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Abstract Axially moving material problems are concerned with the dynamic response, vibration and stability of slender members which are in a state of translation. In Finland these are particularly important in the functioning of paper machines, in which out of plane vibration in the paper web, known as flutter, which from the point of view of mechanics is a phenomenon typical of an axially moving material, limits operation speeds and therefore the productivity of the machines. This subject links together a number of physical phenomena associated with aerodynamics, web movement, material behaviour and the geometry of the system. The aim of this research is to present a theoretical and numerical formulation of the nonlinear dynamic analysis of an axially moving web. The theoretical model is based on a mixed description of the continuum problem in the context of the dynamics of initially stressed solids. Membrane elasticity is included via a finite strain model, and the membrane transport speed through a kinematical study. Hamilton's principle provides nonlinear equations which describe the three-dimensional motion of the membrane. The incremental equations of Hamilton's principle are discretized by the finite element method. The formulation includes geometrically nonlinear effects: large displacements, variations in membrane tension and variations in transport velocity due to deformation. This novel numerical model was implemented by adding an axially moving membrane element to a FEM program which contains acoustic fluid elements and contact algorithms. This allowed analysis of problems including interaction with the surrounding air field and contact between supporting structures. The model was tested by comparing previous experiments and present nonlinear description of the dynamic behaviour of an axially moving web. The effects of contact between finite rolls and the membrane and interaction between the surrounding air and the membrane were included in the model. The results show that nonlinearities and coupling phenomena have a considerable effect on the dynamic behaviour of the system. The nonlinearities cause a noticeable stiffening of the membrane, and the vibration frequency of nonlinear system increases as the amplitude grows. At high values of transport velocity the first mode frequency passes over the second linear harmonic, and even the third. The results also show that the cylindrical supports have a distinct influence on the behaviour of an axially moving sheet. The boundary of the contact region clearly moves and weakens the nonlinear hardening phenomena that otherwise increase the fundamental frequency. This influence strengthens as the radius of the cylinders increases.

Reinforced concrete (RC) shear wall buildings constitute a significant portion of the building inventory in many earthquake-prone regions. A similar type of structural system is fully-grouted reinforced masonry (RM) shear wall structures. The accurate determination of the nonlinear response of reinforced concrete and reinforced masonry (RC/RM) walls subjected to lateral loading is of uttermost importance for ensuring the safety of the built environment. Analytical models provide a cost efficient and comprehensive tool to study the nonlinear response of RC/RM structures, as compared to experimental tests. Predictive models should capture nonlinear material behavior as well as the geometrically nonlinear response of RC/RM shear wall structures during major seismic events. This thesis outlines the formulation and validation of a nonlinear shell element for the simulation of RC/RM structures. The proposed shell element enhances an existing formulation of a four-node Discrete Kirchhoff shell element through the inclusion of a corotational approach to account for geometric nonlinearities and of nonlinear material models to capture the effect of cracking and crushing in concrete or masonry and the nonlinear hysteretic behavior of reinforcing steel. The analytical results obtained from multiple linear and nonlinear analyses are compared against theoretical solutions and experimental test data. These comparative validation studies show the enhanced shell element can satisfactorily capture the salient features of the response of nonlinear reinforced concrete/masonry shear wall structures including axial-shear-flexure interaction, damage patterns, and in-plane and out-of-plane loading. / Master of Science

Este estudo tem como principal objetivo a compreensão de dois dos principais métodos de otimização topológica disponíveis na literatura: o método SIMP e ESO. Estes métodos foram implementados computacionalmente utilizando a linguagem de programação FORTRAN 90. Utiliza-se o Método dos Elementos Finitos (MEF) como parâmetro de solução mecânica neste trabalho, adotando-se a formulação baseada em deslocamentos para elasticidade linear. Ademais, visando avaliar o efeito da não linearidade geométrica na topologia ótima obtida, utiliza-se também o MEF posicional, o qual baseia-se nas posições nodais para solução do sistema não linear. Em conjunto com este método, adota-se a lei constitutiva de Saint-Venant-Kirchhoff, visando considerar os efeitos não lineares. Desta maneira, avalia-se a eficiência dos resultados obtidos por meio da aplicação de exemplos presentes na literatura. Conforme esperado, conclui-se que para exemplos cuja resposta apresenta pequenos deslocamentos, ambas as soluções se sobrepõem. No entanto, em se tratando de problemas em que a não linearidade geométrica tem influência, como estruturas constituídas de baixa densidade, a técnica do MEF posicional apresenta relevância na solução ótima. / This study has as main objective the understanding of two main topology optimization methods available in the literature: the methods SIMP and ESO. These methods were implemented computationally using the FORTRAN 90 programming language. The finite element method (FEM) is used as the mechanical solution parameter in this work, adopting the displacement-based formulation for linear elasticity. In addition, in order to evaluate the effect of geometric non-linearity in the optimal topology obtained, the FEM positional-based formulation is used, which uses the nodal positions for solution of the non-linear system. In conjunction with this method, the constitutive law adopted is the Saint-Venant-Kirchhoff in order to consider the nonlinearity. Hence, benchmarks presented in the literature are used to evaluate the efficiency of the obtained results. As expected, we conclude that the examples subjected to small displacements have similar solutions for both linear and nonlinear behavior. However, when problems that undergo geometrically nonlinear behavior, such as the ones modelled with soft materials, the FEM positional-based formulation has significant influence in the optimal solution.

Thermally cycling a thin plate of nickel-based superalloy with an intense in-plane thermal gradient, or hot spot, produces thermally induced crack growth not represented by classic thermo-mechanical fatigue (TMF). With the max hot spot temperature at 1093 C (2000 F) of a 1.5 mm thick, 82.55 mm diameter circular plate of B-1900+Hf, annular buckling and bending stresses result during each thermal cycle which drive the crack initiation and propagation. A finite element analysis (FEA) model, using ANSYS 7.1, has been developed which models the buckling and as well as represents the stress intensity at simulated crack lengths upon cool down of each thermal cycle. The model approximates the out-of-plane response at heat-up within 5% error and a difference in the final displacement of 0.185 mm after twelve thermal cycles. Using published da/dN vs. Keff data, the number of cycles needed to grow the crack to the experimental arrest distance is modeled within 1 mm. The number of cycles to this point is within 5 out of 462 in comparison to the experimental test.

L'archet, élément indispensable à la production sonore des instruments à cordes frottées, a jusqu'à présent fait l'objet de peu d'études scientifiques. Le travail présenté a pour objectif de mieux comprendre son comportement mécanique en situation de jeu. À cette fin, des modèles numériques sont développés. La baguette, précontrainte par la tension du crin, est modélisée par des éléments finis de poutre en formulation corotationnelle, afin de prendre en compte la non-linéarité géométrique inhérente au problème. Un premier modèle (2D) rend compte du comportement de l'archet dans le plan. Il donne lieu à une étude numérique sur une géométrie standard, visant à mettre en évidence l'influence des paramètres de fabrication et de réglage sur le comportement de l'archet sous tension. Un second modèle (3D) intègre le caractère tridimensionnel des sollicitations rencontrées en situation de jeu, prenant en compte la flexion latérale de la baguette. Une procédure non destructive de détermination des propriétés mécaniques du bois et de la mèche, basée sur une méthode inverse utilisant le modèle 2D, est proposée. À titre de validation expérimentale, des résultats numériques obtenus avec le modèle 3D sont confrontés aux résultats de mesures sur deux archets, pour différents réglages du cambre et de la tension. L'effet de la précontrainte sur la raideur de flexion latérale de la baguette est mis en exergue. Le bon accord observé confère au modèle un caractère prédictif, offrant des perspectives d'utilisation en tant qu'outil d'aide à la facture. Par ailleurs, la stabilité de l'archet est un problème que les facteurs doivent prendre en considération. Un modèle phénoménologique basé sur un système mécanique simple est présenté. Il vise à donner certaines tendances sur les conditions d'apparition d'une instabilité par bifurcation ou par point limite, en faisant une analogie avec les propriétés de l'archet. Le calcul numérique du comportement pré- et post-critique de l'archet permet d'identifier des cas d'instabilité similaires, dont on discute les conséquences possibles sur le jeu et la facture. Dans une dernière partie, des essais en jeu axés sur les réglages du cambre et de la tension sont effectués par des musiciens. Les résultats de ces tests subjectifs tendent à montrer l'influence des paramètres de réglage examinés dans l'appréciation des qualités de jeu. / The bow, which is essential to produce the sound of bowed string instruments, has been little studied. The present work aims to better understand its mechanical behavior in playing situation. To this end, numerical models are developped. The stick, which is prestressed due to hair tension, is modelized by beam finite elements. A corotational formulation is adopted to take into account geometric nonlinearity. A first model (2D) concerns the in-plane behavior of the bow. It is used within a numerical study aiming at showing the influence of making and adjusting parameters on the tightened bow. A second model (3D) takes into account out-of-plane loading that makes the stick bend laterally. A non-destructive procedure to determine mechanical properties of wood and hair is proposed. It is based on an inverse method using the 2D model. As an experimental validation, numerical results obtained with the 3D model are confronted to measurement on two bows, for different settings of camber and hair tension. The effect of prestress on lateral bending stiffness is highlighted. A good agreement is observed. Thus, the model can be considered as predictive and might be used as an aid to bow making. Furthermore, the stability of a bow is a problem considered by bow makers. A phenomenological model based on a simple mechanical system is presented. It aims to give tendancies on conditions at which bifurcation or limit point instability can occur, by drawing an analogy with the bow. The numerical computation of pre- and post-critical behavior of the bow shows similar instability cases. Their possible consequences on playing and making are discussed. Finally, playing tests with musicians are carried out, focusing on the adjustment of camber and hair tension. The results tend to show the influence of the considered adjustment parameters on the assessment of playing qualities.

In this study, methods for the geometric nonlinear analysis and the material nonlinear analysis of plane frames subjected to elevated temperatures are presented. The method of analysis is based on a Eulerian (co-rotational) formulation, which was developed initially for static loads, and is extended herein to include geometric and material nonlinearities. Local element force-deformation relationships are derived using the beam-column theory, taking into consideration the effect of curvature due to temperature gradient across the element cross-section. The changes in element chord lengths due to thermal axial strain and bowing due to the temperature gradient are also taken into account. This "beam-column" approach, using stability and bowing functions, requires significantly fewer elements per member (i.e. beam/column) for the analysis of a framed structure than the "finite-element" approach. A computational technique, utilizing Newton-Raphson iterations, is developed to determine the nonlinear response of structures. The inclusion of the reduction factors for the coefficient of thermal expansion, modulus of elasticity and yield strength is introduced and implemented with the use of temperature-dependent formulas. A comparison of the AISC reduction factor equations to the Eurocode reduction factor equations were found to be in close agreement. Numerical solutions derived from geometric and material analyses are presented for a number of benchmark structures to demonstrate the feasibility of the proposed method of analysis. The solutions generated for the geometrical analysis of a cantilever beam and an axially restrained column yield results that were close in proximity to the exact, theoretical solution. The geometric nonlinear analysis of the one-story frame exhibited typical behavior that was relatively close to the experimental results, thereby indicating that the proposed method is accurate. The feasibility of extending the method of analysis to include the effects of material nonlinearity is also explored, and some preliminary results are presented for an experimentally tested simply supported beam and the aforementioned one-story frame. The solutions generated for these structures indicate that the present analysis accurately predicts the deflections at lower temperatures but overestimates the failure temperature and final deflection. This may be in part due to a post-buckling reaction after the first plastic hinge is formed. Additional research is, therefore, needed before this method can be used to analyze the materially nonlinear response of structures.

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Feasible span-to-depth ratios for many modern bridge systems have been identified and documented in literature. No such parameters have been adequately identified in terms of proportioning bridge piers. This thesis includes a study of 22 existing reinforced concrete highway bridges and their respective pier systems to determine the state-of-the-art in design. The effect of different geometric and material parameters such as concrete strength, reinforcement ratio and slenderness ratio on the structural behavior of individual piers and multiple pier systems was examined. Approximate methods, which may be used for the purposes of preliminary design are discussed and reviewed. Serviceability and ultimate limit states design aids that can be used to identify appropriate preliminary cross-sectional pier dimensions and reinforcement ratios for individual piers given various slenderness ratios were developed. The structural behavior as well as an approach to the preliminary design of multiple pier bridge systems is presented.