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1	Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements Lai, Zhi Cheng 05 May 2008 (has links) The micro-electromechanical systems (MEMS) industry has grown incredibly fast over the past few years, due to the irresistible character and properties of MEMS. MEMS devices have been widely used in various fields such as aerospace, microelectronics, and the automobile industry. Increasing prominence is given to the development and research of MEMS; this is largely driven by the market requirements. Multi-physics coupled fields are often present in MEMS. This makes the modelling and analysis o such devices difficult and sometimes costly. The coupling between electrostatic and mechanical fields in MEMS is one of the most common and fundamental phenomena in MEMS; it is this configuration that is studied in this thesis. The following issues are addressed: 1. Due to the complexity in the structural geometry, as well as the difficulty to analyze the behaviour in the presence of coupled fields, simple analytical solutions are normally not available for MEMS. The finite element method (FEM) is therefore used to model electrostaticmechanical coupled MEMS. In this thesis, this avenue is followed. 2. In order to capture the configuration of the system accurately, with relatively little computational effort, a geometric non-linear mixed assumed stress element is developed and used in the FE analyses. It is shown that the developed geometrically non-linear mixed assumed stress element can produce an accuracy level comparable to that of the Q8 element, while the number of the degrees of freedom is that of the Q4 element. 3. Selected algorithms for solving highly non-linear coupled systems are evaluated. It is concluded that the simple, accurate and quadratic convergent Newton-Raphson algorithm remains best. To reduce the single most frustrating disadvantage of the Newton method, namely the computational cost of constructing the gradients, analytical gradients are evaluated and implemented. It is shown the CPU time is significantly reduced when the analytical gradients are used. 4. Finally, a practical engineering MEMS problem is studied. The developed geometric nonlinear mixed element is used to model the structural part of a fixed-fixed beam that experiences large axial stress due to an applied electrostatic force. The Newton method with analytical gradients is used to solve this geometrically nonlinear coupled MEMS problem. / Dissertation (MEng (Mechanical))--University of Pretoria, 2007. / Mechanical and Aeronautical Engineering / unrestricted Coupled fields Assumed stress Geometrically nonlinear Finite element Newton’s method Mems Analytical gradient UCTD
2	Modélisation quantochimiques des forces de dispersion de London par la méthode des phases aléatoires (RPA) : développements méthodologiques / Quantum chemical studies of London dispersion forces by the random phase approximation (RPA) : methodological developments. Mussard, Bastien 13 December 2013 (has links) Dans cette thèse sont montrés des développements de l'approximation de la phase aléatoire (RPA) dans le contexte de théories à séparation de portée. On présente des travaux sur le formalisme de la RPA en général, et en particulier sur le formalisme "matrice diélectrique" qui est exploré de manière systématique. On montre un résumé d'un travail sur les équations RPA dans le contexte d'orbitales localisées, notamment des développements des orbitales virtuelles localisées que sont les "orbitales oscillantes projetées" (POO). Un programme a été écrit pour calculer des fonctions telles que le trou de d'échange, la fonction de réponse, etc... sur des grilles de l'espace réel (grilles parallélépipédiques ou de type "DFT"). On montre certaines de ces visualisations. Dans l'espace réel, on expose une adaptation de l'approximation du dénominateur effectif (EED), développée originellement dans l'espace réciproque en physique du solide. Également, les gradients analytiques des énergies de corrélation RPA dans le contexte de la séparation de portée sont dérivés. Le formalisme développé ici à l'aide d'un lagrangien permet une dérivation tout-en-un des termes courte- et longue-portée qui émergent dans les expressions du gradient, et qui montrent un parallèle intéressant. Des applications sont montrées, telles que des optimisations de géométries aux niveaux RSH-dRPA-I et RSH-SOSEX d'un ensemble de 16 petites molécules, ou encore le calcul et la visualisation des densités corrélées au niveau RSH-dRPA-I / In this thesis are shown developments in the random phase approximation (RPA) in the context of range-separated theories. We present advances in the formalism of the RPA in general, and particularly in the "dielectric matrix" formulation of RPA, which is explored in details. We show a summary of a work on the RPA equations with localized orbitals, especially developments of the virtual localized orbitals that are the "projected oscillatory orbitals" (POO). A program has been written to calculate functions such as the exchange hole, the response function, etc... on real space grid (parallelepipedic or of the "DFT" type) ; some of those visualizations are shown here. In the real space, we offer an adaptation of the effective energy denominator approximation (EED), originally developed in the reciprocal space in solid physics. The analytical gradients of the RPA correlation energies in the context of range separation has been derived. The formalism developed here with a Lagrangian allows an all-in-one derivation of the short- and long-range terms that emerge in the expressions of the gradient. These terms show interesting parallels. Geometry optimizations at the RSH-dRPA-I and RSH-SOSEX levels on a set of 16 molecules are shown, as well as calculations and visualizations of correlated densities at the RSH-dRPA-I level Énergie de corrélation Interaction de Van der Waals Force de dispersion de London DFT Séparation de portée RSH Approximation de la phase aléatoire RPA Connexion adiabatique Matrice diélectrique Formule de plasmon Équation de Riccati Orbitale oscillante projetée POO Développement multipolaire Grille de l'espace réel Dénominateur effectif EED Règles de somme Gradient analytique Lagrangien Coupled-perturbed Densité corrélée Optimisation de géométrie Correlation energy Van der Waals interaction London dispersion force Density functional theory DFT Range separation RSH Random phase approximation RPA Adiabatic connection Dielectric matrix Plasmon formula Riccati equation Projected oscillatory orbital POO Multipolar expansion Real space grid Effective energy denominator EED Sum-rules Analytical gradient Lagrangian Coupled-perturbed Correlated densities Geometry optimization 541.28

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Finite element analysis of electrostatic coupled systems using geometrically nonlinear mixed assumed stress finite elements

Modélisation quantochimiques des forces de dispersion de London par la méthode des phases aléatoires (RPA) : développements méthodologiques / Quantum chemical studies of London dispersion forces by the random phase approximation (RPA) : methodological developments.