The fluid flow and tracer transport in a single rock fracture during shear processes has been an important issue in rock mechanics and is investigated in this thesis using Finite Element Method (FEM) and streamline particle tracking method, considering evolutions of aperture and transmissivity with shear displacement histories under different normal stresses, based on laboratory tests. The distributions of fracture aperture and its evolution during shear were calculated from the initial aperture fields, based on the laser-scanned surface roughness features of replicas of rock fracture specimens, and shear dilations measured during the coupled shear-flow-tracer tests in laboratory performed using a newly developed testing apparatus in Nagasaki University, Nagasaki, Japan. Three rock fractures of granite with different roughness characteristics were used as parent samples from which nine plaster replicas were made and coupled shear-flow tests was performed under three normal loading conditions (two levels of constant normal loading (CNL) and one constant normal stiffness (CNS) conditions). In order to visualize the tracer transport, transparent acrylic upper parts and plaster lower parts of the fracture specimens were manufactured from an artificially created tensile fracture of sandstone and the coupled shear-flow tests with fluid visualization was performed using a dye tracer injected from upstream and a CCD camera to record the dye movement. A special algorithm for treating the contact areas as zero-aperture elements was used to produce more accurate flow field simulations by using FEM, which is important for continued simulations of particle transport, but was often not properly treated in literature. The simulation results agreed well with the flow rate data obtained from the laboratory tests, showing that complex histories of fracture aperture and tortuous flow channels with changing normal stresses and increasing shear displacements, which were also captured by the coupled shear-flow tests of fracture specimens with visualization of the fluid flow. From the obtained flow velocity fields, the particle transport was predicted by the streamline particle tracking method with calculated flow velocity fields (vectors) from the flow simulations, obtaining results such as flow velocity profiles, total flow rates, particle travel time, breakthrough curves and the Péclet number, Pe, respectively. The fluid flow in the vertical 2-D cross-sections of a rock fracture was also simulated by solving both Navier-Stokes (NS) and Reynolds equations, and the particle transport was predicted by streamline particle tracking method. The results obtained using NS and Reynolds equations were compared to illustrate the degree of the validity of the Reynolds equation for general applications in practice since the later is mush more computationally efficient for large scale problems. The flow simulation results show that the total flow rate and the flow velocity predicted by NS equations are quite different from that as predicted by the Reynolds equation. The results show that a roughly 5-10 % overestimation on the flow rate is produced when the Reynolds equation is used, and the ideal parabolic velocity profiles defined by the local cubic law, when Reynolds equation is used, is no longer valid, especially when the roughness feature of the fracture surfaces changes with shear. These deviations of flow rate and flow velocity profiles across the fracture aperture have a significant impact on the particle transport behavior and the associated properties, such as the travel time and Péclet number. The deviations increase with increasing flow velocity and become more significant when fracture aperture geometry changes with shear. The scientific findings from these studies provided new insights to the physical behavior of fluid flow and mass transport in rock fractures which is the scientific basis for many rock mechanics problems at the fundamental level, and with special importance to rock engineering problems such as geothermal energy extraction (where flow rate in fractures dominates the productivity of a geothermal energy reservoir) and nuclear waste repositories (where radioactive nuclides transport through fractures dominates the final safety evaluations) in fractured rocks. / Vätskeflödet och spårämnestransporten i en enskild bergsspricka under skjuvningsprocesser har varit ett viktigt ämne inom bergmekanik. I denna avhandling undersöks ämnet med hjälp av finita element metoden (FEM) och en strömlinjebaserad partikelspårningsmetod. Hänsyn tas till utveckling av öppningar och transmissivitet med skjuvningens förflyttningshistoria under olika normala belastningar baserat på laboratorietester. Fördelningen av spricköppningar och deras utveckling under skjuvning beräknades från de initiala öppningsfälten baserat på det laserscannade provets ytas grovhetskännetecken sam tskjuvningsöppningar uppmätta under de kopplade skjuvning-flöde-spårämneslaboratorietesterna som utförts med nyutvecklad testapparatur i Nagasaki Universitet i Nagasaki, Japan. Tre bergssprickor i granit med olika grovhetskarakteristika användes som utgångsprover från vilka nio gipskopior gjordes. Kopplade skjuvning-flödes tester utfördes sedan under tre normala belastningstillstånd (två nivåer med konstant normal last (KNL) och en konstant normal styvhetstillstånd (KNS). För att visualisera spårämnestransporten tillverkades en transparent övre del av sprickproverna av akryl och en nedre del av gipsbaserat på en kostgjord spänningsspricka i sandsten och de kopplade skjuvning-flödes testerna med vätskevisualisering utfördes med färgspårämne injekterat uppströms och en CCD kamera monterad ovanför för att registrera färgens rörelse. En särskild algoritm användes för att behandla kontaktytorna som nollöppningsämnen användes för att åstadkomma mer exakta flödesfältssimuleringar med FEM. Detta är viktigt för kontinuerliga simuleringar av partikelflöden men uppmärksammas oftast inte tillräckligt i litteraturen. Simuleringsresultaten överensstämde väl med de flödesnivådata som erhölls från laboratorietesterna vilket visade att komplexa historier av spricköppningar och invecklade flöden överensstämde med ändrade normala belastningar och ökande skjuvningsförflyttningar, vilket även fångades av de kopplade skjuvning-flödestesterna av sprickproverna genom visualisering av vätskeflödet. Från de erhållna flödesfälten förutsågs partikeltransporten genom en strömlinjebaserad partikelspårningsmetod med kalkylerade flödeshastighetsfält (vektorer) från flödessimuleringarna genom vilka resultat som flödeshastighetsprofiler, totala flödesnivåer,partikeltransporttid, genombrottskurvor samt Pécletnumret, Pe, erhölls. Vätskeflödet i det vertikala tvådimensionella tvärsnittet av en bergsspricka simulerades även genom att både Navier-Stokes (NS) och Reynoldsekvationerna löstes och partikeltransporten förutsågs genom den strömlinjebaserade partikelspårningsmetoden. Resultaten som erhöllsmed NS och Reynoldsekvationerna jämfördes för att illustrera graden av tillförlitlighet för Reynoldsekvationen för allmänna tillämpningar i praktiken då den senare är betydligt mer beräkningseffektiv för storskaliga problem. Resultaten från flödessimuleringarna visar att den totala flödesnivån och den totala flödeshastigheten förutsedda med NS ekvationer är helt annorlunda motsvarande värden som förutsågs med Reynoldsekvationen. Resultaten visar att en ca 5-10 % för hög uppskattning av flödesnivån erhålls då Reynoldsekvationen används och de ideala parabola hastighetsprofilerna, som definieras av den lokala kubiklagen när Reynoldsekvationen används, inte längre är giltiga särskilt när sprickytornas grovhetskarakteristika ändras med skjuvning. De här avvikelserna i flödesnivå och flödeshastighetsprofiler längs med spricköppningen har en betydande påverkan på partikeltransportuppträdande och de tillhörande egenskaperna såsom rörelsetid och Pécletnummer. Avvikelserna ökar med ökande flödeshastighet och blir mer signifikanta när spricköppningarnas geometri ändras med skjuvning. Forskningsresultaten från dessa studier gav nya insikter i de fysiska uppträdandet av vätskeflöde och masstransporter i bergssprickor vilket är den vetenskapliga basen för många bergmekanikproblem på grundläggande nivå och som har särskild vikt för bergstekniksproblem såsom geotermisk energiutvinning (där flödesnivå i sprickor dominerar produktiviteten för en geotermisk energikälla) och kärnavfallsförvaringsplatser (där transporten av radioaktiva nuklider genom sprickor dominerar den slutgiltigasäkerhetsutvärderingen) i sprickigt berg. / QC 20100803

Gegenstand dieser Arbeit ist die Bereitstellung eines geeigneten Simulationswerkzeuges für die numerische Untersuchung der beim Rollkontakt zwischen Rad und Schiene auftretenden Phänomene. Hierbei liegt das Hauptaugenmerk auf der kontinuumsmechanischen Formulierung des mechanischen Feldproblems kontaktierender Körper sowie dessen numerischer Lösung mittels der Finite-Element-Methode. Zur Reduzierung des bei der Simulation von Rollkontakt aus der notwendigen sehr feinen Diskretisierung der Kontaktgebiete resultierenden numerischen Aufwandes wird eine relativkinematische Beschreibung herangezogen. Diese gemischte LAGRANGE-EULER-Betrachtungsweise beruht auf der Zerlegung der Bewegung in einen Starrkörperanteil und eine dazu relative Deformation. Die Herleitung der Bewegungsgleichung für das Kontaktproblem erfordert die relativkinematische Formulierung der kontinuumsmechanischen Grundgleichungen, d.h. der Bilanzgleichungen sowie der konstitutiven Beziehungen. Eine geeignete Kontaktmechanik einschließlich der Berücksichtigung des Kontakts rauer Oberflächen und veränderlicher Kontaktrandbedingungen ist ebenfalls notwendig. Die physikalische Einbindung der Körper in die Umgebung erfolgt über NEUMANNsche und DIRICHLETsche Randbedingungen. Auf dieser Basis können die Bewegungsgleichungen der Elastomechanik hergeleitet werden, welche sich jedoch einer analytischen Lösung verschließen. Somit werden sie in ihrer schwachen Form im integralen Mittel formuliert, was der Anwendung des Prinzips der virtuellen Verschiebungen als Ausgangspunkt für die numerische Lösung entspricht. Die rechentechnische Umsetzung erfordert die inkrementelle und diskrete Formulierung der Bewegungsgleichungen unter besonderer Beachtung der Trägheits-und Kontaktterme, wobei auf die Unterscheidung zwischen Haften und Gleiten beim Tangentialkontakt besonderes Augenmerk gelegt wird. Die numerische Lösung des Finite-Element-Gleichungssystems liefert den aktuellen Beanspruchungszustand zweier Körper im Rollkontakt. Die Funktionsfähigkeit der entwickelten Algorithmen wird abschließend anhand aussagekräftiger Beispielrechnungen zum statischen Kontakt und zum stationären Rollkontakt demonstriert, deren Ergebnisse gute Übereinstimmung mit analytischen Vergleichslösungen, soweit verfügbar, aufweisen. / Scope of this work is the preparation of a suitable simulation tool for the numerical investigation of rolling contact phenomena. The main focus lies on the continuum–mechanical formulation of the mechanical field problem of contacting bodies and its numerical solution within the framework of the Finite Element Method. For reducing the numerical effort in rolling contact simulation, induced by the necessity of a very fine discretization within the expected contact area, a relative–kinematical description is utilized. This arbitrary LAGRANGian–EULERian approach is based upon the decomposition of the total motion into a rigid body motion and a superimposed deformation. The derivation of the equation of motion for the contact problem requires the relative–kinematical formulation of the continuum–mechanical fundamental equations, i. e. the balance equations and the constitutive relations. A suitable contact model including the contact of rough surfaces and varying contact boundary conditions is also necessary. The physical embedding into the environment is accomplished by NEUMANN and DIRICHLET boundary conditions. Based upon that foundation the elastomechanics’ equations of motion are derived, which however can not be solved analytically in general. Hence, the equations of motion are transferred into their weak form by the application of the principle of virtual displacements serving for the numerical solution. The implementation of the problem demands for an incremental and discrete formulation of the equations, especially regarding the terms of inertia and the contact terms. Thereby, special attention has to be paid to the distinction between sticking and sliding within the framework of the tangential contact analysis. The numerical solution of the finite elements’ system of equations provides the state of stress, displacement and contact of two bodies in rolling contact. The reliability of the developed algorithms is finally verified by means of meaningful numerical examples for both static contact and for stationary rolling contact, whereby the numerical results coincide well with available analytical reference solutions.

This research investigated the behavior of nonseismically detailed reinforced concrete exterior beam-column joints subjected to bidirectional lateral cyclic loading using nonlinear finite element analysis (NLFEA). Beam-column joints constitute a critical component in the load path of reinforced concrete buildings due to their fundamental role in integrating the overall structural system. Earthquake reconnaissance reports reveal that failure of joints has contributed to partial or complete collapse of reinforced concrete buildings designed without consideration for large lateral loads, resulting in significant economic impact and loss of life. Such infrastructure exists throughout seismically active regions worldwide, and the large-scale risk associated with such deficiencies is not fully known. Computational strategies provide a useful complement to the existing experimental literature on joint behavior and are needed to more fully characterize the failure processes in seismically deficient beam-column joints subjected to realistic failure conditions. Prior to this study, vulnerable reinforced concrete corner beam-column joints including the slab had not been analyzed using nonlinear finite element analysis and compared with experimental results. The first part of this research focused on identification and validation of a constitutive modeling strategy capable of simulating the behaviors known to dominate failure of beam-column joints under cyclic lateral load using NLFEA. This prototype model was formulated by combining a rotating smeared crack concrete constitutive model with a reinforcing bar plasticity model and nonlinear bond-slip formulation. This model was systematically validated against experimental data, and parametric studies were conducted to determine the sensitivity of the response to various material properties. The prototype model was then used to simulate the cyclic response of four seismically deficient beam-column joints which had been previously evaluated experimentally. The simulated joints included: a one-way exterior joint, a two-way beam-column exterior corner joint, and a series of two-way beam-column-slab exterior corner joints with varying degrees of seismic vulnerability. The two-way corner joint specimens were evaluated under simultaneous cyclic bidirectional lateral and cyclic column axial loading. For each specimen, the ability of the prototype model to capture the strength, stiffness degradation, energy dissipation, joint shear strength, and progressive failure mechanisms (e.g. cracking) was demonstrated.

Electromagnetic pulse simulators are essential for testing the ability of electronic devices to withstand high intensity electromagnetic ends. This work presents the analysis of various parallel plate transmission lines used in electromagnetic pulse simulators. Numerical techniques are developed to obtain the characteristic impedance, field map, and cut-infrequencies for the higher order modes of these transmission lines as exact analytical methods are not available for the determination of these quantities. The field map and characteristic impedance are computed using both finite element method (FEM) and boundary element method (BEM). Cut-off frequencies of the higher order modes are computed using FEM. The analysis presented can handle very general transmission line geometries. This analysis is useful for the design of electromagnetic pulse simulators.

Durch die zunehmende technologische Entwicklung des Getriebe-, Gelenkwellen-, Werkzeugmaschinen-, Kraftfahrzeug-, sowie Landmaschinenbaus steigen die zu übertragenden Leistungen und Drehmomente enorm. Dies führt zu einem wachsenden Bedarf an formschlüssigen Profilwellenverbindungen und deren erhöhter Lebensdauer und Genauigkeit. Hierbei bilden die Zahnwellenverbindungen (ZWVen) mit Evolventenflanken nach DIN 5480 /N1/ den Regelfall für eine Vielzahl der Anwendung. Abhängig von Festigkeitsüberlegungen, Herstellungsverfahren und Platzbedarf treten in der Praxis nahezu ausschließlich die folgenden zwei Grundtypen auf. Es handelt sich dabei zum Ersten um die Zahnwelle (ZW) mit freiem Auslauf.Die zweite Geometrievariante ist die Zahnwelle mit gebundenem Auslauf, die eine nach DIN 471 /N2/ genormte Sicherungsringnut (SRN) enthalten kann. Zahnwellenverbindungen dienen zur Übertragung großer, wechselnder und stoßartiger Drehmomente ohne zusätzliches Verbindungselement durch die Profilierung der Welle und Nabe. Axiale Verschiebbarkeit unter Last, Profilverschiebungsmöglichkeit, einfache Montage und Demontage sowie die Herstellung mit hochleistungsfähigen umformenden und spanenden Massenfertigungsverfahren, die die Herstellungskosten verhältnismäßig niedrig halten, sind technisch bedeutsame Eigenschaften, die zum ansteigenden Einsatz von ZWVen führen (z.B. /N1/, /Vil84/, /Koh86/ und /Wes96/). Starke Kerbwirkung und erhebliche Überdimensionierung benachbarter Gestaltungszonen sind die wesentlichen Schwachpunkte der Profilverbindungen. Eine große Anzahl (ca. 80 %) von Ausfällen im Maschinenbau ist auf Schäden an Achsen und Wellen infolge konstruktiv bedingter Kerben zurückzuführen (z.B. /N3/ und /Hai89/). Speziell im Bereich der hochbeanspruchten Profilwellen-Verbindungen kommt es auf Grund der starken Querschnittsveränderungen und der häufig angewandten Ausläufe und Formelemente, z. B. Zahn- und Keilwellen zu Kerbwirkungen, die erhebliche örtliche Spannungskonzentrationen sowohl im Zahnfußbereich und Zahnlückenauslauf als auch im Bereich der Verbindung selbst verursachen. Diese Beanspruchungskonzentrationen sind fast in der Hälfte aller Zahnwellenbrüche die häufigste Ursache für Dauerbrüche (Ermüdungs- bzw. Schwingungsbrüche) und für Schäden (bleibende Verformung, Anriss, Gewaltbruch) infolge Maximalbelastung. Hier trifft die Lastüberhöhung am Welle-Nabe-Verbindungsrand mit dem Steifigkeitssprung des Verzahnungsendes auf der Welle zusammen /Die93/. Die erwähnten Schadensfälle belegen, dass der heutige Kenntnisstand über eine beanspruchungsgerechte Auslegung von Zahnwellen noch recht lückenhaft ist. Deshalb sind neue Erkenntnisse über Form- bzw. Kerbwirkungszahlen bei Einzel- und Mehrfachkerben von scharf und weniger scharf gekerbten Zahnwellen mit Auslauf für eine treffsichere Festigkeitsberechnung erforderlich und stellen damit die Hauptschwerpunkte dieser Arbeit dar. Das vorliegende Forschungsprojekt, welches sich erstmals mit der Ermittlung der Beanspruchungen in torsions-, und biegebelasteten Zahnwellen mit freiem und gebundenem Auslauf befasst, wurde im Rahmen der Forschungsvereinigung für Antriebstechnik e.V. (FVA) unter der Nummer T 467 und dem Forschungsthema „ Ermittlung der Kerbwirkung bei Profilwellen für die praktische Getriebeberechnung von Zahnwellen“ initiiert und untersucht.

Šiame baigiamajame darbe optimizuojama plokščiojo kūno forma esant žinomai apkrovai ir kraštinėms sąlygoms. Aptariami pagrindiniai optimizavimo tipai, globaliojo optimizavimo ir kontinuumo diskretizavimo metodai. Forma optimizuojama trimis skirtingais neadaptyviais genetiniais algoritmais ir trimis adaptyviais, taikant migracijos strategijas. Poslinkiai ir von Mises įtempimai skaičiuojami baigtinių elementų metodu. Darbo užduotis realizuota C++ kalba. Darbą sudaro 9 dalys: įvadas, kūno formos modeliavimo metodų apžvalga, baigtinių elementų metodas, genetiniai algoritmai, kūno formos optimizavimo uždavinys, rezultatų palyginimas, išvados, literatūros sąrašas, priedai. Darbo apimtis - 62 p. teksto be priedų, 39 iliustr., 5 lent., 24 bibliografinių šaltinių. / The task of Master thesis is to optimize shape of plane body with given loading and boundary conditions. The classes of structural optimization problems, the methods of global optimization and discretization of continual structures are discussed. For shape optimization three different not adaptive and three adaptive genetic algorithms with migration strategy are used, displacements and von Mises stresses are calculated using finite element method. The program was created using C++ language. The work consists of 9 parts: introduction, overview of methods used for shape optimization, finite element method, genetic algorithms, shape optimization of plane body, results, conclusions, references, appendixes. Work consist of 62 p. text without appendixes, 39 pictures, 5 tables, 24 bibliographical entries. Appendixes are included.

The development of new materials and technologies, associated to increasingly complex problems in structural engineering, require more robust and accurate numerical analyses with an affordable computational cost. Computer modeling has been evolving by improving existing numerical methods and also developing new ones. Among the methods widely applied, finite elements have become a powerful tool in the search for solutions in structural engineering. Other approaches also emerged as alternative modeling strategies, such as artificial intelligence techniques. One of these techniques, Artificial Neural Networks (ANN), is designed for simulating human conexionism paradigm. ANN has been applied in several areas to solve a range of problems concerning classification, function fitting, forecasting, among others. This work explores ways to coupling ANN to traditional approximation methods such as the Finite Element Method (FEM) for applications in plane elastostatics, considering geometrically nonlinear aspects. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O desenvolvimento de novos materiais e tecnologias, associado a projetos estruturais cada vez mais complexos, demandam análises numéricas robustas e precisas a um custo computacional adequado. Estudos em modelagem computacional têm evoluído no sentido de suprir a essa demanda aprimorando continuamente os métodos numéricos já existentes, bem como propondo novas técnicas. Dentre os métodos amplamente utilizados, o Método dos Elementos Finitos (MEF) tornou-se uma potente ferramenta de busca por soluções no âmbito da engenharia estrutural. Também surgiram abordagens alternativas de resolução relacionadas à modelagem, tais como as técnicas de inteligência artificial. Uma dessas técnicas, as Redes Neurais Artificiais (RNA), são redes projetadas para modelar capacidades humanas como aprendizagem e generalização através de estrutura de processamento que utiliza o conexionismo como paradigma. As RNA têm sido aplicadas nas mais diversas áreas na solução de uma gama de problemas que envolvem classificação, aproximação de funções, previsão, dentre outros. Este trabalho explora maneiras de incorporar RNA a métodos aproximativos tradicionais como o Método dos Elementos Finitos para aplicação em problemas de elasticidade plana, considerando não linearidade geométrica.

The finite element method (FEM) is a widely-used numerical tool in the fields of structural dynamics, acoustics and electromagnetics. In this work, our goal is to develop robust FEM strategies for solving problems in the areas of acoustics, structures and electromagnetics, and then extend these strategies to solve multi-physics problems such as magnetohydrodynamics and structural acoustics. We now briefly describe the finite element strategies developed in each of the above domains. In the structural domain, we show that the trapezoidal rule, which is a special case of the Newmark family of algorithms, conserves linear and angular momenta and energy in the case of undamped linear elastodynamics problems, and an ‘energy-like measure’ in the case of undamped acoustic problems. These conservation properties, thus, provide a rational basis for using this algorithm. In linear elastodynamics variants of the trapezoidal rule that incorporate ‘high-frequency’ dissipation are often used, since the higher frequencies, which are not approximated properly by the standard displacement-based approach, often result in unphysical behavior. Instead of modifying the trapezoidal algorithm, we propose using a hybrid FEM framework for constructing the stiffness matrix. Hybrid finite elements, which are based on a two-field variational formulation involving displacement and stresses, are known to approximate the eigenvalues much more accurately than the standard displacement-based approach, thereby either bypassing or reducing the need for high-frequency dissipation. We show this by means of several examples, where we compare the numerical solutions obtained using the displacementbased and hybrid approaches against analytical solutions. We also present a monolithic formulation for the solution of structural acoustic problems based on the hybrid finite element approach. In the area of electromagnetics, since our goal is to ultimately couple the electromagnetic analysis with structural or fluid variables in a ‘monolithic’ framework, we focus on developing nodal finite elements rather than using ‘edge elements’. It is well-known that conventional nodal finite elements can give rise to spurious solutions, and that they cannot capture singularities when the domains are nonconvex and have sharp corners. The commonly used remedies of either adding a penalty term or using a potential formulation are unable to address these problems satisfactorily. In order to overcome this problem, we first develop several mixed finite elements in two and three dimensions which predict the eigenfrequencies (including their multiplicities) accurately, even for non-convex domains. In this proposed formulation, no ad-hoc terms are added as in the penalty formulation, and the improvement is achieved purely by an appropriate choice of the finite element spaces for the different variables. For inhomogeneous domains, ‘double noding’ is used to enforce the appropriate continuity conditions at an interface. Although the developed mixed FEM works very accurately for all 2D geometries and regular Cartesian 3D geometries, it has so far not yielded success for curved 3D geometries. Therefore, for 3D harmonic and transient analysis problems, we propose and use a modified form of the potential formulation that overcomes the disadvantages of the standard potential method, especially on non-convex domains. Electromagnetic radiation and scattering in an exterior domain traditionally involved imposing a suitable absorbing boundary condition (ABC) on the truncation boundary of the numerical domain to inhibit reflection from it. In this work, based on the Wilcox asymptotic expansion of the electric far-field, we propose an amplitude formulation within the framework of the nodal FEM, whereby the highly oscillatory radial part of the field is separated out a-priori so that the standard Lagrange interpolation functions have to capture a relatively gently varying function. Since these elements can be used in the immediate vicinity of the radiator or scatterer (with few exceptions which we enumerate), it is more effective compared to methods of imposing ABCs, especially for high-frequency problems. We show the effectiveness of the proposed formulation on a wide variety of radiation and scattering problems involving both conducting and dielectric bodies, and involving both convex and non-convex domains with sharp corners. The Time Domain Finite Element Method (TDFEM) has been used extensively to solve transient electromagnetic radiation and scattering problems. Although conservation of energy in electromagnetics is well-known, we show in this work that there are additional quantities that are also conserved in the absence of loading. We then show that the developed time-stepping strategy (which is closely related to the trapezoidal rule) mimics these continuum conservation properties either exactly or to a very good approximation. Thus, the developed numerical strategy can be said to be ‘unconditionally stable’ (from an energy perspective) allowing the use of arbitrarily large time-steps. We demonstrate the high accuracy and robustness of the developed method for solving both interior and exterior domain radiation problems, and for finding the scattered field from conducting and dielectric bodies. In the field of magneto-hydrodynamics, we develop a monolithic strategy based on a continuous velocity-pressure formulation that is known to satisfy the Babuska-Brezzi (BB) conditions. The magnetic field is interpolated in the same way as the velocity field, and the entire formulation is within a nodal finite element framework. Both transient and steady-state formulations are developed for two- and three-dimensional geometries. An exact linearization of the monolithic strategy ensures that rapid (quadratic) convergence is achieved within each time (or load) step, while the stable nature of the interpolations used ensure that no instabilities arise in the solution. Good agreement with analytical solutions, even with the use of very coarse meshes, shows the efficacy of the developed formulation.

Le travail présenté intègre l'utilisation des vibrations mécaniques dans les procédés de mise en forme à froid des matériaux de comportement viscoplastique. Les avantages de procédé de mise en forme assisté par vibrations se mesurent par une réduction de l'intensité de la force de mise en forme, une diminution de la contrainte d'écoulement, la réduction du frottement entre l'outil et lopin, une distribution uniforme de la déformation viscoplastique et une amélioration de l'état de surface de la pièce finale. A cet effet, un modèle analytique avec une seule source de vibration a été développé pour le procédé de forgeage. Les vibrations sinusoïdale et triangulaire ont été intégrées dans le modèle et il se trouve que les vibrations triangulaire est plus avantageux comparer à les vibrations sinusoïdal a cause du contrôle sur le rapport cyclique. On observe également que les paramètres principaux qui contrôlent la réduction de la force de forgeage sont : le rapport de vitesse définie par l'amplitude de la vitesse de vibration et la vitesse moyenne de l'outillage et la sensibilité à la vitesse de déformation. Le modèle analytique a été validé au moyen des simulations éléments finis réalisés avec le code de calcul FORGE2011 ® et les essais expérimentaux en dispositif expérimentale de pot vibrant a été conçu et les essais ont été réalisé sur les machines Lloyd LR30K ou ZWICK / Roell 1200. L'étude a ensuite été enrichi avec les plusieurs sources de vibrations. L'étude cinématique montre que les vibrations multiples générés une onde progressive. Cette nouvelle cinématique a été intégrée dans un modèle numérique sur le code de simulation par éléments finis FORGE2011 ® pour étudier le forgeage assisté par plusieurs sources des vibrations. L'analyse de résultats montre une réduction considérable de la force de forgeage et de la contrainte de l'écoulement ainsi qu'une modification de la loi de frottement générer par le changement de la direction du vecteur de vitesse. / This work is focused on the application of mechanical vibrations in cold metal forming process for visco-plastic domain to improve it by obtaining mean forming load reduction, low stresses, less friction, uniform distribution of strains and good surface qualities. For this purpose, analytical model has been developed for vibration assisted forming process with single vibration source. Sinusoidal and triangular vibration waveforms have been integrated in these models and it is found that triangular vibration is more advantageous as compare to traditional sinusoidal due to the control on cycle duty time. It is also observed that the main parameters that control the amount of forging force reduction are: the speed ratio defined by the amplitude of the vibration speed over the mean speed of the die and the sensitivity to strain rate. Analytical model is verified with the help of Finite element simulations performed in FORGE2011 ® and experiments performed with the help of specifically design vibration pot and Lloyd LR30K Universal testing machine or ZWICK/Roell 1200. The scope of this work is further extended by the use multiple vibration sources in the metal forming process. Kinematic study is carried out and it is found that application of multiple vibrations generates progress wave. This kinematic is applied in FORGE2011 ® during the metal forging process with the help of generic press and the reduction in forging load has been observed along with reduction in stress in the material and the modification of the friction on the lower die due to the change in velocity vector direction.

Dans les structures en béton précontraint, les phénomènes de fluage et de retrait tendent à réduire les efforts de précontrainte initialement prévus pour maintenir le béton dans un état minimisant les forces de traction et donc la fissuration. La compréhension et la prédiction de ces phénomènes par le biais de modèles sont donc primordiales pour la conception et la maintenance à long terme des ouvrages du génie civil tels que les enceintes de confinement des centrales nucléaires.L’objectif de cette thèse est d’élaborer un cadre de modélisation micromécanique pour décrire de manière unifiée le retrait et le fluage dans les matériaux cimentaires. Pour cela, l’étude se base sur l’échelle de la microstructure poreuse du gel de C-S-H où les mécanismes intrinsèques de ces déformations différées du béton opèrent. Une approche d’homogénéisation numérique modélisant ces phénomènes dans des microstructures poreuses à morphologies quelconques est développée. Une description explicite du réseau poreux ainsi que de la phase liquide de l’eau pendant les processus de séchage/humidification est prise en compte. Les mécanismes concernant lesdéformations différées dans la phase solide sont modélisés par la théorie de la microprécontrainte-solidification (MPS). Les simulations à l’échelle microscopique sont réalisées par une approche originale couplant la méthode de Lattice Boltzmann (LBM) et la méthode des éléments finis (FEM). La LBM est utilisée pour décrire la distribution du liquide capillaire à l’échelle du pore,tandis que la FEM est employée pour simuler la déformation du squelette solide sous l’action combinée de l’eau dans l’espace poreux et d’un chargement macroscopique.La démarche proposée permet, au travers des simulations, de mieux comprendre les mécanismes liés à la non saturation et aux effets capillaires dans les milieux poreux. En particulier, la prise en compte de morphologies réalistes de microstructures et des ménisques formés conduit à différents régimes de retrait/gonflement. Ainsi les effets de l’intensité de la pression capillaire,de la tension de surface et des surfaces de chargement sur la réponse élastique du squelette solide sont évalués. Enfin, nous proposons une extension des approches précédentes au cas d’un squelette viscoélastique se déformant sous les effets de la pression capillaire et des tensions de surface. A partir des observations numériques réalisées, nous proposons un modèle pour décrire le fluage et le retrait du gel de C-S-H de manière unifiée / In pre-stressed concrete structures, creep and shrinkage tend to reduce the pre-stress forces which are initially produced so as to maintain concrete in a state minimizing traction forces and then cracks. Understanding and predicting these phenomena through models are thus highly important for the design and durability of civil engineering structures, such as containment buildings in nuclear power plants.The objective of this thesis is to develop a micromechanical modeling framework to describe shrinkage and creep in cementitious materials in a unified manner. For this purpose, the study focuses on the scale of the porous structure of the C-S-H gel where the intrinsic mechanisms of delayed strains are active. A computational homogenization approach is developed to model these phenomena in porous structures with arbitrary morphologies. An explicit description of the porous network and of the liquid phase of water during the drying/humidification process is taken into account. The mechanisms related to delayed strains in the solid phase are modeled by the microprestress-solidification theory (MPS). The simulations at the microscale are conductedbased on an original approach coupling the Lattice Boltzmann method (LBM) and the finite element method (FEM). The LBM is used to describe the distribution of capillary water in the porous structure, whereas the FEM serves as modeling the strain of the solid skeleton under the capillary water effets and a macroscopic load.The proposed method allows, by means of the simulations, to better understand the mechanisms related to the capillary effects in the porous structure. More specifically, taking into account realistic morphologies of microstructures and of the formed menisci lead to different regimes of shrinkage/swelling. Then, the effects of capillary pressure intensity, of surface tension and of morphologies of capillary surfaces on the elastic response of the solid skeleton are evaluated. Finally, the above approaches are extended to the case of a viscoelastic solid deformed under the action of the capillary water. From numerical observations, we propose a model is proposed to describe the creep and shrinkage of C-S-H gel in a unified way