La simulation directe des ondes de souffle générées par une explosion maîtrisée, ou accidentelle, est un problème délicat du fait des différentes échelles spatiales en jeu. De plus, en environnement réel (topographie, zone urbaine, …), l’onde de souffle interagit avec les obstacles géométriques en se réfléchissant, se diffractant et se recombinant. La forme du front devient complexe, rendant difficile voire impossible une estimation a priori des effets des explosions.Ce travail de thèse contribue à la mise au point d’une méthode de calcul rapide des ondes de souffle en présence d’obstacles. Il repose sur des modèles hyperboliques simplifiés de propagation d'ondes de choc extraits de la littérature, où seul le front incident est modélisé. Ceci permet une réduction significative du coût des simulations : les 5 équations d'Euler 3D sont réduites à un problème 2D à 2 équations. L’analyse du problème de Riemann met en évidence l’absence de solution de ces modèles lors de la diffraction sur un coin convexe dans certaines configurations fréquemment rencontrées en pratique. L’extension des modèles aux ordres supérieurs ne permet pas de corriger ce défaut. Nous levons cette limitation au travers d'une modification ad hoc. L’effet de souffle consécutif à une explosion est ensuite introduit à partir d’une loi expérimentale pression/distance. Du point de vue numérique, un algorithme Lagrangien conservatif de suivi de front est développé en 2D. Les tests montrent que ce nouveau modèle se compare favorablement à l’expérience, avec une réduction de plusieurs ordres de grandeur du temps de calcul en comparaison des méthodes de résolution directe des équations d’Euler. / The direct numerical simulation of blast waves (accidental or industrial explosions) is a challenging task due to the wide range of spatial and temporal scales involved. Moreover, in a real environment (topography, urban area …), the blast wave interacts with the geometrical obstacles resulting in reflection, diffraction and waves recombination phenomena. The shape of the front becomes complex, which limits the efficiency of simple empirical methods.This thesis aims at contributing to the development of a fast running method for blast waves propagation in presence of obstacles. This is achieved through the use of simplified hyperbolic models for shock waves propagation such as Geometrical Shock Dynamics (GSD) or Kinematic models. These models describe only the leading shock front. This leads to a drastic reduction of the computational cost, from 5 Euler equations at 3D to a 2D problem with 2 equations. However, the study of the Riemann problem shows that the solution of these models does not always exist in the case of the diffraction over a convex corner. We propose an ad-hoc extension of GSD in order to remove this limitation. The blast effects are also recovered through an empirical law available in free field. From a numerical point of view, a 2D conservative Lagrangian algorithm has been implemented and validated. First comparisons with experimental data show the good behaviour of this new model at nearly free computational cost compared to direct Euler methods.

Published Article / This paper explores the manipulation of Van der Waals' forces by geometrical parameters in a micro-material handling system. It was observed that the flat-flat interactive surfaces exerted the highest intensity of Van der Waals' forces followed by cone-flat, cylinder-flat, sphere-flat and sphere-sphere interactive surfaces, respectively. A conical micro-gripper proved to be versatile in manipulating the Van der Waals' forces efficiently in a 'picking up' and 'releasing' mechanism of micro-work parts. It was deduced that the pick-up position should be rough and spherical, and the placement position should be smooth and flat for an effective 'pick-and-place' cycle to be realised.

This paper describes a high fidelity simulation model for GEROTOR pumps. The simulation approach is based on the coupling of different models: a geometric model used to evaluate the instantaneous volumes and flow areas inside the unit, a lumped parameter fluid dynamic model for the evaluation of the displacing action inside the unit and mechanical models for the evaluation of the internal micro-motions of the rotors axes. This paper particularly details the geometrical approach, which takes into account the actual geometry of the rotors, given as input as CAD files. This model can take into account the actual location of the points of contact between the rotors as well for the actual clearances between the rotors. The potentials of the model are shown by considering a particular GEROTOR design. A specific test set-up was developed within this research for the model validation, and comparisons in terms of steady-state pressure versus flow curves and instantaneous pressure ripples are shown for the reference pump.

Wireless devices and applications have been an unavoidable part of human lives in the past decade. In the past few years, the global mobile data traffic has grown considerably and is expected to grow even faster in future. Given the fact that the number of wireless nodes has significantly increased, the contention and interference on the license-free industrial, scientific, and medical band has become severer than ever. Cognitive radio nodes were introduced in the past decade to mitigate the issues related to spectrum scarcity. In this dissertation, we focus on the interference and performance analysis of networks coexisting with cognitive radio networks and address the design and analysis of spectrum allocation and routing for cognitive radio networks. Spectrum allocation enables nodes to construct a link on a common channel at the same time so they can start communicating with each other. We introduce a new approach for the modeling and analysis of interference and spectrum allocation schemes for cognitive radio networks with arbitrarily-shaped network regions. First, for the first time in the literature, we propose a simple and efficient approach that can derive the distribution of the distance between an arbitrary interior/exterior reference point and a random point within an arbitrary convex/concave irregular polygon. This tool is essential in analyzing important distance-related performance metrics in wireless communication networks. Second, considering the importance of interference analysis in cognitive radio networks and its important role in designing spectrum allocation schemes, we model and analyze a heterogeneous cellular network consisting of several cognitive femto cells and a coexisting multi-cell network. Besides the cumulative interference, important distance-related performance metrics have been investigated, such as the signal-to-interference ratio and outage probability. Finally, the spectrum allocation and routing problems in cognitive radio networks have been discussed. Considering a wireless cognitive radio network coexisting with a cellular network with irregular polygon-shaped cells, we have used the tools developed in this dissertation and proposed a joint spectrum allocation and routing scheme. / Graduate

Disertaciniame darbe aprašyti autoriaus sudaryti geometriškai netiesinių tamprių plastinių statybinių strypinių konstrukcijų skaičiavimo ir optimizavimo uždavinių, ribojant konstrukcijos poslinkius, matematiniai modeliai. Sukurtas geometriškai netiesinių erdvinių strypinių konstrukcijų optimizavimo, ribojant poslinkius, uždavinio sprendimo originalus algoritmas. Disertaciją sudaro įvadas, trys skyriai, rezultatų apibendrinimas, naudotos literatūros ir autoriaus publikacijų disertacijos tema sąrašai bei 8 priedai. Įvadiniame skyriuje aptariama tiriamoji problema, aprašomas tyrimų objektas ir metodai, formuluojamas darbo tikslas bei uždaviniai, aprašomas darbo mokslinis naujumas bei aktualumas, darbo rezultatų praktinė reikšmė. Įvado pabaigoje pristatomos disertacijos tema autoriaus paskelbtos publikacijos ir pranešimai konferencijose bei disertacijos struktūra. Pirmajame skyriuje analizuojamos projektavimo ir konstrukcijų optimizavimo uždavinių sąsajos, pateikiama trumpa konstrukcijų optimizavimo metodų analitinė apžvalga. Nagrinėjama netamprių geometriškai netiesinių plieninių rėminių konstrukcijų optimizavimo ribojant poslinkius problematika. Aprašomos pasirinktos pagrindinės prielaidos ir fizinės priklausomybės bei dydžiai, apibrėžiantys konstrukcijos įtemptąjį-deformuotąjį būvį (ĮDB). Pateikiamas konstrukcijų optimizavimo uždavinio matematinis modelis. Pasiūlomas algoritmas šiam uždaviniui spręsti. Apžvelgiamos optimizavimo uždavinio skaitinės realizacijos galimybės... [toliau žr. visą tekstą] / The optimization mathematical models of geometrically nonlinear elastic plastic frameworks structures optimization under displacement constraints are created in the thesis. Original solution algorithm was created for the optimization of geometrically nonlinear elastic-plastic frameworks structures under displacement constraints. The dissertation consists of introduction, 3 chapters, conclusions, references and 8 annexes. The introduction reveals the investigated problem, the object of research and describes the purpose and tasks of the thesis, research methodology, scientific novelty, the practical significance of results examined in the thesis. The introduction ends in presenting the author’s publications on the subject of the defended dissertation, offering the material of made presentations in conferences and defining the structure of the dissertation. Construction design and structures optimization problems correlation is describing in chapter 1. Short historical review of optimization methods and structures optimization analytical analysis are presented. Reviewing problematic of non-elastic geometrically nonlinear steel frame structures optimization under displacements constraints. Describing basic accepted assumptions and physical dependences and values describing structures real stress-strain state (SSS). Structure optimization problem mathematical model is presented. Algorithm for such optimization problem solution is suggested. Optimization problem numerical... [to full text]

We consider random fractals generated by random recursive constructions, prove zero-one laws concerning their dimensions and find their packing and Minkowski dimensions. Also we investigate the packing measure in corresponding dimension. For a class of random distribution functions we prove that their packing and Hausdorff dimensions coincide.

QC 351 A7 no. 49 / The use of the two -dimensional Fourier transform to compute the form of the optical image has led to new insights into the form of images. The techniques involved are discussed in some detail, and the application to tolerancing of surface errors is used as an ex- ample of the results.

Ces travaux proposent une méthode d’assistance à la sélection des techniques d’assemblage et à l’allocation de tolérances sur les écarts géométriques des composants dans le cadre de l’assemblage de structures aéronautiques composites. Cette méthode consiste à formuler et à résoudre un problème d’optimisation multiobjectif afin de minimiser un indicateur de cout et un indicateur de non-conformité des structures assemblées. L’indicateur de coût proposé prend en compte le coût associé à l’allocation des tolérances géométriques ainsi que le coût associé aux opérations d’assemblage. Les indicateurs de non-conformités proposés sont évalués à partir des probabilités de non-respect des exigences géométriques sur les structures assemblées. Ces probabilités sont évaluées en propageant les tolérances géométriques allouées et les dispersions des techniques sélectionnées au travers d’une fonction appelée Relation de Comportement de l’assemblage (RdCa). Dans le cas de l’assemblage de structures aéronautiques composites, des exigences peuvent porter sur les jeux aux interfaces entre composants. Dans ce cas, la RdCa est évaluée par la résolution d’un problème mécanique quasi-statique non-linéaire par la méthode des éléments finis. Un méta-modèle de la RdCa est construit afin de la rendre compatible avec les méthodes probabilistes utilisées pour évaluer la non-conformité. Finalement, la définition d’un modèle structuro-fonctionnel du produit et d’une bibliothèque de techniques d’assemblage permet de construire un avant-projet de gamme d’assemblage paramétrique. Ce paramétrage permet de formuler le problème d’optimisation multiobjectif résolu à l’aide d’un algorithme génétique. / The purpose of this PhD is to develop a method to assist assembly technique selection and component geometrical tolerance allocation in the context of composite aeronautical structure assembly. The proposed method consists in formulating and solving a multiobjective optimisation problem aiming at minimising a cost indicator and a non-conformity indicator. The cost indicator account for both the cost involved by the geometrical tolerance allocation and the cost associated with the assembly operations. The proposed non-conformity indicators are evaluated according to the probabilities of non-satisfied requirements on the assembled structures. These probabilities are computed thanks to Geometrical Variation Propagation Relation (GVPR) that expresses the characteristics of the product as a function of the geometrical deviation of the components and the dispersion occurring during the assembly. In the case of composite aeronautical structures, the product characteristics can be gaps at interfaces between components. In this case, the GVPR is evaluated by solving a non-linear quasi-static mechanical problem by the mean of the finite element method. A metamodel of the GVPR is built in order to reduce the computing time and to make it compatible with the probabilistic methods used to evaluate the non-conformity. Finally, the use of a structure-functional model of the product together with an assembly technique library allows defining a parametric assembly process plan. The multiobjective optimisation problem built thanks to set of parameters defining the assembly process plan is solved using a genetic algorithm.

This work is a collection of solved problems in descriptive geometry, supplemented by elementary theory needed for their solution. The theory includes definitions and elementary properties of polygons and their constructions. Theory about solids, mostly prisms and pyramids, is also included. The second chapter introduces theory of projection, including definitions of projection methods (Monge, center, etc.) and corresponding terms. The second part contains a collection of problems, where each problem is solved in four projection methods (there are problems of construction of a point, line, plane, prism and pyramid). For each problem there is an animation for Lisa Viewer program attached, which makes an integral part of the work. These animations allow to look at figures of the problems interactively and even in three dimensions. There is also a PDF document with problem assignment and solution for each problem, suitable for print. Powered by TCPDF (www.tcpdf.org)

Cette thèse introduit le concept de comportement géométrique d'un assemblage mécanique. Cette notion permet de rendre compte du caractère assemblable ou mobile d'un mécanisme sous la forme d'un système de relations algébriques entre les paramètres géométriques permettant de le décrire. Dans un premier temps, cette thèse montre l'intérêt de ce concept pour traiter des problèmes faisant intervenir plusieurs effets physiques et plusieurs scénarios d'utilisation. Ce chapitre est appliqué à l'étude de l'assemblabilité d'un treillis pyramidal de conception à 4 barres décrit par un modèle géométrique non cartésien issu de la littérature. Dans un second temps, après avoir constaté le manque de modèles adaptés permettant de représenter des mécanismes mobiles, ce travail en propose un non cartésien. Il détaille aussi une méthode de mise en équation afin de traduire la mobilité d'un mécanisme. Une application de ce modèle et de la méthode est également faite. Elle permet de résoudre localement le problème de la mobilité d'un mécanisme de Bennett. Enfin, la dernière partie de ce travail expose une solution pour associer et comparer deux objets décrits par des représentations non cartésiennes. Cette technique est utile pour comparer deux états physiques du même objet utilisé dans différents scénarios pour assurer le suivi d'une exigence géométrique. Elle peut également être utilisée pour associer des objets réels et des objets idéalisés pour traiter des problèmes de tolérancement / This thesis introduces the concept of geometrical behavior of mechanical assembly. The geometrical behavior is constituted by a set of algebraic relations that translate the assemblability or mobility conditions of a product. It is expressed thanks to a specific geometrical model for the early phases of product design. Firstly, this work shows the interest of the geometrical behavior to tackle multi-physics problems at the early stages of product design. This part is illustrated on a ten bar pyramid subjected to mechanical and thermal strains. Secondly, this thesis proposes a coordinate free geometrical model dedicated to the representation of mobile mechanisms. This part also indicates a technique to express the mobility conditions of a loop as mathematical equations. An application of these model and technique is proposed to express the geometrical behavior of the Bennett mechanism. Finally, this work exposes a solution to associate and compare two objects described in the above-mentioned coordinate free model. This technique is useful to compare two states of the same object used under different operating conditions. It can also be used to associate ideal and real objects to tackle tolerancing issues.