In this thesis, the main objects of study are probability measures on the isomorphism classes of countable, connected rooted graphs. An important class of such measures is formed by unimodular measures, which satisfy a certain equation, sometimes referred to as the intrinsic mass transport principle. The so-called law of a finite graph is an example of a unimodular measure. We say that a measure is sustained by a countable graph if the set of rooted connected components of the graph has full measure. We demonstrate several new results involving sustained unimodular measures, and provide thorough arguments for known ones. In particular, we give a criterion for unimodularity on connected graphs, deduce that connected graphs sustain at most one unimodular measure, and prove that unimodular measures sustained by disconnected graphs are convex combinations. Furthermore, we discuss weak limits of laws of finite graphs, and construct counterexamples to seemingly reasonable conjectures.

This thesis presents an investigation of the modelling and optimal design of a particular 3-degree-of-freedom (DOF) XYθz micro-motion stage. This stage provides micron-scale motion in X and Y directions and a rotation about the Z-axis. Such a stage can be used for applications where positioning of components with micrometre, or even nanometre positioning accuracy is required. Some applications are; the positioning of samples in a scanning-electron-microscope; the positioning of masks in lithography; aligning fibre-optics and lasers; and manipulation of micro-scale objects in micro-biology or micro-systems assembly. The XYθz micro-motion stage investigated in this study uses a particular topology of monolithic compliant mechanism and three stack piezoelectric actuators. The compliant mechanism used is a 3RRR (three revolute-revolute-revolute) parallel compliant mechanism using flexure hinges. This parallel mechanism uses three RRR linkages. Each of the three RRR linkages uses three circular profile flexure hinges. Each flexure hinge provides predominantly rotational motion about one axis. This topology of mechanism has a symmetrical structure and provides numerous advantages that make it appropriate for use in a micro-motion stage. However, as yet this topology of compliant mechanism has only been investigated by a handful of researchers and it has not been used in any commercially developed systems. The design methodology of a stage using the 3RRR compliant mechanism has not been investigated in detail. In this thesis a study is presented that investigates different approaches to model the 3RRR compliant mechanism and also considers the piezo-actuator modelling, to give the complete XYθz micro-motion stage. Three models are presented and compared; the Pseudo-Rigid-Body Model (PRBM); a two-dimensional Finite-Element-Model (2-D FEM); and a third model is developed that is similar to the PRBM, but uses analytical equations to model the multiple degree-of-freedom compliance of the flexure hinges. The models developed are then used in parametric study so that the relationship between design parameters and output behaviour can be understood. An optimal design approach is then presented to develop an XYθz micro-motion stage for a particular application in a Scanning-Electron-Microscope (SEM). Finally experimental validation of the models is presented. The results of this study indicate which modelling approaches are accurate enough to prove useful for design, while also considering which models are computationally simple enough to be efficient and easy to use. The kinematic and dynamic behaviour of the 3RRR compliant mechanism and XYθz micro-motion stage is discussed in detail. This includes; a comprehensive description of the stage workspace, defining reachable and constant-rotation workspace areas; a discussion of actuator coupling; and in depth investigation of the modes of vibration. The results of the parametric study provide useful insight to aid the design of the XYz micro-motion stage and help simplify optimal design. The parametric study also highlights the difference in trends predicted by different modelling methods, which demonstrates the importance of using an appropriate model in design. The experimental validation demonstrates the accuracy of some modelling approaches while highlighting the limited accuracy of others. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1272186 / Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 2007

Βασικός άξονας της παρούσας διατριβής είναι οι σχετικιστικοί υπολογισμοί πολυτροπικών μοντέλων περιστρεϕόμενων αστέρων νετρονίων. Επειδή δεν υπάρχει ακριβής αναλυτική λύση των εξισώσεων του Einstein για το ϐαρυτικό πεδίο ενός περιστρεϕόμενου αστέρα νετρονίων, επιχειρούμε την αϱιθμητική επίλυση στο μιγαδικό επίπεδο όλων των διαϕορικών εξισώσεων, που εμπεριέχονται στην διαταρακτική μέθοδο του Hartle. Δίνουμε έμϕαση στον υπολογισμό φυσικών ποσοτήτων, που περιγράϕουν την γεωμετρία ταχέως περιστρεϕόμενων μοντέλων. Συγκρίνοντας τα αριθμητικά αποτελέσματα που ϐρίσκουμε με ορισμένες πολύπλοκες επαναληπτικές μεθόδους, ελέγχουμε την αξιόλογη ϐελτίωση των αποτελεσμάτων μας, έναντι εκείνων που δίνονται από το κλασσικό διαταρακτικό σχήμα του Hartle. Η παρούσα διατριβή χωρίζεται σε τέσσερα μέρη, που αναπτύσσονται στα κεϕάλαια 1, 2, 3 και 4. Στο πρώτο κεϕάλαιο, ϑα εστιάσουμε την προσοχή μας στο σύστημα διαφορικών εξισώσεων Oppenheimer − Volkov, που εξάγονται από τις εξισώσεις πεδίου του Einstein. Σε συνδυασμό με μια καταστατική εξίσωση περιγράφουμε σχετικιστικά πολυτροπικά μοντέλα μη περιστρεϕόμενων αστέρων νετρονίων σε υδροστατική ισορροπία. Ακολούθως, περιγράϕουμε ένα καθαϱά σχετικιστικό φαινόμενο, τον συρμό των αδρανειακών συστημάτων λόγω της περιστροϕής του αστέρα. Στην συνέχεια, χρησιμοποιούμε την μέθοδο διαταραχής του Hartle, σύμϕωνα με την οποία δεχόμαστε ότι ο στατικός αστέρας είναι το αδιατάρακτο σύστημα, πάνω στο οποίο εϕαρμόζουμε μικρές διαταραχές (ϑεωρώντας την ομοιόμορϕη περιστροϕή ως διαταραχή) και έτσι υπολογίζουμε τις διορθώσεις στην μάζα και την ακτίνα, λόγω των σϕαιρικών και τετραπολικών παραμορϕώσεων. Τέλος, εϕαρμόζουμε μία διαταρακτική προσέγγιση με όρους τρίτης τάξης στην γωνιακή ταχύτητα. Στο δεύτερο κεϕάλαιο, ϑα κάνουμε μια εκτενή περιγραϕή της στρατηγικής του μιγαδικού επιπέδου (Complex-Plane Strategy, εν συντομία CPS). Σύμϕωνα με αυτή την μέθοδο, η αριθμητική ολοκλήρωση των διαϕορικών εξισώσεων γίνεται στο μιγαδικό επίπεδο και όλες οι εμπλεκόμενες συναρτήσεις του προβλήματός μας είναι μιγαδικές, μιγαδικής μεταβλητής. Συνεπώς, για την αποϕυγή διαϕόρων ιδιομορϕιών ή και απροσδιόριστων μορϕών, που προκύπτουν από τις οριακές συνθήκες του προβλήματος, κυρίως στο κέντρο και στην επιϕάνεια του αστέρα, μας δίνεται η δυνατότητα να επιλέξουμε ένα κατάλληλο μιγαδικό μονοπάτι για την εκτέλεση πάνω σ΄ αυτό της αριθμητικής ολοκλήρωσης των διαϕορικών εξισώσεων. Επιπλέον, οι αριθμητικές ολοκληϱώσεις όλων των διαϕορικών εξισώσεων του προβλήματος συνεχίζονται πολύ πέραν της επιϕάνειας του αδιατάρακτου μοντέλου, με αποτέλεσμα η ακτίνα υπολογίζεται εύκολα ως η ϱίζα του πραγματικού μέρους της συνάρτησης της πυκνότητας (χωρίς να είμαστε αναγκασμένοι να εκτελέσουμε οποιεσδήποτε αριθμητικές προεκβολές, που είναι γνωστό ότι επιϕέρουν σημαντικά σϕάλματα). Στο τρίτο κεϕάλαιο, υπολογίζουμε σημαντικές φυσικές ποσότητες που αφορούν τον αστέρα νετρονίων, ολοκληρώνοντας αριθμητικά ένα σύστημα διαφορικών εξισώσεων πρώτης τάξης. Ιδιαίτερα, υπολογίζουμε το σύνορο της περιστρεϕόμενης αστρικής δομής με δύο τρόπους. Ο πρώτος είναι με ϐάση την κλασική διαπραγμάτευση της διαταρακτικής μεθόδου του Hartle και ο δεύτερος με τον αλγόριθμο λεπτής ϱύθμισης που αναπτύσσουμε με την ϐοήθεια του οποίου παίρνουμε αξιόλογα αριθμητικά αποτελέσματα. Στην συνέχεια περιγράϕουμε το λογισμικό πακέτο ATOMFT System. Ακολούθως, με την ϐοήθεια των λύσεων των διαϕορικών εξισώσεων τρίτης τάξης ως προς την γωνιακή ταχύτητα, υπολογίζουμε τις διορθώσεις στην στροϕορμή, την ϱοπή αδράνειας, την περιστροϕική κινητική ενέργεια και την ϐαρυτική δυναμική ενέργεια του αστέρα. Εϕαρμόζοντας τέλος μια κατάλληλη μέθοδο, υπολογίζουμε το όριο της μάζας διαϕυγής. Στο τέταρτο κεϕάλαιο, εκθέτουμε πίνακες αποτελεσμάτων και κάποιες σημαντικές γραϕικές παραστάσεις. Δίνουμε επίσης ορισμένες λεπτομέρειες της εϕαρμογής του προγράμματός μας. Επιπλέον, δίνουμε έμϕαση στο γνωστό «παράδοξο» που αϕορά την μέθοδο διαταραχών του Hartle,σύμϕωνα με την οποία αυτή η μέθοδος αν και αντιπροσωπεύει μια προσέγγιση αργής πεϱιστροϕής ενός αστέρα νετρονίων, δίνει αξιόλογα αποτελέσματα ακόμη και όταν εϕαρμόζεται σε ταχέως περιστρεϕόμενα μοντέλα. Στην παρούσα έρευνα αϕαιρέσαμε τον κρίσιμο περιορισμό του τερματισμού των αριθμητικών ολοκληρώσεων λίγο πριν από την επιϕάνεια του μη περιστρεϕόμενου αστέρα, συνεχίζοντας την ολοκλήρωση αρκετά πέραν του συνόρου του. Αυτό σημαίνει ότι η CPS ¨γνωρίζει¨ την παραμόρϕωση που προκαλείται από την περιστροϕή για ένα αρκετά εκτεταμένο διάστημα που περιβάλλει την αρχικά σϕαιρική μορϕή του αστέρα. Συνεπώς, για τους υπολογισμούς που απαιτούνται για τον περιστρεϕόμενο αστέρα, η CPS δεν προεκβάλλει ποτέ, με αποτέλεσμα τα σϕάλματα των υπολογισμών είναι πολύ μικρά. Τέλος, λαμβάνοντας υπόψη κατάλληλα στους υπολογισμούς μας ένα ορισμένο αριθμό συνθηκών, συνδυάζοντας την κλασική διαπραγμάτευση του διαταρακτικού σχήματος του Hartle και τις σχέσεις που απορρέουν από την δομή της στρατηγικής του μιγαδικού επιπέδου, οδηγηθήκαμε τελικά στην επινόηση του αλγόριθμου λεπτής ϱύθμισης, αποτέλεσμα του οποίου είναι η σημαντική ϐελτίωση της ακρίβειας των αριθμητικών αποτελεσμάτων που αϕορούν την γεωμετρία του συνόρου του αστέρα νετρονίων. ΄Αμεση συνέπεια όλων αυτών είναι ο υπολογισμός με ικανοποιητική ακρίβεια του ορίου της μάζας διαϕυγής, εϕαρμόζοντας μια κατάλληλη μέθοδο. / In the present dissertation we solve numerically in the complex plane all the differential equations involved in Hartle’s perturbation method for computing general-relativistic polytropic models of rotating neutron stars. We give emphasis on computing quantities describing the geometry of models in rapid rotation. Compared to numerical results obtained by certain sophisticated iterative methods, we verify appreciable improvement of our results vs to those given by the classical Hartle’s perturbative scheme. The description of the present investigation is constituted by four parts and has as follows. In the first chapter, we start to describe the nonrotating neutron star model. Then, according to "Hartle’s perturbation method", the solid rotation is added as a perturbation. So, the equations of structure for uniformly rotating stars are given up to second order in the angular velocity and the distortions to mass and radius are calculated as corrections owing to spherical and quadrupole deformations. Subsequently, the equations are given up to third order in the angular velocity. In the second chapter, we describe extensively the numerical method called Complex-Plane Strategy (abbreviated CPS). According to this method, we solve numerically in the complex plane all the differential equations involved in Hartle’s perturbation method. Any function of our problem is interpreted as a complex-valued function of a complex variable. CPS offers an alternative for avoiding any singularities and/or indeterminate forms, especially near the center and the surface of the nonrotating star, by performing numerical integration along a proper complex path. Moreover, the numerical integrations of all the differential equations governing the problem are continued well beyond the surface of the nonrotating star, thus, the radius is readily calculated as root of the density function (without been forced to perform any numerical extrapolations). In the third chapter, we solve numerically in the complex plane the system of first-order differential equations resulting from Hartle’s perturbation method. We give emphasis on computing the boundary of the rotating configuration by the so-called fine tuning algorithm which gives appreciably improved results. Then, we describe the software systems that we use in our investigation, with emphasis on the ATOMFT System. Finally, we compute the third order corrections in the uniform angular velocity for the angular momentum, moment of inertia, rotational kinetical energy and gravitational potential energy. Furthermore, we describe a method for computing the mass-shedding limit. In the fourth chapter, we present several numerical results and some significant graphical representations. We also give certain details of our program implementation. Concluding, we emphasize on the well-known "paradox" concerning Hartle’s perturbation method, according to which this method, although representing a slow-rotation approximation, gives remarkably accurate results even when applied to rapidly rotating models. In the present work, we have removed the certain critical limitations of terminating integrations below the radius of the star. Instead, the numerical integration of our problem continues well beyond the boundary of the star. This means that CPS knows the distortion to be caused by rotation over a sufficiently extended space surrounding the initially spherical configuration. So, to the computation of a particular rotating configuration, CPS never extrapolates beyond the end of the function tables computed by such extended numerical integrations. It is exactly the avoidance of any extrapolation which keeps the error in the computations appreciably small. Finally, we have properly taken into account certain conditions matching Hartle’s perturbative scheme and the relations arising in the framework of the Complex-Plane Strategy. This treatment has led to the fine tuning algorithm which, in turn, has improved appreciably the accuracy of our numerical results related to the geometry of the star’s boundary. Consequently, the mass-shedding limit can be calculated using a proper procedure which gives remarkably accurate results.

Ce travail de thèse concerne les écoulements de fluides à seuil de contrainte autour d‘un obstacle cylindrique en milieu confiné avec une configuration d‘écoulement de Poiseuille.Expérimentalement, un banc d‘essai permettant d‘obtenir un écoulement en continu dans un circuit fermé a été mis en place. Les régimes d‘écoulement rampant, recirculant et instationnaire périodique ont été étudiés. De nouveaux résultats ont été obtenus avec un fluide newtonien et des solutions de Carbopol, polymère permettant de réaliser des fluides à seuil modèles utilisés en recherche et développement et dans l‘industrie. Une caméra rapide et un éclairage plan laser a servi pour l‘établissement d‘images qui ont ensuite été traitées par PIV. Les champs de vitesses cinématiques, les morphologies d‘écoulement et les paramètres critiques de transitions de régimes ont été déterminés.Numériquement, un modèle viscoplastique basé sur la loi de Herschel-Bulkley régularisée a été utilisé. Des résultats comme les morphologies d‘écoulement, la localisation des zones rigides, les champs de vitesses ont été obtenus. Ceci a permis de comparer les différences entre les effets liés à la nature des gels de Carbopol et la modélisation viscoplastiques. Une étude spécifique sur le glissement à l‘interface fluide-structure a également été réalisée avec l‘utilisation d‘un modèle de lubrification élasto-hydrodynamique. / The flow of yield stress fluids around a circular cylinder in a confined geometry has been investigated with a Poiseuille flow configuration.Experimentally, a test set-up was built which provides a continuous flow in a closed loop. We studied creeping, recirculating and vortex shedding flow regimes. New results has been realised with a Newtonian fluid and Carbopol solutions, models for yield stress behaviour in laboratory experiments and in industry. A high speed camera and a laser sheet have been used to perform images which are treated by PIV. Kinematic fields, flow morphologies and critical transition parameters have been determined.Numerically, a viscoplastic model based on the regularised Herschel-Bulkley law has been used. Results as flow morphologies, rigid areas and local flow parameters fields have been performed. That allowed us to compare the intrinsic effects of Carbopol solutions and the viscoplastic numerical model. A specific study on the wall slip has also been considered with an elasto-hydrodynamic lubrication model.

Les risques naturels tels que les laves torrentielles constituent des menaces réelles pourles zones urbanisées de montagne. Les bâtiments et infrastructures peuvent être exposésà de grandes forces d’impact en cas d’évènement extrême. La réduction de cette menace,par des ouvrages de protection, impose de quantifier l’impact de ces écoulements sur lesstructures, qu’elles soient flexibles ou rigides.Tout d’abord, un écoulement granulaire sec, composé de particules non-sphériquesglissant sur un plan incliné, est modélisé en utilisant une loi de contact visco-élastiqueavec critère de rupture de Mohr-Coulomb. Des données expérimentales de la littératureont été utilisé pour calibrer et valider le modèle. À cette fin, la forme de la particule,l’épaisseur de l’écoulement et la forme finale du dépôt sur le mur sont considerés. Lavalidation est basée sur l’impact sur un mur rigide divisé en six segments. La principalecontribution de la force totale normale appliquée sur le mur est due à la composantedynamiques. La distribution hétérogène de la force normale sur chaque partie du murest due au développement des chaînes de force différent pour chaque arrangement desparticules.Ensuite, un filet est modélisé en utilisant des éléments cylindriques. L’impact sur lefilet est modélisé en utilisant le même modèle d’écoulement que précédemment. Le rôledes dissipateurs d’énergie apparaît essentiel pour réduire la force d’impact sur le filet etlimiter la force appliquée sur les points d’ancrage latéraux.Pour la première fois, des simulations montrent que pour un même écoulementgranulaire la force d’impact est plus élevée pour un obstacle rigide, avec une différencede 50% par rapport à un obstacle flexible. les simulations permettent de définir quelquesrecommandation pour le dimensionnement des filets. Il est constaté que l’utilisationviiid’un maillage de filet plus petit que D90 de l’écoulement est acceptable en termes decapacité à retenir les matériaux en écoulement. En plus, si le câble en bas du filet n’estpas fixé, le filet pourrait perdre totalement sa capacité de retenue. / Natural hazards such as debris flows are real threat to the urbanization of mountainousareas. Local communities and infrastructures can be exposed to large impact forces inextreme debris events. Mitigation of such threats requires, along other measures, theestimation of the impact of such flows on protection structures (rigid walls and flexiblebarriers). In this thesis, Discrete Element Method (DEM) is used to model the granularflow, the rigid walls and flexible barriers.First, a dry granular flow made of non-spherical particles flowing in inclined plane ismodeled using a visco-elastic contact law with Mohr-Coulomb failure criterion. Experimentaldata from the literature is used to calibrate and validate the model. The modelis calibrated based on the shape of the particle, the flow thickness and the final shapeof the deposit on the wall. Validation procedure is based on the impact on a rigid walldivided into six segments. The main contribution of total normal force applied on thewall is found to be due to the dynamic component. On the micro-scale, development offorce chains is believed to cause heterogeneous distribution of normal force on each partof the wall, for multiple same-test conditions.Next, a flexible barrier is modeled using cylindrical elements. The impact on thebarrier is modeled using the same flow model used for wall-impact problem. The use ofenergy dissipators is found to be essential for minimizing the impact force on the barrier,and thus controlling the force applied on the lateral anchors.By comparing a rigid wall and a flexible barrier for the same flow, we found thatthe rigid wall is exposed to higher impact force, due its high global stiffness comparedwith the flexible barrier. Next, different simulations are carried out to recommend designguidelines for the flexible barrier. It is found that using a mesh size as large as D90 of theviflow is acceptable in terms of mass retaining capacity. In addition, not fixing the bottomcable of flexible barriers might lead to the total loss of its retaining capacity in extremeevents.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Usualmente, o projeto de pórticos em estruturas de aço assume que as ligações viga-coluna são rígidas ou flexíveis. As ligações rígidas, onde não ocorre nenhuma rotação entre os membros conectados, transferem não só momento fletor, mas também força cortante e força normal. Por outro lado, as ligações flexíveis são caracterizadas pela liberdade de rotação entre os membros conectados impedindo a transmissão de momento fletor. Sabe-se que a grande maioria das ligações não possuem este comportamento idealizado. Na realidade, a maioria das ligações transfere algum momento fletor com um nível de rotação associado. Estas ligações são denominadas semi-rígidas e seu dimensionamento deve ser executado de acordo com este comportamento estrutural. Contudo, algumas ligações viga-coluna estão sujeitas a uma combinação de momento fletor (M) e força axial (N). O nível de esforço normal pode ser significativo, principalmente em ligações de pórticos metálicos com vigas inclinadas, em pórticos não- contraventados ou em pórticos com pavimentos incompletos. As normas atuais de dimensionamento de ligações estruturais em aço não consideram a presença de esforço normal (tração e/ou compressão) nas ligações. Uma limitação empírica de 5% da resistência plástica da viga é a única condição imposta no Eurocode 3. O objetivo deste trabalho é realizar uma análise paramétrica de dois tipos de ligações aparafusadas para se avaliar a influência de combinações M/N no comportamento global destas ligações. Para se cumprir este objetivo, os resultados experimentais de quinze ensaios realizados por Lima [1] são comparados com os resultados obtidos através de um modelo analítico proposto por Cerfontaine [2], [3]. / Traditionally, the steel portal frame design assumes that beam-to-column joints are rigidor pinned. Rigid joints, where no relative rotations occur between the connected members, transfer not only substantial bending moments, but also shear and axial forces. On the other extreme, pinned joints, are characterised by almost free rotation movement between the connected elements that prevents the transmission of bending moments. Despite these facts, it is largely recognised that the great majority of joints does not exhibit such idealised behaviour. In fact, many joints transfer some bending moments with associated rotations. These joints are called semi-rigid, and their design should be performed according to their real structural behaviour. However, some steel beam-to-column joints are often subjected to a combination of bending (M) and axial forces (N). The level of axial forces in the joint may be significant, typical of pitched-roof portal frames, sway frames or frames with incomplete floors. Current standard for steel joints do not take into account the presence of axial forces (tension and/or compression) in the joints. A single empirical limitation of 5% of the beams plastic axial capacity is the only enforced provision in Eurocode 3. The objective of the present work is to perform a parametrical analysis of two bolted joints types in order to evaluate the influence of M/N combinations in the joints global response. To fulfil this objective, the experimental results obtained by Lima [1] are compared to the analytical results using the Cerfontaine analytical model [2], [3].

Tradicionalmente, na análise e dimensionamento de estruturas de aço, assume-se que as ligações viga-coluna são rígidas ou flexíveis (rotuladas). Por outro lado, é de conhecimento geral que a grande maioria das ligações viga-coluna apresenta um comportamento intermediário, ou seja, semi-rígido. Inúmeros trabalhos de pesquisa têm sido desenvolvidos nos últimos vinte e cinco anos, de forma a estudar o comportamento desse tipo de ligação. Um dos principais objetivos desta investigação é o de propor uma metodologia de análise que represente de forma apropriada a influência do comportamento semi-rígido de placas de base e de ligações viga-coluna, sobre a resposta dinâmica (linear e não-linear) de estruturas de aço. Outra contribuição desta dissertação diz respeito à investigação do comportamento dinâmico (linear e não-linear) de pórticos de aço, a partir da consideração de ligações viga-coluna simétricas e não-simétricas e especialmente das placas de base. A análise estrutural é desenvolvida com base no emprego do programa de elementos finitos ANSYS [27]. Nos modelos em elementos finitos foram considerados os efeitos de não-linearidade geométrica (efeitos de segunda ordem), o comportamento não-linear das placas de base e das ligações viga-coluna e, bem como, o efeito de histerese que ocorre quando a estrutura é submetida a cargas cíclicas. Os resultados alcançados indicaram que o fenômeno físico da ressonância não ocorre no que se refere à resposta dinâmica dos modelos semi-rígidos não-lineares. A ressonância não ocorre na resposta dos modelos devido ao fato de que, na análise dinâmica não-linear, o efeito de histerese presente nas ligações (placas de base e viga-coluna), essencialmente com comportamento não-linear, provoca um amortecimento na resposta dinâmica da estrutura. / Traditionally, the steel portal frame design assumes that beam-to-column connections are rigid or pinned. Despite these facts, it is largely recognized that the great majority of joints does not exhibit such idealized behaviour. These connections are called semi-rigid, and their design should be performed according to their actual structural behaviour. Extensive research has been performed over the past twenty-five years to estimate the actual behaviour of such joints. One of the main objectives of this work is to propose an analysis methodology to properly represent the influence of the semi-rigid behaviour of base plates and beam-to-column joints on the dynamical response of steel structures (linear and non-linear). Another important investigated issue concerned the assessment of the steel frames dynamical behaviour (linear and non-linear) due to the presence of symmetrical and non-symmetrical beam-to-column semi-rigid joints and, especially, the column base plates. The structural analysis was made with the aid of the ANSYS [27] finite element program. The finite element model included geometric non-linearity, column base plates and beam-to-column non-linear behaviour and considered the influence of non-linear and hysteretic moment versus rotation curve of the joints. The results indicated that the resonance physical phenomenon was not reached in the nonlinear semi-rigid frames dynamic response. The resonance did not occurred in these systems due to the hysteretic damping induced by the energy dissipation of the non-linear hysteretic loops at the non-linear joints.

Fundação Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro / Usualmente, o projeto de pórticos em estruturas de aço assume que as ligações viga-coluna são rígidas ou flexíveis. As ligações rígidas, onde não ocorre nenhuma rotação entre os membros conectados, transferem não só momento fletor, mas também força cortante e força normal. Por outro lado, as ligações flexíveis são caracterizadas pela liberdade de rotação entre os membros conectados impedindo a transmissão de momento fletor. Sabe-se que a grande maioria das ligações não possuem este comportamento idealizado. Na realidade, a maioria das ligações transfere algum momento fletor com um nível de rotação associado. Estas ligações são denominadas semi-rígidas e seu dimensionamento deve ser executado de acordo com este comportamento estrutural. Contudo, algumas ligações viga-coluna estão sujeitas a uma combinação de momento fletor (M) e força axial (N). O nível de esforço normal pode ser significativo, principalmente em ligações de pórticos metálicos com vigas inclinadas, em pórticos não- contraventados ou em pórticos com pavimentos incompletos. As normas atuais de dimensionamento de ligações estruturais em aço não consideram a presença de esforço normal (tração e/ou compressão) nas ligações. Uma limitação empírica de 5% da resistência plástica da viga é a única condição imposta no Eurocode 3. O objetivo deste trabalho é realizar uma análise paramétrica de dois tipos de ligações aparafusadas para se avaliar a influência de combinações M/N no comportamento global destas ligações. Para se cumprir este objetivo, os resultados experimentais de quinze ensaios realizados por Lima [1] são comparados com os resultados obtidos através de um modelo analítico proposto por Cerfontaine [2], [3]. / Traditionally, the steel portal frame design assumes that beam-to-column joints are rigidor pinned. Rigid joints, where no relative rotations occur between the connected members, transfer not only substantial bending moments, but also shear and axial forces. On the other extreme, pinned joints, are characterised by almost free rotation movement between the connected elements that prevents the transmission of bending moments. Despite these facts, it is largely recognised that the great majority of joints does not exhibit such idealised behaviour. In fact, many joints transfer some bending moments with associated rotations. These joints are called semi-rigid, and their design should be performed according to their real structural behaviour. However, some steel beam-to-column joints are often subjected to a combination of bending (M) and axial forces (N). The level of axial forces in the joint may be significant, typical of pitched-roof portal frames, sway frames or frames with incomplete floors. Current standard for steel joints do not take into account the presence of axial forces (tension and/or compression) in the joints. A single empirical limitation of 5% of the beams plastic axial capacity is the only enforced provision in Eurocode 3. The objective of the present work is to perform a parametrical analysis of two bolted joints types in order to evaluate the influence of M/N combinations in the joints global response. To fulfil this objective, the experimental results obtained by Lima [1] are compared to the analytical results using the Cerfontaine analytical model [2], [3].

Tradicionalmente, na análise e dimensionamento de estruturas de aço, assume-se que as ligações viga-coluna são rígidas ou flexíveis (rotuladas). Por outro lado, é de conhecimento geral que a grande maioria das ligações viga-coluna apresenta um comportamento intermediário, ou seja, semi-rígido. Inúmeros trabalhos de pesquisa têm sido desenvolvidos nos últimos vinte e cinco anos, de forma a estudar o comportamento desse tipo de ligação. Um dos principais objetivos desta investigação é o de propor uma metodologia de análise que represente de forma apropriada a influência do comportamento semi-rígido de placas de base e de ligações viga-coluna, sobre a resposta dinâmica (linear e não-linear) de estruturas de aço. Outra contribuição desta dissertação diz respeito à investigação do comportamento dinâmico (linear e não-linear) de pórticos de aço, a partir da consideração de ligações viga-coluna simétricas e não-simétricas e especialmente das placas de base. A análise estrutural é desenvolvida com base no emprego do programa de elementos finitos ANSYS [27]. Nos modelos em elementos finitos foram considerados os efeitos de não-linearidade geométrica (efeitos de segunda ordem), o comportamento não-linear das placas de base e das ligações viga-coluna e, bem como, o efeito de histerese que ocorre quando a estrutura é submetida a cargas cíclicas. Os resultados alcançados indicaram que o fenômeno físico da ressonância não ocorre no que se refere à resposta dinâmica dos modelos semi-rígidos não-lineares. A ressonância não ocorre na resposta dos modelos devido ao fato de que, na análise dinâmica não-linear, o efeito de histerese presente nas ligações (placas de base e viga-coluna), essencialmente com comportamento não-linear, provoca um amortecimento na resposta dinâmica da estrutura. / Traditionally, the steel portal frame design assumes that beam-to-column connections are rigid or pinned. Despite these facts, it is largely recognized that the great majority of joints does not exhibit such idealized behaviour. These connections are called semi-rigid, and their design should be performed according to their actual structural behaviour. Extensive research has been performed over the past twenty-five years to estimate the actual behaviour of such joints. One of the main objectives of this work is to propose an analysis methodology to properly represent the influence of the semi-rigid behaviour of base plates and beam-to-column joints on the dynamical response of steel structures (linear and non-linear). Another important investigated issue concerned the assessment of the steel frames dynamical behaviour (linear and non-linear) due to the presence of symmetrical and non-symmetrical beam-to-column semi-rigid joints and, especially, the column base plates. The structural analysis was made with the aid of the ANSYS [27] finite element program. The finite element model included geometric non-linearity, column base plates and beam-to-column non-linear behaviour and considered the influence of non-linear and hysteretic moment versus rotation curve of the joints. The results indicated that the resonance physical phenomenon was not reached in the nonlinear semi-rigid frames dynamic response. The resonance did not occurred in these systems due to the hysteretic damping induced by the energy dissipation of the non-linear hysteretic loops at the non-linear joints.

Le SLAM, « Simultaneous Localisation And Mapping », représente à l'heure actuelle l'une des principales thématiques investiguées dans le domaine des robots mobiles autonomes. Il permet, à l'aide de capteurs extéroceptifs (laser, caméra, radar, etc.) et proprioceptifs (odomètre, gyromètre, etc.), de trouver l'orientation et la localisation d'un robot dans un environnement extérieur vaste, inconnu ou modifié, avec la possibilité de créer une carte au fur et à mesure des déplacements du véhicule. Les travaux de thèse décrits dans ce manuscrit s'intègrent dans ce courant de recherche. Ils visent à développer un SLAM innovant qui utilise un radar à modulation de fréquence continue « FMCW » comme capteur extéroceptif. Ce capteur est insensible aux conditions climatiques et possède une portée de détection importante. Néanmoins, c'est un capteur tournant qui, dans une utilisation mobile, va fournir des données corrompues par le déplacement du véhicule. Pour mener à bien ces travaux, nous avons proposés différentes contributions : une correction de la distorsion par l'utilisation de capteurs proprioceptifs ; le développement d'une technique de localisation et cartographie simultanées nommée RS-SLAM-FMT qui effectue un scan matching sur les observations et utilise un algorithme estimatif de type EKF-SLAM ; l'utilisation, pour la première fois en SLAM, de la mise en correspondance par Transformée de Fourier-Mellin pour réaliser l'opération de scan matching ; la création d'un outil expérimental pour déterminer la matrice de covariance associée aux observations ; des tests de robustesse de l'algorithme dans des conditions d'utilisation réelles : dans des zones avec un faible nombre de points d'intérêts, sur des parcours effectués à vitesse élevée, dans des environnements péri-urbains avec une forte densité d'objets mobiles ; la réalisation d'une application temps réel pour le test du procédé sur un véhicule d'exploration qui se déplace dans un environnement extérieur vaste. / Simultaneous Localization And Mapping (SLAM) is one of the main topics investigated in the field of autonomous mobile robots. It permits the Localization and mapping of a robot in a large outdoor environment, using exteroceptive (laser, camera, radar, etc.) and proprioceptive (odometer, gyroscope, etc.) sensors. The objective of this PhD thesis is to develop innovative SLAM that uses a radar frequency modulated continuous wave (FMCW) as an exteroceptive sensor. Microwave radar provides an alternative solution for environmental imaging and overcomes the shortcomings of laser, video and sonar sensors such as their high sensitivity to atmospheric conditions. However, data obtained with this rotating range sensor is adversely affected by the vehicle’s own movement. In order to efficiently manage the work, we propose : a correction, on-the-fly, of the rotating distortion with an algorithm that uses the proprioceptive sensors’ measurements ; development of a new technique for simultaneous localization and mapping named RS-SLAM-FMT ; for the first time in SLAM, the use of the Fourier-Mellin Transform provides an accurate and efficient way of computing the rigid transformation between consecutive scans ; creation of an experimental tool to determine the covariance matrix associated with the observations. It is based on an uncertainty analysis of a Fourier-Mellin image registration ; tests of the robustness of the SLAM algorithm in real-life conditions : in an environment containing a small number of points of interest, in real full speed driving conditions, in peri-urban environments with a high density of moving objects etc. ; creation and experiment of a real-time RS-SLAM-FMT implemented on a mobile exploration vehicle in an extensive outdoor environment.