L'OBJET DE CETTE THESE EST LA MISE AU POINT D'UNE METHODE ITERATIVE PERMETTANT LA RESOLUTION NUMERIQUE D'UN PROBLEME DYNAMIQUE (P) D'INTERACTION FLUIDE-STRUCTURE. LA DIFFICULTE ESSENTIELLE (TOUT AU MOINS POUR CETTE METHODE ET DANS LE CAS D'UN FLUIDE LOURD) PROVIENT DE L'AMPLIFICATION DE L'ERREUR DUE A LA DISCRETISATION TEMPORELLE DU TERME DE COUPLAGE A L'INTERFACE. POUR Y REMEDIER NOUS N'AVONS PAS RESOLU LE PROBLEME (P), MAIS UN PROBLEME PENALISE, NOTE (PE), DONT ON MONTRE QUE LA SOLUTION CONVERGE VERS LA SOLUTION DU PROBLEME (P). EN PREMIER LIEU NOUS PRESENTONS LES EQUATIONS DYNAMIQUES DU PROBLEME (P) MODELISANT UN SYSTEME COUPLE PLAQUE-EAU EXPERIMENTAL. NOUS DONNONS ENSUITE DES CONDITIONS D'EXISTENCE, D'UNICITE, DE REGULARITE DES SOLUTIONS DES PROBLEMES (P) ET (PE) AINSI QU'UNE ESTIMATION DE L'ERREUR COMMISE LORS DE LA RESOLUTION DU PROBLEME APPROCHE (PE). AU CHAPITRE 3, APRES AVOIR PRESENTE LA METHODE, NOUS ETABLISSONS UNE CONDITION DE CONVERGENCE DE LA SOLUTION POUR LE PROBLEME (PE). POUR VALIDER LA METHODE NOUS CONSTRUISONS DES SOLUTIONS ANALYTIQUES DANS LE CAS DE CONDITIONS AUX LIMITES PARTICULIERES ET NOUS PRESENTONS LES RESULTATS EXPERIMENTAUX OBTENUS (PAR ANALYSE SPECTRALE) LORS DE L'ETUDE D'UN MONTAGE CONSTITUE D'UNE PLAQUE MINCE EN ACIER SURMONTEE D'UNE CUVE EN PLEXIGLASS CONTENANT DE L'EAU. ENFIN NOUS COMPARONS LES RESULTATS NUMERIQUES A CEUX OBTENUS DANS LE CAS ANALYTIQUE ET DANS LE CAS EXPERIMENTAL

This book is dedicated to the general study of fluid structure interaction with consideration of uncertainties. The fluid-structure interaction is the study of the behavior of a solid in contact with a fluid, the response can be strongly affected by the action of the fluid. These phenomena are common and are sometimes the cause of the operation of certain systems, or otherwise manifest malfunction. The vibrations affect the integrity of structures and must be predicted to prevent accelerated wear of the system by material fatigue or even its destruction when the vibrations exceed a certain threshold.

Written by an eminent authority in the field, Modelling of Mechanical Systems: Fluid-Structure Interaction is the third in a series of four self-contained volumes suitable for practitioners, academics and students alike in engineering, physical sciences and applied mechanics. The series skilfully weaves a theoretical and pragmatic approach to modelling mechanical systems and to analysing the responses of these systems. The study of fluid-structure interactions in this third volume covers the coupled dynamics of solids and fluids, restricted to the case of oscillatory motions about a state of static equilibrium. Physical and mathematical aspects of modelling these mechanisms are described in depth and illustrated by numerous worked out exercises.· Written by a world authority in the field in a clear, concise and accessible style · Comprehensive coverage of mathematical techniques used to perform computer-based analytical studies and numerical simulations · A key reference for mechanical engineers, researchers and graduate students

This book is dedicated to the general study of fluid structure interaction with consideration of uncertainties. The fluid-structure interaction is the study of the behavior of a solid in contact with a fluid, the response can be strongly affected by the action of the fluid. These phenomena are common and are sometimes the cause of the operation of certain systems, or otherwise manifest malfunction. The vibrations affect the integrity of structures and must be predicted to prevent accelerated wear of the system by material fatigue or even its destruction when the vibrations exceed a certain threshold.

Fluid-Structure Interaction: An Introduction to Finite Element Coupling fulfils the need for an introductive approach to the general concepts of Finite and Boundary Element Methods for FSI, from the mathematical formulation to the physical interpretation of numerical simulations. Based on the author’s experience in developing numerical codes for industrial applications in shipbuilding and in teaching FSI to both practicing engineers and within academia, it provides a comprehensive and self–contained guide that is geared toward both students and practitioners of mechanical engineering. Composed of six chapters, Fluid–Structure Interaction: An Introduction to Finite Element Coupling progresses logically from formulations and applications involving structure and fluid dynamics, fluid and structure interactions and opens to reduced order-modelling for vibro-acoustic coupling. The author describes simple yet fundamental illustrative examples in detail, using analytical and/or semi–analytical formulation & designed both to illustrate each numerical method and also to highlight a physical aspect of FSI. All proposed examples are simple enough to be computed by the reader using standard computational tools such as MATLAB, making the book a unique tool for self–learning and understanding the basics of the techniques for FSI, or can serve as verification and validation test cases of industrial FEM/BEM codes rendering the book valuable for code verification and validation purposes.

Fluid-structure interaction is a new theme of investigation in computational methods, covering many applications in both engineering and medical sciences. This book deals with various examples of interaction between a fluid and a structure, and each author presents, for the different problems involved, the method which is considered to be the most appropriate.

Cette thèse est consacrée à l'analyse mathématique et numérique d'un problème d'interaction fluide-structure stationnaire, couplant un fluide newtonien, visqueux et incompressible, modélisé par les équations de Stokes 2D et une structure déformable, décrite par les équations d'une poutre 1D. Le fluide et la structure sont couplés via une condition aux limites de type frottement à l'interface.Dans l'étude théorique, nous montrons un résultat d'existence et unicité de solutions faibles, dans le cadre de petits déplacements, du problème de couplage fluide structure avec une condition de glissement de type Tresca en utilisant le théorème de point fixe de Schauder.Dans l'analyse numérique, nous étudions d'abord, l'approximation du problème de Stokes avec la condition de Tresca par une méthode d'éléments finis mixtes à quatre champs. Nous montrons ensuite une estimation d'erreur a priori optimale pour des données régulières et nous réalisons des tests numériques. Enfin, nous présentons un algorithme de point fixe pour la simulation numérique du problème couplé avec des conditions aux limites non linéaires.