Group Representation Theory is the mathematical language best suited to describing the symmetry properties of a structure, and a structural analysis can utilises Group Representation Theory to provide the most efficient and systematic method of exploiting the full symmetry properties of any symmetric structure. Group Representation Theory methods currently exist for the Stiffness Niethod of structural analysis, where the stiffness matrix of a structure is block-diagonalised into a number of independent submatrices, each of which relates applied loads and displacements with a particular type of symmetry. This dissertation extends the application of Group Representation Theory to the equilibrium and compatibility matrices which are commonly used in the Force Method of structural analysis. Group Representation Theory is used to find symmetry-adapted coordinate systems for both the external vector space which is suitable for representing the loads applied to a structure, and the internal vector space wh",t-k is-suitable for representing the internal forces. Using these symmetry-adapted coordinate systems the equilibrium matrix is block-diagonalised into a number of independent submatrix blocks, thus decomposing the analysis into a number of subproblems which require less computational effort. Each independent equilibrium submatrix block relates applied loads and internal forces with particular symmetry properties, and hence any states of self-stress or inextensional mechanisms in one of these equilibrium submatrix blocks will necessarily have ~rresponding symmetry properties. Thus, a symmetry analysis provides valuable insight into the behaviour of symmetric structures by helping to identify and classif:)'. any states of self-stress .or inextensional mechanisms present in a structure. In certain cases it is also possible for a symmetry analysis to identify when a structure contains a :ijnite rather than infinitesimal mechanism. To do this a symmetry analysis must b~ carried out using the symmetry properties of the inextensional mechanism of interest. If the analysis shows that any states of self-stress which exist in the structure have "lesser" symmetry properties, then the states of self-stress exist independently from the mechanism and cannot prevent its finite motion.

Java applets are developed to assist in the learning of basic structural analysis concepts. In order for these programs to be easily available over the Internet, they are written in the object-oriented Java programming language. The Java programs known as applets are embedded in HTML documents. The HTML documents, part of a series of instructional units, present the topics demonstrated by the applets. The applets include truss and frame determinacy applets; a three-hinged arch bridge applet; determinate and indeterminate truss analysis applets; determinate and indeterminate frame analysis applets and an influence line analysis applet. These programs are available to any student or instructor with Internet access. The applets provide good examples of the application of object-oriented programming and the development of software for a graphical user interface. They also serve as excellent tools that facilitate the understanding of structural engineering concepts utilizing a medium that allows independent learning at an individual pace. / Master of Science

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In this thesis, formulas for the local tangent stiffness matrix of a plane frame member are derived by differentiating the member resistance vector in the displaced position. This approach facilitates an analysis using only one element per member. The formulas are checked by finite difference. The derivation leads to the familiar elastic and geometric stiffness matrices used by other authors plus an additional higher order geometric stiffness matrix. Contributions of each of the three sub-matrices to the tangent stiffness matrix are studied on both the member and structure levels through two numerical examples. These same examples are analyzed three different ways for comparison. First, the examples are analyzed using the method presented in this thesis. Second, they are analyzed with the finite element modeling software ABAQUS/CAE using only one element per member. Third, they are analyzed with ABAQUS using 200 elements per member. Comparisons are made assuming the ABAQUS analysis which uses 200 elements per member is the most accurate. The element presented in this thesis performs much better than the ABAQUS analysis which uses one element per member, with maximum errors of 1.0% and 40.8% respectively, for a cantilever column example. The maximum error for the two story frame example using the ABAQUS analysis with one element per member is 42.8%, while the results from the analysis using the element presented in this thesis are within 1.5%. Using the element presented in this thesis with only one element per member gives good and computationally efficient results for second-order analysis.

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Cette thèse traite du développement d’un élément continu de plaques orthotropes, sandwichs et multicouches. La démarche consiste dans un premier temps à établir la matrice de raideur dynamique de plaques orthotropes pour des conditions aux limites naturelles à partir d’une reformulation des éléments de plaques isotropes développés au laboratoire QUARTZ (EA7393). La démarche est basée d’une part sur la décomposition des conditions aux limites libres décrite par Gorman et d’autre part sur la résolution des équations de mouvement en se basant sur les développements en séries de Levy. La matrice de raideur dynamique est ensuite obtenue par projection des déplacements et des efforts de frontières sur des bases fonctionnelles compatibles avec les opérations d’assemblage. Dans un second temps, la formulation des éléments sandwichs et multicouches est décrite par superposition des plaques orthotropes précédemment développées.Les formulations présentées prennent en compte les vibrations de flexion et les vibrations dans le plan, dites vibrations de membrane. La validation de ces éléments est menée par une confrontation systématique de réponses harmoniques non amorties avec celles obtenues par diverses modélisations éléments finis. / This thesis deals with the development of a continuous element for orthotropic, sandwich and multilayer plates. This approach is based essentially on the construction of the dynamic stiffness matrix of orthotropic plates using natural boundary conditions from a reformulation of the isotropic plate elements developed in the QUARTZ laboratory (EA 7393). In order to develop the dynamic stiffness matrix of the studied element we resort on the first hand to the decomposition of free boundary conditions described by Gorman, on the second hand to the resolution of the equations of motion by using Levy series expansions. The dynamic stiffness matrix is then obtained by projecting movements and frontier efforts on functional bases compatible with assembly operations. Finally the continuous sandwich and multilayer plate element is described by superposition of continuous orthotropic plates element previously developed.The formulations presented takes into account the bending vibration and the vibration in the plane, called membrane vibration. The validation of all obtained results is conducted by a systematic comparison of undamped harmonic responses with those obtained by various finite element models.

Un des outils numériques les plus utilisés en ingénierie est la méthode des éléments finis, qui peut être mise en o euvre grâce à l'utilisation de nombreux codes de calcul. Toutefois, une difficulté apparaît lors de l'utilisation de la méthode des éléments finis, spécialement en géotechnique, lorsque la structure étudiée est en interaction avec un domaine de dimensions infinies. L'usage courant en ingénierie est alors de réaliser les calculs sur des domaines bornés, mais la définition de la frontière de tels domaines bornés pose de sérieux problèmes. Pour traiter convenablement les problèmes comportant des frontières à l'infini, l'utilisation d'éléments discrets "infinis" est maintenant souvent délaissée au profit de la méthode des équations intégrales ou "méthode des éléments de frontière" qui permet de résoudre un système d'équations aux dérivées partielles linéaire dans un domaine infini en ne maillant que la frontière du domaine à distance finie. La mise en oeuvre du couplage entre la méthode des éléments finis et la méthode des éléments de frontière apparaît donc comme particulièrement intéressante car elle permet de bénéficier de la flexibilité des codes de calcul par éléments finis tout en permettant de représenter les domaines infinis à l'aide de la méthode des éléments de frontière. La méthode est basée sur la construction de la "matrice de raideur" du domaine infini grâce à l'utilisation de la méthode des équations intégrales. Il suffit alors d'assembler la matrice de raideur du domaine infini avec la matrice de raideur du domaine fini représenté par éléments finis. L'utilisation de la méthode la plus simple de traitement des équations intégrales, dite méthode de « collocation » conduit à une matrice de raideur non-symétrique. Par ailleurs, la méthode dite «Singular Galerkin» conduit à une formulation symétrique, mais au prix du calcul d'intégrales hypersingulières. La thèse porte sur une nouvelle formulation permettant d'obtenir une matrice de raideur symétrique sans intégrales hypersingulières, dans le cas de problèmes plans. Quelques applications numériques sont abordées pour des problèmes courants rencontrés en géotechnique / One of the most used numerical tools in engineering is the finite element method, which can be implemented through the use of many computer codes. However, a difficulty arises when using the finite element method, especially in geotechnical engineering, where the structure is studied in interaction with a field of infinite dimensions. The commonly used in engineering is then performming the calculations on bounded domains, but the definition of the border of the domain also poses serious problems. To properly solve the problems which have the boundary at infinity, the use of discrete elements "infinite" is now often neglected in favor of the integral equations method or "boundary element method", which allows to solve a linear partial differential equations system in an infinite domain by the discretization of the only boundary of the domain at finite distance. The implementation of coupling between the finite element method and boundary element method is therefore particularly interesting because it allows to benefit the flexibility of computer codes by the finite element method, while the infinite domains is represented by the help of the integral equations method. It is sufficient to assemble the stiffness matrix of infinite domain with the stiffness matrix of finite domain represented by finite elements. Using the simplest method of treatment of integral equations, known as method of "collocation" leads to a non-symmetric stiffness matrix. Furthermore, a method known “Galerkin Singular” leads to a symmetric formulation, but it is at the cost of computing hypersingular integrals. The thesis focuses on a new formulation to obtain a symmetric stiffness matrix without full hypersingular, in the case of plane problems. Some numerical applications are discussed for common problems encountered in geotechnical engineering

This study presents Computer-Aided Fixture Design Verification (CAFDV) - the methods and implementations to define, measure and optimize the quality of fixture designs. CAFDV verifies a fixture for its locating performance, machining surface accuracy, stability, and surface accessibility. CAFDV also optimizes a fixture for its locator layout design, initial clamping forces, and tolerance specification. The demand for CAFDV came from both fixture design engineers and today's supply chain managers. They need such a tool to inform them the quality of a fixture design, and to find potential problems before it is actually manufactured. For supply chain managers, they will also be able to quantitatively measure and control the product quality from vendors, with even little fixture design knowledge. CAFDV uses two models - one geometric and one kinetic - to represent, verify and optimize fixture designs. The geometric model uses the Jacobian Matrix to establish the relationship between workpiece-fixture displacements, and the kinetic model uses the Fixture Stiffness Matrix to link external forces with fixture deformation and workpiece displacement. Computer software for CAFDV has also been developed and integrated with CAD package I-DEAS TM. CAD integration and a friendly graphic user interface allows the user to have easy interactions with 3D models and visual feedback from analysis results.

Ce travail porte sur l'étude de structures multicouches à gradient de propriétés (FGM : Functionnally Graded Materials). Ces matériaux sont apparus afin d'obtenir des dépôts aux caractéristiques nouvelles et innovantes. Les FGM sont désormais présents dans divers applications de haute technologie.Un système multicouche à gradient de composition entre le cuivre et le nickel, a fait l'objet d'une étude expérimentale par l'application de la technique des ultrasons laser (LU) couplée à une étude numérique basée sur le formalisme de Stroh et la méthode de la matrice de raideur. Le travail de thèse est organisé autour de quatre chapitres. Le premier chapitre est dédié à l'aspect théorique de la propagation des ondes de surface dans une structure multicouche et à gradient de propriétés. Ainsi, un développement des méthodes numériques pour les matériaux dotés de la piézoélectricité est fourni. Le second chapitre se consacre à l'élaboration des échantillons utilisés dans notre étude et obtenus par pulvérisation cathodique. Le troisième chapitre présente la méthode opto-acoustique utilisée pour caractériser les échantillons réalisés. le dernier chapitre présente les résultats expérimentaux, confrontés aux résultats théoriques, décrivant le comportement dispersif des multicouches submicrométriques. / This thesis focuses on the study of multilayered and FGM systems (FGM : Functionnally Graded Materials). The main purpose of this type of materials is to obtain deposits with new and innovative features and to increase the fracture toughness. From now on, FGM have been used in various high technology applications.A multilayer system with a composition gradient of copper and nickel was studied experimentally by the application of the laser ultrasonics (LU) technique which was coupled to a theoretical study based on the ordinary differential equations (ODE) and the Stiffness Matrix Method (SMM). This PhD thesis is organized around four chapters. The first chapter is dedicated to a theoretical study of the propagation behavior of surface acoustic wave (SAW) in a multilayer system with à gradient of properties. Thus, the numerical methods developped for the piezoelectric materials (FGPM) are presented. The second chapter is devoted to describe the setup for making the samples used in this study which were obtained by sputtering technique. The third chapter presents the experimental study dedicated to the measurement of surface wave velocities in many crystal orientations. The last chapter of the manuscript presents experimental results, compared to the theoretical results, describing the dispersive behavior of submicrometer multilayers.

La fibrose hépatique est un problème de santé publique. Cette pathologie est caractérisée par une accumulation excessive de matrice extracellulaire, composée principalement de collagène, augmentant la rigidité du foie. Environ 90% des hépatocarcinomes se développent sur un foie fibrotique / cirrhotique, laissant présager une relation entre la rigidité tissulaire et le développement tumoral. Pour étudier le rôle des forces exercées par la matrice extracellulaire sur le phénotype des cellules hépatiques, nous avons développé un modèle de culture 3D de cellules hépatiques dans des gels de collagène de rigidités variables. Dans ces conditions, les cellules hépatiques présentent une forte prolifération et un maintien de la différenciation dans les matrices les plus rigides. En parallèle, les cellules hépatiques transformées peuvent modifier la matrice de collagène pour former des signatures de collagène TACS (Tumor Associated Collagen Signatures). Une analyse des voies de signalisation impliquées dans la formation des TACS 3 nous a permis de déterminer 2 voies indispensables pour ces mécanismes: MEK/ERK et MLCK. Le bon maintien des fonctions différenciées et de biotransformation des cellules hépatiques font des cultures 3D en gel de collagène un excellent modèle pour des applications en biotechnologie. Nous avons également développé une technique de quantification standardisée et automatisée du collagène, dans un modèle murin de fibrose hépatique, par utilisation de la microscopie SHG, qui permet de détecter de faibles variations de quantité de collagène. Cette technique permet également de caractériser qualitativement, après analyse d'images, le collagène et de renforcer la discrimination entre les différents stades fibrotiques. La caractérisation des cross-links de collagène, par cette approche, est actuellement en cours d'étude et permettrait d'appréhender les capacités de réversion. / Liver fibrosis is a real public health problem. This pathology is characterized by an excessive accumulation of extracellular matrix, mainly composed of collagen, increasing liver rigidity. Approximately 90% of hepatocellular carcinomas develop from a fibrotic/cirrhotic liver, suggesting a relationship between tissue rigidity and tumor development. To investigate the role of stiffness on the hepatic phenotype, we have developed a 3D culture model of collagen gels of varying stiffness. Our results show a better survival, an increase of proliferation and differentiation of liver cells in rigid matrices. In addition, the cells are able to modify the collagen matrix and to form collagen signatures TACS (Tumor Associated Collagen Signatures). An analysis of the signaling pathways involved in the formation of TACS 3 allowed us to determine that 2 pathways are important for these mechanisms: MEK/ERK and MLCK. The high level of differentiated functions and biotransformation of the hepatic cells make 3D collagen cultures an excellent model for applications in biotechnology. Using the SHG microscopy, we have also developed a standardized and automated quantification of collagen to detect small amount of collagen in a mouse liver fibrosis model. This technique allows us to characterize qualitatively the collagen and to strengthen the discrimination between fibrotic scores. The characterization of the collagen cross-links by this approach is under study and would allow to study the reversion capacity.