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A geotechnical composite foundation system that has become increasingly popular over the years is a column-supported, geosynthetic-reinforced embankment. This system consists of strong columns or piles placed in soft clay, a bridging layer of sand or sand and gravel, and one or more layers of geosynthetic reinforcement. It is often used in soft ground situations where there is a need for faster construction and/or where there are adjacent structures that would be affected by settlement caused by the new embankment. The geosynthetic reinforcement is placed in the bridging layer to help transfer the load to the columns and decrease the total and differential settlements. Current methods of analysis for this material are extremely simplified, and do not thoroughly model the behavior of the system. Therefore, a more comprehensive analysis needs to be conducted that will better predict the true effect of the geosynthetic layer or layers. In this thesis, one geosynthetic layer was considered. Models were developed using two different computer programs: Mathematica and ABAQUS. In Mathematica, the Rayleigh-Ritz method was used to approximate the deflections and tensile forces in the membrane. This method considered the geosynthetic reinforcement as a plate and minimized the total energy of the system. In ABAQUS, a finite element modeling program, the membrane was analyzed as a shell, and results were compared with some results from Mathematica. A parametric study was completed in Mathematica to determine the effects of different parameters. The parameters varied involved the geogrid properties (Poisson's ratio, modulus of elasticity, and thickness), the vertical load, the soil stiffness above the piles, the soil stiffness between the piles, the size of the piles, and the distance between the piles. / Master of Science

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.

A displacement-based Rayleigh-Ritz finite element model is developed to simulate the static and dynamic behavior of stiffened plates. By con1paring natural frequency, time-history, and power density predictions with experimental results, it is shown that the model can be used to predict the vibratory behavior of wood floor systems constructed With either solid-sawn joists, I-Joists, or parallel-chard-trusses. Furthermore. using the model. it is shown that appropriate structural modifications can be used to improve the performance of wood floor systems by increasing natural frequency and reducing peak time-history velocity. Using the techniques described. a design example is included that indicates ho,v floor acceptability can be achieved. / Ph. D.

L’emploi de matériaux composites à matrice organique (CMO) pour la réalisation de structures aéronautiques « tièdes », peut exposer ces matériaux à l’action d’environnements agressifs, qui peuvent entrainer des phénomènes de vieillissement et de dégradation sévères associés à la diffusion d’espèces au sein du réseau macromoléculaire des matrices polymères. La complexité de la microstructure des CMO utilisés pour ces applications peut complexifier la compréhension de phénomènes de dégradation. Le vieillissement humide des CMO préoccupe particulièrement les industriels du secteur aéronautique ; la diffusion de l’eau dans la matrice polymère du composite peut entrainer des phénomènes de gonflement hygroscopique, des modifications des propriétés mécaniques. Des méthodes expérimentales existent pour la caractérisation de ces phénomènes et pour l’identification des paramètres associés : ces méthodes préconisent souvent l’emploi d’éprouvettes saturées en humidité,ce qui nécessite de longs temps de conditionnement et un nombre élevé d’échantillons. Cette thèse a pour but d’établir des protocoles d’identification rapide des propriétés diffuso-mécaniques de matériaux polymères et CMO pour applications aéronautiques. La démarche mise en place dans cette thèse s’organise autour de quatre chapitres. Le premier chapitre présente une étude bibliographique sur les outils de modélisation des couplages diffuso-mécaniques et sur les méthodes de caractérisation des propriétés diffuso-mécaniques. L’étude bibliographique permet de préciser le cadre de travail, qui prévoit l’emploi d’un modèle diffuso-mécanique faiblement couplé où la diffusion d’eau suit la loi de Fick et le comportement mécanique est hygroélastique linéaire, dépendant de la concentration en eau. Le second chapitre présente la mise en place et le développement d’une méthode d’identification rapide des propriétés de diffusion anisotrope, adaptée à des CMO à architecture complexe.La méthode s’appuie sur des mesures de prise de masse d’échantillons de CMO, l’anisotropie de diffusion de ces matériaux est obtenue par rotation des axes principaux d’orthotropie. La méthode proposée représente une extension de la « méthode de la pente » introduite par Shen et Springer pour l’identification des propriétés de diffusion de matériaux orthotropes, et basée sur l’exploitation des courbes gravimétriques aux temps courts. A travers cette méthode, les coefficients principaux et les axes principaux d’orthotropie peuvent être identifiés. Une discussion sur les conditions d’équivalence de la diffusion 3D à la diffusion 1D en fonction de l’épaisseur de l’échantillon est également présentée à la fin de ce chapitre. Le troisième chapitre explore à travers une étude numérique la possibilité d’identifier rapidement les propriétés mécaniques affectées par la concentration en eau de matériaux polymères à travers des essais mécaniques sur plaques minces avec des gradients de concentration en eau. Des essais de traction et de flexion sont considérés. Pour des matériaux isotropes, dans un cadre hygroélastique, il est montré que cette méthode permet l’identification du module d’Young et du coefficient de Poisson dépendant de la concentration en eau avec un gain remarquable de temps d’essai par rapport à des essais sur des échantillons saturés en humidité. Enfin, le dernier chapitre propose à travers une étude numérique une méthode d’identification rapide des propriétés diffuso-mécaniques de matériaux isotropes basée sur l’emploi de plaques sollicitées par un champ asymétrique de concentration en eau. L’identification est ainsi effectuée à partir du suivi des déflexions engendrées par les champs de concentration. Le coefficient de dilatation hygroscopique et le module d’Young dépendant de la concentration en eau peuvent être identifiés durant l’essai, à l’état transitoire du conditionnement, avec un gain remarquable du temps d’essai par rapport à des essais sur échantillons saturés en humidité. / The use of organic matrix composite materials (OMC) for the realization of "warm" aeronautical structures, may expose these materials to aggressive environments: wet or gaseous environments,high temperatures, which may promote severe aging and degradation phenomena related to species diffusion within the macromolecular network of the polymer matrices. The complexity of the OMC microstructure used for these applications can complicate the understanding of degradation phenomena : for example, species diffusion can be isotropic, orthotropic or anisotropic, depending on the texture of the fibrous reinforcement. Humid aging of OMC is of particular concern for the aeronautical industry ; the diffusion of water in the polymer matrix of the composite may promote hygroscopic swelling, changes in mechanical properties (stiffness, strength). Experimental methods exist for the characterization of these phenomena and for the identification of the associated parameters : these methods often recommend the use of moisture saturated specimens, which require long conditioning times, sometimes often a relevant number of samples (1 sample for each saturated state), high costs. The aim of this work is to establish protocols for fast identification of the diffusomechanical properties of polymers and polymer based OMC materials for aeronautical applications. The approach implemented in this thesis is organized in four chapters. The first chapter presents a bibliographic study on coupled diffuso-mechanics modeling tools and on methods of characterization/identification of diffuso-mechanical properties, more particularly for OMC for aeronautical applications. The bibliographic study allows specifying the framework of the present research, which foresees the employment of a weakly coupled diffuso-mechanical model, where water diffusion follows the Fick’s law and the mechanical behavior is linear hygroelastic, depending on water content. The second chap-ter presents the setting up and the development of a method for fast identification of anisotropic diffusion properties, suitable for OMC with complex architecture, such as for instance, 2D or 3Dwoven OMC. The method relies on mass-gain measures of OMC samples, the diffusion anisotropy ofthese materials is obtained by rotating the axes of orthotropy. The proposed method represents an extension of the "slope method" introduced by Shen and Springer in the 1970s for the identification of the diffusion properties of orthotropic materials (such as laminated composites), and is based onthe exploitation of gravimetric curves at short times. Through this method, the principal coefficients and the principal axes of orthotropy can be identified. A discussion about the transition from 3Dto 1D diffusion as a function of the sample geometry is also presented at the end of this chapter. The third chapter explores through a numerical study the possibility of identifying in a fast way the mechanical properties affected by moisture of polymeric materials by the use of mechanical tests on thin plates with water concentration gradients. Traction and bending tests are taken into account.For isotropic materials, in a hygroelastic setting, it is showed that this method allows identifyng the water concentration dependent Young’s modulus and the Poisson’s ratio with a remarkable time gain compared to tests on moisture saturated samples. Finally, the last chapter proposes through a numerical study a method for fast identification of the diffuso-mechanical properties of isotropic materials based on the use of plates loaded by an asymmetric water concentration field. The identification is thus carried out from the monitoring deflections generated by the concentration fields. The moisturedependent hygroscopic expansion coefficient and Young’s modulus can be identified during the test,by exploiting the transient state of conditioning, with a remarkable time gain compared with moisture saturated samples.

Proposed designs for Very Large Floating Structures motivate us to understand water-wave propagation through arrays of hundreds, or possibly thousands, of floating structures. The water-wave problems we study are each formulated under the usual conditions of linear wave theory. We study the frequency-domain problem of water-wave propagation through a periodically arranged array of structures, which are solved using a variety of methods. In the first instance we solve the problem for a periodically arranged infinite array using the method of matched asymptotic expansions for both shallow and deep water; the structures are assumed to be small relative to the wavelength and the array periodicity, and may be fixed or float freely. We then solve the same infinite array problem using a numerical approach, namely the Rayleigh-Ritz method, for fixed cylinders in water of finite depth and deep water. No limiting assumptions on the size of the structures relative to other length scales need to be made using this method. Whilst we aren t afforded the luxury of explicit approximations to the solutions, we are able to compute diagrams that can be used to aid an investigation into negative refraction. Finally we solve the water-wave problem for a so-called strip array (that is, an array that extends to infinity in one horizontal direction, but is finite in the other), which allows us to consider the transmission and reflection properties of a water-wave incident on the structures. The problem is solved using the method of multiple scales, under the assumption that the evolution of waves in a horizontal direction occurs on a slower scale than the other time scales that are present, and the method of matched asymptotic expansions using the same assumptions as for the infinite array case.

Este trabalho apresenta os resultados obtidos para carga crítica de flambagem de placas de material composto laminado com duas bordas engastadas e duas bordas simplesmente apoiadas sujeitas a diversas combinações de carregamento. A carga crítica ée obtida através do método de Rayleigh-Ritz, utilizando uma série polinomial e uma senoidal. Foi desenvolvido um programa computacional para que os resultados numéricos fossem obtidos. Os resultados numéricos são analisados e discutidos, e são comparados com resultados apresentados pelo ESDU (Engineering Science Data Unit) e com aproximações obtidas por elementos finitos.

A instabilidade de placas laminadas se tornou um problema de grande importância no projeto de estruturas leves e seguras. Desta forma, o estudo de métodos e o desenvolvimento de programas computacionais para a obtenção de cargas críticas de flambagem neste tipo de estrutura são muito úteis. Este trabalho apresenta o estudo da aplicação da série trigonométrica de duplo seno na obtenção de cargas críticas de laminados retangulares simétricos, com os bordos simplesmente apoiados, baseado nas hipóteses de Kirchhoff, utilizando o método de Rayleigh-Ritz. Um programa computacional no Matlab 6.5 foi desenvolvido e validado por comparação com resultados encontrados na literatura. Em seguida, comparou-se os resultados do programa com os resultados obtidos pelo método dos elementos finitos utilizando-se o Nastran. Verificou-se que a série de duplo seno não ée adequada para a solução de laminados altamente anisotrópicos.

Tese de Mestrado Integrado. Engenharia Mecânica. Faculdade de Engenharia. Universidade do Porto. 2013

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.