomography (Micro-CT). The damage analysis revealed that through thickness matrix cracking, inter-ply delaminations, intra-ply delamination such as tow debonding, and fabric fracture was the prominent damage modes. These mechanical tests and microstructural studies are accompanied by advanced numerical models developed in a commercial code Abaqus. Among those models are (i) 2D FE models to simulate experimentally observed inter-ply delamination, intra-ply fabric fracture and their subsequent interaction under quasi-static bending conditions and (ii) 3D FE models based on multi-body dynamics used to analyse interacting damage mechanisms in CFRP under large-deflection dynamic bending conditions. In these models, multiple layers of bilinear cohesive-zone elements are placed at the damage locations identified in the Micro CT study. Initiation and progression of inter-laminar delamination and intra-laminar ply fracture are studied by employing cohesive elements. Stress-based criteria are used for damage initiation while fracture-mechanics techniques are employed to capture its progression in composite laminates. The developed numerical models are capable to simulate the studied damage mechanisms as well as their subsequent interaction observed in the tests and microstructural damage analysis. In this study, a novel damage modelling technique based on the cohesive-zone method is proposed for analysis of interaction of various damage modes, which is more efficient than the continuum damage mechanics approach for coupling between failure modes. It was observed that the damage formation in the specimens was from the front to the back at the impact location in the large-deflection impact tests, unlike the back-to-front one in drop-weight tests. The obtained results of simulations showed a good agreement with experimental data, thus demonstrating that the proposed methodology can be used for simulations of discrete damage mechanisms and their interaction during the ultimate fracture of composites in bending. The main outcome of this thesis is a comprehensive experimental and numerical analysis of the deformation and fracture behaviours of CFRP composites under large-deflection bending caused by quasi-static and dynamic loadings. Recommendations on further research developments are also suggested.

ABSTRACT EXPERIMENTAL ANALYSIS OF CURVED LAMINATED GLASS BEAM Uzhan, Tevfik M.S., Department of Engineering Sciences Supervisor: Prof. Dr. M. Z&uuml / lf&uuml / ASik May 2010, 33 Pages In this thesis, experimental studies are carried out on curved laminated glass beams to form a database for the scientists who may like to test their mathematical models. Beams which are only free to rotate and constrained in radial direction at both ends are tested to make the data available for further calculations. Test setup is prepared to minimize error that could occur due to test setup and data readings. Material testing machine and 4 channel data collecting machine are used to measure the signals at the strain gauges located over the glass beam. Within the range of force applied to the specimens, laminated curved beam shows linear behavior without any fracture. Data collected from the specimens are in conformance with each other. Results obtained from experiments are compared with the results obtained from the mathematical model developed by ASik and Dural (2006). As it is observed from the graphs presented, experimental results from the tests and numerical results from the mathematical model are in good agreement.

The diploma thesis is focused on the creation of the aneurysm finite element model and the making of the aneurysm wall stess-strain analysis using ANSYS software. The model of abdominal aortic aneurysm geometry starts from the CT scan of the particular patient. In the thesis there are compared two chosen constitutive models, each of them appears from different mechanical tests done on human arterial fibre samples. Furthermore, a limiting condition for aneurysm wall structure damage is expressed. On the basis of the results of stress calculation in the aneurysm wall and the limiting condition, the safety coefficient and rupture factors risk are worked out.

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