Ces dernières décennies ont vu un renouveau d’intérêt pour les matériaux composites élastiques qui s’avèrent très utiles dans la conception de structures. Pour comprendre le comportement macroscopique de ces matériaux, on fait appel aux méthodes d’homogénéisation. Dans cette thèse, nous nous intéressons à étudier rigoureusement le comportement macroscopique des matériaux composites élastiques périodiques présentant des hétérogénéités à fort contraste dans le cadre de l'élasticité linéaire. Dans un premier temps, nous étudions l’homogénéisation de structures périodiques constituées d’un matériau élastique linéaire isotrope homogène de grande rigidité. Sous certaines hypothèses sur la géométrie des structures considérées, nous montrons que leur étude peut se réduire à l’étude de systèmes discrets correspondant à des réseaux périodiques de nœuds reliés entre eux par des interactions élastiques. Ensuite, en prenant en compte les différents ordres de grandeur des raideurs en extension, en flexion et en torsion, nous montrons que l’homogénéisation des structures considérées peut conduire à des matériaux de « second gradient », c’est-à-dire, des matériaux dont l’énergie élastique homogénéisée dépend des composantes du premier gradient et du second gradient du champ de déplacement. Dans un deuxième temps, nous réalisons des essais de traction sur des structures pantographiques pour étudier la faisabilité des matériaux de second gradient. / Recent decades have seen renewed interest in elastic composite materials that are proving to be very useful in structural design. To understand the macroscopic behavior of these materials, we use homogenization methods. In this thesis, we are interested in rigorously studying the macroscopic behavior of periodic elastic composite materials with high contrast heterogeneities in the framework of linear elasticity. Firstly, we study the homogenization of periodic structures made of a homogeneous isotropic linear elastic material with high rigidity. Under certain hypotheses on the geometry of the considered structures, we show that their study can be reduced to the study of discrete systems corresponding to frame lattices. Then, taking into account the different orders of magnitude of extensional, flexural and torsional stiffnesses, we show that the homogenization of the considered structures can lead to second gradient materials, that is, materials whose homogenized elastic energy depend on the components of the first gradient and the second gradient of the displacement field. In a second step, we carry out tensile tests on pantographic structures to study the feasibility of second gradient materials.

A scaled gradient descent method for competition of applications of conjugate gradient with priori estimations of the minimum value / This research proposes a novel method of improving the Gradient Descent method in an effort to be competitive with applications of the conjugate gradient method while reducing computation per iteration. Iterative methods for unconstrained optimization have found widespread application in digital signal processing applications for large inverse problems, such as the use of conjugate gradient for parallel image reconstruction in MR Imaging. In these problems, very good estimates of the minimum value at the objective function can be obtained by estimating the noise variance in the signal, or using additional measurements. The method proposed uses an estimation of the minimum to develop a scaling for Gradient Descent at each iteration, thus avoiding the necessity of a computationally extensive line search. A sufficient condition for convergence and proof are provided for the method, as well as an analysis of convergence rates for varying conditioned problems. The method is compared against the gradient descent and conjugate gradient methods. A method with a computationally inexpensive scaling factor is achieved that converges linearly for well-conditioned problems. The method is tested with tricky non-linear problems against gradient descent, but proves unsuccessful without augmenting with a line search. However with line search augmentation the method still outperforms gradient descent in iterations. The method is also benchmarked against conjugate gradient for linear problems, where it achieves similar convergence for well-conditioned problems even without augmenting with a line search. / Thesis / Master of Science (MSc) / This research proposes a novel method of improving the Gradient Descent method in an effort to be competitive with applications of the conjugate gradient method while reducing computation per iteration. Iterative methods for unconstrained optimization have found widespread application in digital signal processing applications for large inverse problems, such as the use of conjugate gradient for parallel image reconstruction in MR Imaging. In these problems, very good estimates of the minimum value at the objective function can be obtained by estimating the noise variance in the signal, or using additional measurements. The method proposed uses an estimation of the minimum to develop a scaling for Gradient Descent at each iteration, thus avoiding the necessity of a computationally extensive line search. A sufficient condition for convergence and proof are provided for the method, as well as an analysis of convergence rates for varying conditioned problems. The method is compared against the gradient descent and conjugate gradient methods. A method with a computationally inexpensive scaling factor is achieved that converges linearly for well-conditioned problems. The method is tested with tricky non-linear problems against gradient descent, but proves unsuccessful without augmenting with a line search. However with line search augmentation the method still outperforms gradient descent in iterations. The method is also benchmarked against conjugate gradient for linear problems, where it achieves similar convergence for well-conditioned problems even without augmenting with a line search.

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This investigation will use this ability in a different way. Studies have shown that a category can create a grade structure of prototypical items. We will take a graded structure generated by a category, and see if we can recreate the category based on presenting prototypical examples in a variety of ways. Five different sampling techniques will be used to determine which one is the best for category reconstruction. Since the items themselves have bits of information about the category, the number of samples presented will also be manipulated to determine if this is a factor in determining the category. The independent variables investigated were: sampling technique, and prompt conditions. In determining the effect of the independent variables on matching a category, the independent variables were also considered as mediating variables of each other. The method of opportunistic sampling was used for the surveys. The main participants were undergraduate 3rd year students taking a MSci 311 course at the University of Waterloo. Results indicate that there was no statistical significance. Fluctuations in significance levels indicate some random findings. Participants are not discriminating the samples or prompts which were given. This research is a contribution to this field because little research has been conducted in this area and implications are drawn for future research on the saliency of a category or attribute that can vary by context or knowledge

The purpose of this study is to investigate the behaviour of functionally graded materials in the coating design through analytical and numerical work. Functionally graded materials are advanced composite materials formed from two or more constituents with a continuously varying composition, which results in a continuous variation of material properties from one surface of the material to the other. The concept of functionally graded material is actively explored in coating design where structural and/or functional failures of the coating can happen due to a mismatch between the material properties of the coating and substrate, particularly at the coating/substrate interface. This work focuses on the performance of coated plates with homogeneous and graded coatings under various types of loading to develop a better understanding of their response. Firstly, the three dimensional elasticity solution for an isotropic coated plate with a stiffness gradient in the coating is extended to cover different types of applied loading and then a three dimensional elasticity solution for transversely isotropic materials with gradients in elastic properties is also developed. Based on the extended/developed solutions, a MATLAB code is created to produce a model that would enable the analysis of coated plates for a range of material, geometric and loading parameters. To test the analytical models, a finite element analysis is performed using the commercial finite element software ABAQUS, in which a user material subroutine is employed to generate a gradient in the material properties within each element and increase the accuracy of the results. All the developed analytical and numerical models are then used to carry out a comparative study of three-dimensional stress and displacement fields in the coated plates with homogeneous and graded coatings and establish the effect of various parameters such as coating thickness, coating position, plate dimensions, stiffness gradient, loading distributions and anisotropy on the coated plate response.

Thèse de doctorat : Mathématiques : Metz : 2000. / Thèse soutenue sur ensemble de travaux. Bibliogr. Index.

Thesis--Auburn University, 2009. / Abstract. Vita. Includes bibliographic references (p.50-52).

Ocean salinity is a renewable energy source that has not been recognized and could provide an opportunity to capture significant amount of clean energy when it mixes with river water. One of the processes emerging as a sustainable method for capturing energy from seawater is reverse electrodialysis (RED), which generates power via the transport of the positive and negative ions in the water through selective ion exchange membranes (IEMs). RED power generation is relatively close to commercialization, but its application is often limited by system power efficiency in natural water conditions. Although various types of salt ions exist in environmental saline water, most efforts have been focused on sodium chloride as a single ionic source in the water and the effects of other common multivalent ions (e.g., magnesium and sulfate) on power generation remain unexplored. Moreover, the commercial feasibility of RED is highly challenged by the absence of specialized RED membranes. Currently available IEMs are not optimized for RED power conversion systems, but successful operation is highly dependent on the membranes used. Major advances in manufacturing of proper IEMs will be a critical pathway to accelerate large-scale energy conversion by RED. Therefore, this study aimed at advancing our understanding of the RED power system for efficient and stable salinity gradient energy generation. Specifically, it is comprised of three parts. First, a mathematical model is developed for three different monovalent and multivalent ion combinations to determine the effect of different ionic compositions of the feed solution on the power density. Efforts are further made to optimize the RED system with respect to improving power density by investigating the sensitivity of key response parameters such as flow rate ratios and intermembrane distance ratios. Second, novel organic-inorganic nanocomposite cation exchange membranes (CEMs) are synthesized for RED application by introducing functionalized inorganic materials into an organic polymer matrix. The effect of inorganic particle filler loading within the organic polymer matrix on physico- and electrochemical performance is investigated. The results revealed that the increase of functionalized nanoparticle loading controls the effective ion transport in the membrane structure and there exists an optimum amount of nanoparticles (i.e., charged groups), which performs the best in selectively exchanging counter-ions, while excluding co-ionic species. Third, the membrane structure modification is demonstrated to enhance ion transport while maintaining large surface-charged functional groups in the polymer matrix. We have synthesized custom nanocomposite CEMs to tailor porous membrane structures of various thicknesses, aging (evaporation) time, and inorganic nanoparticle loadings. We have further tailored the membrane structure by incorporating different inorganic particle filler sizes. These engineered design approaches are found to be highly effective in obtaining desired physico- and electrochemical properties, which allowed higher ionic current flow throughout the system. Furthermore, for the first time we showed the successful application of tailor-made nanocomposite CEMs in a RED stack and achieved superb power density, which exceeds the power output obtained with the commercially available membranes. In summary, this dissertation has advanced our understanding of salinity gradient energy generation using RED technique. Specifically, computational modeling and simulation study investigates the development and optimization approaches of the RED process for practical application of RED using natural water conditions. Furthermore, the RED membranes developed in this dissertation focuses on fabrication, characterization, and optimization of cation exchange membranes. Overall, the results of this study are anticipated to benefit the future optimization of energy-capturing mechanisms in RED and provide the better pathway for the sustainable salinity gradient power generation.

Thesis (M.S.) in Mechanical Engineering--University of Maine, 2005. / Includes vita. Includes bibliographical references (leaves 135-142).

The study was conducted on Mt. Hallasan (1950 a.s.l.) in South Korea. Forest plots were established along altitudinal gradient (950-1770 a.s.l.) from oak-hornbeam (Quercus serrata, C. laxiflora), to mixed-oak (Quercus mongolica, Taxus cuspidata), and fir (Abies koreana, Sorbus commixta) forests. Vascular plants were identified to species, and their total cover and covers of individual species in herb ({>} 1 m), shrub (1 - 5 m) and tree ({<} 5 m) layers estimated using Braun-Blanquet scale. Dentrended Correspondence Analyses was used to analyze relationship between environment and species composition, lifeforms spectra and plant diversity. The spatio-temporal variations in stem dispersion, radial growth, and mode of competition among trees were examined using the mapped location of trees and tree-rings. Changes in radial-growth were used to analyse stand disturbance history using 36647 measured tree-rings. Histories of radial-growth of individuals trees were further examined using visual classification to 5 different groups of growth trends. Ripley´s K-function was used to determine whether the spatial distribution pattern of trees was random, regular or clumped. Spatial size autocorrelations were used to determine the mode and extant of neighbor interactions. Spatial associations of different groups of trees and random mortality test were also computed for tree stands where Abies koreana was a dominant species.