Rozprawy doktorskie na temat „Elastic boundary condition”

Dans ce projet, nous proposons une série d’expériences modèles à l’échelle du laboratoire pour explorer la dynamiqueet les instabilités des films liquides minces inspirés par la géophysique.Nous étudions des phénomènes similaires aux laccolithes, où l’écoulement de magma déforme les couches rocheusesenvironnantes. Dans la limite où leur hauteur h est très faible devant leur taille horizontale R, ces formations dynamiquespeuvent être raisonnablement comparées à des cloques liquides minces recouvertes d’un film élastique. Nous proposonsainsi de revisiter les expériences classiques de la dynamique de gouttes en surface libre en modifiant la condition limiteimposée par la nature de l’interface.Nous tenterons de répondre à plusieurs questions relatives à cette configuration.Quelle est la forme et la dynamique d’une poche de fluide piégée sous une membrane élastique ? Comment se dé-roule la coalescence de deux poches voisines avec cette nouvelle condition limite ? Comment les régimes dynamiquesd’étalement en sont-ils affectés ?Pour répondre à ces questions, nous avons mis en place un dispositif expérimental afin d’observer et de caractériser cephénomène d’étalement en utilisant des techniques de démodulation FCD que nous avons adaptées à notre configura-tion.Nous injectons de l’huile végétale de viscosité dynamique μ, à débit contrôlé Q, à travers une plaque de PMMA surlaquelle nous déposons un film élastique d’épaisseur millimétrique. Nous étudions trois configurations principales :1. L’étalement d’une cloque visqueuse unique.2. La coalescence de deux cloques identiques.3. Une instabilité de Rayleigh-Taylor en présence d’une membrane élastique.Pour chaque configuration étudiée, nous commençons par reconstruire la forme générale des cloques obtenues et carto-graphons leur champ de hauteur h(r, t) au cours du temps. Nous montrons la présence de plusieurs régimes d’expansionqui évoluent selon des lois de puissance précises que nous vérifions à la fois théoriquement et expérimentalement. Pourles deux premières études, nous tentons systématiquement d’ajuster la forme de chaque régime à un comportementauto-similaire associé. En complément de cette double approche, une analyse numérique fut également développée envue d’une comparaison avec les données expérimentales obtenues pour les différentes configurations testées
In this project, we propose a series of laboratory-scale model experiments to explore the dynamics and instabilities of geophysically inspired thin liquid films.We are studying phenomena similar to laccoliths, where magma flow deforms the surrounding rock layers. In the limit where their height is very small compared to their horizontal size, these dynamic formations can be reasonably compared to thin liquid blisters covered by an elastic film. We thus propose to revisit classical experiments on free-surface drop dynamics by modifying the boundary condition imposed by the nature of the interface.What is the shape and dynamics of a fluid pocket trapped beneath an elastic membrane? How does the coalescence of two adjacent pockets proceed under this new boundary condition? How are dynamic spreading regimes affected?To answer these questions, we set up an experimental device to observe and characterize this spreading phenomenon, using demodulation techniques that we adapted to our configuration.We inject vegetable oil, at a controlled flow rate, through a PMMA plate onto which we deposit an elastic film of millimetric thickness. We are studying three main configurations:1 Spreading of a single viscous blister.2 The coalescence of two identical blisters.3 A Rayleigh-Taylor instability in the presence of an elastic membrane.For each configuration studied, we begin by reconstructing the general shape of the blisters obtained and map their height field over time. We show the presence of several expansion regimes that evolve according to precise power laws, which we verify both theoretically and experimentally. For the first two studies, we systematically attempt to fit the shape of each regime to an associated self-similar behavior.To complement this dual approach, a numerical analysis was also developed for comparison with the experimental data obtained for the different configurations tested

Thesis (M. S.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2009.
Committee Chair: Jacobs, Laurence; Committee Co-Chair: Qu, Jianmin; Committee Member: DesRoches, Reginald. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Cette thèse porte sur la Half-Space Matching Method qui a été développée pour traiter certains problèmes de diffraction dans des domaines complexes infinis pour lesquels les méthodes numériques existantes ne s'appliquent pas. En 2D, elle consiste à coupler plusieurs représentations en ondes planes dans des demi-espaces entourant les obstacles et une représentation éléments finis dans un domaine borné. Afin d'assurer la compatibilité entre les différentes représentations, les traces de la solution sont liées par des équations intégrales de Fourier posées sur les frontières infinies des demi-espaces. Dans le cas d'un milieu dissipatif, il a été montré que ce système d'équations intégrales est coercif plus compact dans un cadre L².Dans cette thèse, nous établissons des estimations d'erreur par rapport aux paramètres de discrétisation (à la fois pour les variables spatiales et les variables de Fourier). Pour traiter le cas non-dissipatif, nous proposons une version modifiée de la Half-Space Matching Method, obtenue en appliquant une dilatation complexe aux inconnues afin de retrouver le cadre L².Nous étendons ensuite la Half-Space Matching Method aux problèmes de diffraction dans une plaque élastique infinie 3D en vue d'applications au Contrôle Non Destructif. La difficulté par rapport au cas 2D vient de la décomposition sur les modes de Lamb utilisée dans les représentations de demi-plaque. La relation de bi-orthogonalité des modes des Lamb impose de considérer comme inconnues non seulement le champ de déplacement, mais aussi le champ de contrainte sur les bandes infinies au bord des demi-plaques. Certaines questions théoriques soulevées par cette formulation multi-inconnues sont étudiées dans le cas 2D scalaire. Des connexions avec les méthodes intégrales sont aussi abordées dans le cas où la fonction de Green est connue, au moins partiellement dans chaque sous-domaine.Les différentes versions de la méthode ont été mises en oeuvre dans la bibliothèque XLiFE++ et des résultats numériques sont présentés pour les cas 2D et 3D
This thesis focuses on the Half-Space Matching Method which was developed to treat some scattering problems in complex infinite domains, when usual numerical methods are not applicable. In 2D, it consists in coupling several plane-wave representations in half-spaces surrounding the obstacle(s) with a Finite Element computation of the solution in a bounded domain. To ensure the matching of all these representations, the traces of the solution are linked by Fourier-integral equations set on the infinite boundaries of the half-spaces. In the case of a dissipative medium, this system of integral equations was proved to be coercive plus compact in an L² framework.In the present thesis, we derive error estimates with respect to the discretization parameters (both in space and Fourier variables). To handle the non-dissipative case, we propose a modified version of the Half-Space Matching Method, which is obtained by applying a complex-scaling to the unknowns, in order to recover the L² framework.We then extend the Half-Space Matching Method to scattering problems in infinite 3D elastic plates for applications to Non-Destructive Testing. The additional complexity compared to the 2D case comes from the decomposition on Lamb modes used in the half-plate representations. Due to the bi-orthogonality relation of Lamb modes, we have to consider as unknowns not only the displacement, but also the normal stress on the infinite bands limiting the half-plates. Some theoretical questions concerning this multi-unknown formulation involving the trace and the normal trace are studied in a 2D scalar case. Connections with integral methods are also addressed in the case where the Green's function is known, at least partially in each subdomain.The different versions of the method have been implemented in the library XLiFE++ and numerical results are presented for both 2D and 3D cases

A model for stress and strain accumulation in strike slip earthquake faults is presented in which a finite width cuboidal fault region is embedded between two cuboidal tectonic plates. Elasto-plastic continuum constitutive equations model the gouge in the fault and the tectonic plates are linear elastic solids obeying the generalised Hooke's law. The model predicts a velocity field which is comparable to surface deformations. The plastic behaviour of the fault material allows the velocities in the tectonic plate to increase to values which are independent of the distance from the fault. Both of the non-trivial stress and strain components accumulate most significantly in the vicinity of the fault. The release of these strains during a dynamic earthquake event would produce the most severe deformations at the fault which is consistent with observations and the notion of an epicenter. The accumulations in the model, however, are at depths larger than would be expected. Plastic strains build up most significantly at the base of the fault which is in yield for the longest length of time but additionally is subject to larger temperatures which makes the material more ductile. The speed of propagation of the elasto-plastic boundary is calculated and its acceleration towards the surface of the fault may be indicative of a dynamic earthquake type event.

The properties of a one-dimensional phononic crystal made of identical piezoelectric elements separated by thin metallic electrodes connected to the ground are studied theoretically for cases where the locations of the electrical connections change as a function of time with a specific speed. This spatio-temporal modulation of the electrical boundary conditions results in significant non-linear effects that are evidenced numerically. The interaction between an incident harmonic longitudinal wave and the time-dependent phononic crystal is shown to lead to frequency splitting analogous to Brillouin scattering. Moreover, the boundaries of the Bragg bandgaps are strongly affected, and for some specific modulation speed, one-way wave propagation can be achieved. Published by AIP Publishing.

Dans ce travail un modele original de calcul des champs elastiques des reseaux hexagonaux de dislocations d'hetero-interfaces est propose en elasticite anisotrope. Les conditions aux limites sont les suivantes: a) les dislocations sont intrinseques et n'engendrent pas de contraintes a longue distance. B) la condition de raccordement des deux milieux a l'interface est representee par un deplacement relatif lineaire a l'interieur d'un hexagone, et discontinue le long de ses cotes. Les champs des deplacements et des contraintes sont etablis et calcules numeriquement par des programmes fortran. Une formule analytique, obtenue par integration, est etablie pour determiner l'energie elastique stockee par unite de surface du joint. Elle est appliquee dans les cas suivants: a) hetero-interface cu/fe, b) hetero-interface cosi#2/si, c) hetero-interface gamma/gamma dans les superalliages, d) joints de torsion dans les metaux cfc

Problème de la transmission du son sur l'axe d'une structure élastique fermée à symétrie de révolution. Problème de Neumann, associé à la pression acoustique par la méthode de la phase stationnaire et problème de structure par une méthode d'éléments finis.

La méthode d’imagerie la plus répandue dans l’industrie pétrolière est la RTM (Reverse Time Migration) qui repose sur la simulation de la propagation des ondes dans le sous-sol. Nous nous sommes concentrés sur un propagateur d'ondes élastiques 3D en milieu anisotrope de type TTI (Tilted Transverse Isotropic). Nous avons directement travaillé dans le code de recherche de Total DIVA (Depth Imaging Velocity Analysis), basé sur une discrétisation par la méthode de Galerkin Discontinue et le schéma Leap-Frog, et développé pour le calcul parallèle intensif – HPC (High Performance Computing). Nous avons ciblé plus particulièrement deux contributions possibles qui, si elles supposent des compétences très différentes, ont la même finalité : réduire les coûts de calculs requis pour la simulation. D'une part, les conditions aux limites classiques de type PML (Perfectly Matched Layers) ne sont pas stables dans des milieux TTI. Nous avons proposé de formuler une CLA (Conditions aux Limites Absorbantes) stable dans des milieux anisotropes. La méthode de construction repose sur les propriétés des courbes de lenteur, ce qui donne à notre approche un caractère original. D'autre part, le parallélisme initial, basé sur une décomposition de domaine et des communications par passage de messages à l'aide de la bibliothèque MPI, conduit à un déséquilibrage de charge qui détériore son efficacité parallèle. Nous avons corrigé cela en remplaçant le paradigme parallélisme par l'utilisation de la programmation à base de tâches sur support d'exécution. Cette thèse a été réalisée dans le cadre de l'action de recherche DIP (Depth Imaging Partnership) qui lie la compagnie pétrolière Total et Inria
The most common method of Seismic Imaging is the RTM (Reverse Time Migration) which depends on wave propagation simulations in the subsurface. We focused on a 3D elastic wave propagator in anisotropic media, more precisely TTI (Tilted Transverse Isotropic). We directly worked in the Total code DIVA (Depth Imaging Velocity Analysis) which is based on a discretization by the Discontinuous Galerkin method and the Leap-Frog scheme, and developed for intensive parallel computing – HPC (High Performance Computing). We choose to especially target two contributions. Although they required very different skills, they share the same goal: to reduce the computational cost of the simulation. On one hand, classical boundary conditions like PML (Perfectly Matched Layers) are unstable in TTI media. We have proposed a formulation of a stable ABC (Absorbing Boundary Condition) in anisotropic media. The technique is based on slowness curve properties, giving to our approach an original side. On the other hand, the initial parallelism, which is based on a domain decomposition and communications by message passing through the MPI library, leads to load-imbalance and so poor parallel efficiency. We have fixed this issue by replacing the paradigm for parallelism by the use of task-based programming through runtime system. This PhD thesis have been done in the framework of the research action DIP (Depth Imaging Partnership) between the Total oil company and Inria

[EN] Phononic crystals are artificial materials formed by a periodic arrangement of inclusions embedded into a host medium, where each of them can be solid or fluid. By controlling the geometry and the impedance contrast of its constituent materials, one can control the dispersive properties of waves, giving rise to a huge variety of interesting and fundamental phenomena in the context of wave propagation. When a propagating wave encounters a medium with different physical properties it can be transmitted and reflected in lossless media, but also absorbed if dissipation is taken into account. These fundamental phenomena have been classically explained in the context of homogeneous media, but it has been a subject of increasing interest in the context of periodic structures in recent years as well. This thesis is devoted to the study of different effects found in sonic and phononic crystals associated with transmission, reflection and absorption of waves, as well as the development of a technique for the characterization of its dispersive properties, described by the band structure. We start discussing the control of wave propagation in transmission in conservative systems. Specifically, our interest is to show how sonic crystals can modify the spatial dispersion of propagating waves leading to control the diffractive broadening of sound beams. Making use of the spatial dispersion curves extracted from the analysis of the band structure, we first predict zero and negative diffraction of waves at frequencies close to the band-edge, resulting in collimation and focusing of sound beams in and behind a 3D sonic crystal, and later demonstrate it through experimental measurements. The focusing efficiency of a 3D sonic crystal is limited due to the strong scattering inside the crystal, characteristic of the diffraction regime. To overcome this limitation we consider axisymmetric structures working in the long wavelength regime, as a gradient index lens. In this regime, the scattering is strongly reduced and, in an axisymmetric configuration, the symmetry matching with acoustic sources radiating sound beams increase its efficiency dramatically. Moreover, the homogenization theory can be used to model the structure as an effective medium with effective physical properties, allowing the study of the wave front profile in terms of refraction. We will show the model, design and characterization of an efficient focusing device based on these concepts. Consider now a periodic structure in which one of the parameters of the lattice, such as the lattice constant or the filling fraction, gradually changes along the propagation direction. Chirped crystals represent this concept and are used here to demonstrate a novel mechanism of sound wave enhancement based on a phenomenon known as "soft" reflection. The enhancement is related to a progressive slowing down of the wave as it propagates along the material, which is associated with the group velocity of the local dispersion relation at the planes of the crystal. A model based on the coupled mode theory is proposed to predict and interpret this effect. Two different phenomena are observed here when dealing with dissipation in periodic structures. On one hand, when considering the propagation of in-plane sound waves in a periodic array of absorbing layers, an anomalous decrease in the absorption, combined with a simultaneous increase of reflection and transmission at Bragg frequencies is observed, in contrast to the usual decrease of transmission, characteristic in conservative periodic systems at these frequencies. For a similar layered media, backed now by a rigid reflector, out-of-plane waves impinging the structure from a homogeneous medium will increase dramatically the interaction strength. In other words, the time delay of sound waves inside the periodic system will be considerably increased resulting in an enhanced absorption, for a broadband spectral range.
[ES] Los cristales fonónicos son materiales artificiales formados por una disposición periódica de inclusiones en un medio, pudiendo ambos ser de carácter sólido o fluido. Controlando la geometría y el contraste de impedancias entre los materiales constituyentes se pueden controlar las propiedades dispersivas de las ondas. Cuando una onda propagante se encuentra un medio con diferentes propiedades físicas puede ser transmitida y reflejada, en medios sin pérdidas, pero también absorbida, si la disipación es tenida en cuenta. La presente tesis está dedicada al estudio de diferentes efectos presentes en cristales sónicos y fonónicos relacionados con la transmisión, reflexión y absorción de ondas, así como el desarrollo de una técnica para la caracterización de sus propiedades dispersivas, descritas por la estructura de bandas. En primer lugar, se estudia el control de la propagación de ondas en transmisión en sistemas conservativos. Específicamente, nuestro interés se centra en mostrar cómo los cristales sónicos son capaces de modificar la dispersión espacial de las ondas propagantes, dando lugar al control del ensanchamiento de haces de sonido. Haciendo uso de las curvas de dispersión espacial extraídas del análisis de la estructura de bandas, se predice primero la difracción nula y negativa de ondas a frecuencias cercanas al borde de la banda, resultando en la colimación y focalización de haces acústicos en el interior y detrás de un cristal sónico 3D, y posteriormente se demuestra mediante medidas experimentales. La eficiencia de focalización de un cristal sónico 3D está limitada debido a las múltiples reflexiones existentes en el interior del cristal. Para superar esta limitación se consideran estructuras axisimétricas trabajando en el régimen de longitud de onda larga, como lentes de gradiente de índice. En este régimen, las reflexiones internas se reducen fuertemente y, en configuración axisimétrica, la adaptación de simetría con fuentes acústicas radiando haces de sonido incrementa la eficiencia drásticamente. Además, la teoría de homogenización puede ser empleada para modelar la estructura como un medio efectivo con propiedades físicas efectivas, permitiendo el estudio del frente de ondas en términos refractivos. Se mostrará el modelado, diseño y caracterización de un dispositivo de focalización eficiente basado en los conceptos anteriores. Considérese ahora una estructura periódica en la que uno de los parámetros de la red, sea el paso de red o el factor de llenado, cambia gradualmente a lo largo de la dirección de propagación. Los cristales chirp representan este concepto y son empleados aquí para demostrar un mecanismo novedoso de incremento de la intensidad de la onda sonora basado en un fenómeno conocido como reflexión "suave". Este incremento está relacionado con una ralentización progresiva de la onda conforme se propaga a través del material, asociado con la velocidad de grupo de la relación de dispersión local en los planos del cristal. Un modelo basado en la teoría de modos acoplados es propuesto para predecir e interpretar este efecto. Se observan dos fenómenos diferentes al considerar pérdidas en estructuras periódicas. Por un lado, si se considera la propagación de ondas sonoras en un array periódico de capas absorbentes, cuyo frente de ondas es paralelo a los planos del cristal, se produce una reducción anómala en la absorción combinada con un incremento simultáneo de la reflexión y transmisión a las frecuencias de Bragg, de forma contraria a la habitual reducción de la transmisión, característica de sistemas periódicos conservativos a estas frecuencias. En el caso de la misma estructura laminada en la que se cubre uno de sus lados mediante un reflector rígido, la incidencia de ondas sonoras desde un medio homogéneo, cuyo frente de ondas es perpendicular a los planos del cristal, produce un gran incremento de la fuerza de
[CAT] Els cristalls fonònics són materials artificials formats per una disposició d'inclusions en un medi, ambdós poden ser sòlids o fluids. Controlant la geometría i el contrast d'impedàncies dels seus materials constituents, és poden controlar les propietats dispersives de les ondes, permetent una gran varietatde fenòmens fonamentals interessants en el context de la propagació d'ones. Quan una ona propagant troba un medi amb pèrdues amb propietats físiques diferents es pot transmetre i reflectir, però també absorbida si la dissipació es té en compte. Aquests fenòmens fonamentals s'han explicat clàssicament en el context de medis homogenis, però també ha sigut un tema de creixent interés en el context d'estructures periòdiques en els últims anys. Aquesta tesi doctoral tracta de l'estudi de diferents efectes en cristalls fonònics i sònics lligats a la transmissió, reflexió i absorció d'ones, així com del desenvolupament d'una tècnica de caracterització de les propietats dispersives, descrites mitjançant la estructura de bandes. En primer lloc, s'estudia el control de la propagació ondulatori en transmissió en sistemes conservatius. Més específicament, el nostre interés és mostrar com els cristalls sonors poden modificar la dispersió espacial d'ones propagants donant lloc al control de l'amplària per difracció dels feixos sonors. Mitjançant les corbes dispersió espacial obtingudes de l'anàlisi de l'estructura de bandes, es prediu, en primer lloc, la difracció d'ones zero i negativa a freqüències próximes al final de banda. El resultat és la collimació i focalització de feixos sonors dins i darrere de cristalls de so. Després es mostra amb mesures experimentals. L'eficiència de focalització d'un cristall de so 3D està limitada per la gran dispersió d'ones dins del cristall, que és característic del règim difractiu. Per a superar aquesta limitació, estructures axisimètriques que treballen en el règim de llargues longituds d'ona, i es comporten com a lents de gradient d'índex. En aquest règim, la dispersió es redueix enormement i, en una configuració axisimètrica, a causa de l'acoblament de la simetría amb les fonts acústiques que radien feixos sonors, l'eficiència de radiació s'incrementa significativament. D'altra banda, la teoria d'homogeneïtzació es pot utilitzar per a modelar, dissenyar i caracteritzar un dispositiu eficient de focalització basat en aquests conceptes. Considerem ara una estructura periòdica en la qual un dels seus paràmetres de xarxa, com ara la constant de xarxa o el factor d'ompliment canvia gradualment al llarg de la direcció de propagació. Els cristalls chirped representen aquest concepte i s'utilitzen ací per a demostrar un mecanisme nou d'intensificació d'ones sonores basat en el fenòmen conegut com a reflexió "suau". La intensificació està relacionada amb la alentiment progressiva de l'ona conforme propaga al llarg del material, que està associada amb la velocitat de grup de la relació de dispersió local en els diferents plànols del cristall. Es proposa un model basat en la teoria de modes acoblats per a predir i interpretar este efecte. Dos fenòmens diferents cal destacar quan es tracta d'estructures periòdiques amb dissipació. Per un costat, al considerar la propagació d'ones sonores en el plànol en un array periòdic de capes absorbents, s'observa una disminució anòmala de l'absorció i es combina amb un augment simultani de reflexió i transmissió en les freqüències de Bragg que contrasta amb la usual disminució de transmissió, característica dels sistemes conservatius a eixes freqüències. Per a un medi similar de capes, amb un reflector rígid darrere, les ones fora del pla incidint l'estructura des de un medi homogeni, augmentaran considerablement la interacció. En altres paraules, el retràs temporal de les ones sonores dins del sistema periòdic augmentarà significativament produint un augmen
Cebrecos Ruiz, A. (2015). Transmission, reflection and absorption in Sonic and Phononic Crystals [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/56463
TESIS
Premiado

We study elastic moduli of trabecular bone. Trabecular bone structure is very complex due to its randomness and spatial heterogeneity. To simplify the analysis one can choose to represent bone as having an idealized periodic structure. In this thesis we model bone as having a periodic prismatic structure, either two- or three-dimensional. More specifically, we are interested in predicting the apparent elastic moduli of such an idealized model of trabecular bone. We conduct our analysis using a finite element method (ANSYS). We investigate the effect of mesh size, the mismatch in moduli (elastic modulus of bone versus bone marrow), the size of "region of observation", the effects of bone structures geometries, and boundary conditions on the elastic moduli of the idealized models of trabecular bone. This research can give guidance in determining the sufficient size of bone samples used in experiments or computations so the effect of boundary conditions is minimized. These results are also applicable to other porous/cellular materials.

碩士
國立成功大學
機械工程學系
86
A solution procedure for studying the dynamic responses of a nouniform Timoshenko beam with general time-dependent boundaryconditions is develpoed by generalizing the method of Mindlin-Goodman and utilizing the exact solution of nonuniform Timoshenkobeam vibration given by Lee and Lin. A general change of dependentvariable with shifting functions are further explored. The orthogonality condition for the eigenfunctions of a nonuniformtimoshenko beam with elastic boundary conditions is also derived.Several limiting cases and their corresponding procedures are reveled.

In this work we consider the incompressbile Navier-Stokes equations from fluid mechanics in combination with two different types of boundary conditions. One problem that we consider is a free boundary problem. Here, the upper, elastic boundary part of a cylindric container, that contains a viscous fluid, is set in motion due to an interior force, induced by the velocity field of the fluid, and due to a given exterior force. In Chapter 2, we consider this problem formulated on the fixed, upper half space. Via partial Fourier transform we show the existence of solutions which belong to homogeneous Sobolev spaces. Then, we identify admissible spaces for the initial values. The second boundary condition models friction of a viscous fluid with the boundary of the domain. In Chapter 3, we show the existence of global, weak solutions that are strong solutions with respect to time in two dimensions. In the three-dimensional case, we show short time existence of strong solutions and global existence if the given data are small enough. Furthermore, strong-weak uniqueness is shown, as well as a connection of this boundary condition to the Dirichlet- and perfect slip boundary condition. In Chapter 4, we combine the above boundary conditions in order to quantify the elasticity of an upper, free boundary of a container, that is filled with a viscous fluid. We show the existence of weak solutions for this hybrid model.

碩士
國立臺灣科技大學
營建工程系
102
The main purpose of this thesis is to establish the equilibrium and compatibility equations for FGM rectangular plate subjected simple-support at both x side and arbitrary support at the other side , uniform elastic support on the bottom plate, by using the Levy-solution. The buckling equation obtained after giving the boundary condition of y side and analyze the critical load after giving the parameter of material property. Two kinds of boundary conditions are considered. One is to subjected simple-support at both x side with free end at both y side and another is simple-support at both x side with fixed end at both y side. It is assumed that the Poisson’s ratio of the plate remains constant and the Young’s modulus vary along the thickness direction. The research is concentrated to three kind of distribution of Young’s modulus, which are power-law (P-FGM), sigmoid function (S-FGM), and exponential function (E-FGM). Moreover, extending the research to FGM coated plate and FGM undercoated plate to complete this article. To prove the accuracy of analytical solution, the numerical solutions by MARC software of finite element method are obtained and compare with the analytical solution. Results show that the variation of Young's modulus distribution affects the buckling behaviors of the FGM plates seriously. When the plate resist buckling fixed end better than free end. Increase elastic support’s stiffness can Improve the buckling load.

碩士
國立臺灣科技大學
營建工程系
104
The main purpose of this article is utilizing Equivalent Homogeneous Beam Theory to analyze the buckling behavior of FGM rectangular plates with uniform elastic support under axial load. Using Equivalent Homogeneous Beam Theory to establish the relationship between material coefficient C11 to analyze the equivalent homogeneous results of FGM plates. The research is concentrated on three kinds of material distribution type which are power-law function (P-FGM), sigmoid function (S-FGM) and exponential function (E-FGM). Two kinds of boundary conditions are considered. One is simply-support at the opposite of x-axis, the others is simply-support at the x-axis with fixed end at the opposite of y axis. Moreover, extending the concept of equivalent homogeneous to FGM coated plates and FGM undercoated plates and calculated by finite element method using MARC program. To prove the accuracy of solution, compare the results with FGM plates and FGM theory value which was researched by Yu-Ting Cheng[32]. Discuss the behavior of buckling load under different kinds of parameters such as material index, stiffness of elastic support…etc. The result shows that buckling load will change seriously under same material index and Young’s modulus, equivalent homogeneous plates behave same as functionally graded material plates, increasing stiffness of elastic support could improve the buckling load of all structure and S-FGM coated plates is the best material to resist the buckling load under three kinds of material distribution and plate type.

High-frequency wave phenomena is observed in many physical settings, most notably in acoustics, electromagnetics, and elasticity. In all of these fields, numerical simulation and modeling of the forward propagation problem is important to the design and analysis of many systems; a few examples which rely on these computations are the development of metamaterial technologies and geophysical prospecting for natural resources. There are two modes of modeling the forward problem: the frequency domain and the time domain. As the title states, this work is concerned with the former regime. The difficulties of solving the high-frequency wave propagation problem accurately lies in the large number of degrees of freedom required. Conventional wisdom in the computational electromagnetics commmunity suggests that about 10 degrees of freedom per wavelength be used in each coordinate direction to resolve each oscillation. If K is the width of the domain in wavelengths, the number of unknowns N grows at least by O(K^2) for surface discretizations and O(K^3) for volume discretizations in 3D. The memory requirements and asymptotic complexity estimates of direct algorithms such as the multifrontal method are too costly for such problems. Thus, iterative solvers must be used. In this dissertation, I will present fast algorithms which, in conjunction with GMRES, allow the solution of the forward problem in O(N) or O(N log N) time.
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