Tesis sobre el tema "FEM discretization"

In this dissertation an approach is presented for the three-dimensional electrical resistivity tomography (ERT) using unstructured discretizations. The geoelectrical forward problem is solved by the finite element method using tetrahedral meshes with linear and quadratic shape functions. Unstructured meshes are suitable for modelling domains of arbitrary geometry (e.g., complicated topography). Furthermore, the best trade-off between accuracy and numerical effort can be achieved due to the capability of problem-adapted mesh refinement. Unstructured discretizations also allow the consideration of spatial extended finite electrodes. Due to a corresponding extension of the forward operator using the complete electrode model, known from medical impedance tomography, a study about the influence of such electrodes to geoelectrical measurements is given. Based on the forward operator, the so-called triple-grid-technique is developed to solve the geoelectrical inverse problem. Due to unstructured discretization, the ERT can be applied by using a resolution dependent parametrization on arbitrarily shaped two-dimensional and three-dimensional domains. A~Gauss-Newton method is used with inexact line search to fit the data within error bounds. A global regularization scheme is applied using special smoothness constraints. Furthermore, an advanced regularization scheme for the ERT is presented based on unstructured meshes, which is able to include a-priori information into the inversion and significantly improves the resulting ERT images. Structural information such as material interfaces known from other geophysical techniques are incorporated as allowed sharp resistivity contrasts. Model weighting functions can define individually the allowed deviation of the final resistivity model from given start or reference values. As a consequent further development the region concept is presented where the parameter domain is subdivided into lithological or geological regions with individual inversion and regularization parameters. All used techniques and concepts are part of the open source C++ library GIMLi, which has been developed during this thesis as an advanced tool for the method-independent solution of the inverse problem.

In this thesis a theory for large deformation of plates is presented. Herein aspects of the common 3D-theory for large deformation with the Kirchhoff hypothesis for reducing the dimension from 3D to 2D is combined. Even though the Kirchhoff assumption was developed for small strain and linear material laws, the deformation of thin plates made of isotropic non-linear material was investigated in a numerical experiment. Finally a heavily deformed shell without any change in thickness arises. This way of modeling leads to a two-dimensional strain tensor essentially depending on the first two fundamental forms of the deformed mid surface. Minimizing the resulting deformation energy one ends up with a nonlinear equation system defining the unknown displacement vector U. The aim of this thesis was to apply the incremental Newton technique with a conformal, C^1-continuous finite element discretization. For this the computation of the second derivative of the energy functional is the key difficulty and the most time consuming part of the algorithm. The practicability and fast convergence are demonstrated by different numerical experiments.

Cette thèse traite de la modélisation, de la discrétisation et du contrôle de forme des systèmes mécaniques flexibles dans le cadre des systèmes Port-Hamiltoniens (PHS). Les contributions sont triples. Tout d'abord, nous proposons des méthodologies généralisées pour la modélisation des systèmes mécaniques multidimensionnels, linéaires et non linéaires, en utilisant le principe de Hamilton généralisé et étendu, fournissant des représentations explicites et implicites des PHS. Ensuite, nous développons des techniques de discrétisation préservant la structure à travers des méthodes d'éléments finis mixtes (FEM), incluant des approches à deux, trois et quatre champs adaptées aux systèmes PHS et PH-DAE linéaires et non linéaires. Enfin, nous introduisons un contrôleur en dimension finie basé sur des approximations d'ordre faible de systèmes PHS linéaires discrétisés à grande échelle. Ce contrôleur garantit la convergence vers les formes optimales, offrant la meilleure approximation des configurations désirées, tout en assurant la stabilité asymptotique du système discrétisé à grande échelle
This thesis addresses the modeling, discretization, and shape control of flexible mechanical systems within the Port-Hamiltonian Systems (PHS) framework. The contributions are threefold. First, we propose generalized methodologies for modeling both linear and nonlinear multidimensional mechanical systems using the generalized extended Hamilton's principle, providing explicit and implicit PHS representations. Second, we develop structure-preserving discretization techniques via mixed Finite Element Methods (FEM), including two, three, and four-field approaches tailored to linear and nonlinear PHS and PH-DAE systems. Finally, we introduce a finite-dimensional controller based on low-order approximations of large-scale discretized linear PHS. This controller ensures convergence to the optimal shapes, offering the best approximation to the desired configurations, while guaranteeing asymptotic stability of the large-scale discretized system

Baigiamajame magistro darbe nagrinėjami struktūrų modeliavimo, diskretizavimo ir optimizavimo uždaviniai, jų sprendimo būdai ir algoritmai. Pasiūlyta originali strypinių struktūrų optimizavimo ir diskretizavimo technika, kurioje naudojami vaizdų algebros metodai ir baigtinių elementų metodo (toliau – BEM) programiniai paketai. Atlikta BEM programinių paketų apžvalga, parinkti tinkamiausi paketai darbo tikslams realizuoti ir rezultatams verifikuoti. Išanalizuoti skaitmeninių vaizdų skeletų išgavimo metodai. Pasiūlytas originalus vaizdo skeleto apdorojimo algoritmas skerspjūvio charakteristikoms nustatyti. Sudarytas ir programiškai realizuotas strypinių struktūrų optimizavimo-diskretizavimo algoritmas. Realizuota programinė sistema susideda iš vaizdų apdorojimo ir duomenų paruošimo dalies (MATLAB kalba) bei BEM skaičiavimų dalies (ANSYS vidine programavimo kalba APDL). Skaičiavimo rezultatai atvaizduojami ir verifikuojami STAAD.Pro paketu. Diskretizavimo metu strypinės struktūros mazgų vieta randama vaizdo skeleto segmentų sankirtos taškuose, o segmentų skerspjūvių plotai randami atkarpų, jungiančių šiuos mazgus, vidurio taškuose. Kai struktūros mazgų padėtis fiksuota arba mazgai yra per arti vienas kito atliekamas mazgų padėties koregavimas. Darbe atlikti testiniai skaičiavimai, rezultatų analizė ir verifikavimas, suformuluotos išvados.
In the master thesis the problems of structure modeling, discretization-optimization and their solution methods and algorithms are analyzed. The original technique for optimization and discretization of beam structures has been suggested; The packages of image algebra methods and of the finite element methods were employed for that. Several packages of finite element method have been reviewed and the most suitable packages for the current problems were identified. The methods for obtaining skeletons of digital images were explored. The algorithms for optimization and discretization of beam structures has been suggested and coded. The program created consents of the part for image processing and input data preparing, and the part for image the finite element via method. The results obtained are represented and verified by STAAD.Pro package. During the discretization, the positions of structure nodes are obtained in the intersection of skeleton segments. The segments' cross-section areas are obtained in the middle-points between two adjacent nodes. The positions of nodes may be corrected if the nodes close to each other. The test-calculation, analysis of results and verification are presented and conclusions are drawn.

Shallow water models of geophysical flows must be adapted to geometric characteristics in the presence of a general bottom topography with non-negligible slopes and curvatures, such as a mountain landscape. In this thesis we derive an intrinsic shallow water model starting from the Navier-Stokes equations defined on a local reference frame anchored on the bottom surface. The resulting equations are characterized by non-autonomous flux functions and source terms embodying only geometric information. We show that the proposed model is rotational invariant, admits a conserved energy, is well-balanced, and it is formally a second order approximation of the Navier-Stokes equations with respect to a geometry-based order parameter. We then derive numerical discretization schemes compatibles with the intrinsic setting of the formulation, starting from studying a first order upwind Godunov Finite Volume scheme intrinsically defined on the bottom surface. We analyze convergence properties of the resulting scheme both theoretically and numerically. Simulations on several synthetic test cases are used to validate the theoretical results as well as more experimental properties of the solver. The results show the importance of taking into full consideration the bottom geometry even for relatively mild and slowly varying curvatures. The low-order discretization method is subsequently extended to the Discontinuous Galerkin framework. We implement a linear version of the DG scheme defined intrinsically on the surface and we start from the resolution of the scalar transport equation. We test the scheme for convergence and then we move towards the intrinsic shallow water model. Simulations on synthetic test cases are reported and the improvement with respect to the first order finite volume discretization is clearly visible. Finally, we consider a finite element method for advection-diffusion-reaction equations on surfaces. Unlike many previous techniques, this approach is based on the geometrically intrinsic formulation and the resulting finite element method is fully intrinsic to the surface. In the last part of this work, we lay out in detail the formulation and compare it to a well-established finite element scheme for surface PDEs. We then evaluate the method for several steady and transient problems involving both diffusion and advection-dominated regime. The experimental results show the theoretically expected convergence rates and good performance of the established finite element methods.

Dans cette thèse, une nouvelle approche est présentée, combinant la méthode des éléments finis étendus (X-FEM) et un raffinement adaptatif et automatique de maillage (AMR). La méthode X-FEM, développée durant les deux dernières par une importante communauté, a prouvé son efficacité pour gérer l'évolution de discontinuités dans de nombreux problèmes de mécanique de la rupture. Comme cette méthode permet de décrire la fissure indépendamment du maillage de la structure, un raffinement hiérarchique relativement simple peut être appliqué sur ce dernier pour adapter localement l'échelle de discrétisation à celle des phénomènes physiques mis en jeux. Cela permet d'obtenir une description précise de quantités physiques d'intérêt dans une zone limitée autour du front de fissure et réduire considérablement le coût numérique, particulièrement lorsque le trajet de propagation n'est pas connu a priori. Dans ce travail, on propose une stratégie pour combiner X-FEM et AMR : les relations de compatibilité cinématique et les méthodes de projection nécessaires pour les matériaux dépendant de l'histoire de chargement doivent inclure correctement le modèle d'enrichissement. L'implémentation de cette approche combinant X-FEM et AMR, dans le code éléments finis industriel Cast3M, est présentée en détails. En particulier, une nouvelle méthode de projection spécifique à ce contexte est proposée. Des applications numériques et une étude expérimentale de propagation par fatigue en plasticité confinée ont été réalisées pour démontrer la précision, la robustesse et l'efficacité de cette méthode
To guarantee the high level of safety of industrial components under fatigue cycles it is essential to be able to predict the initiation and growth of cracks during their entire lifetime. However the numerical cost of a propagation simulation on engineer-sized problems with non-linear behavior may be prohibitive, with the classical techniques. Here, a new approach combining the eXtended Finite Element Method (X-FEM) and automatic Adaptive Mesh Refinement (AMR) is presented taking advantage of both methods. The X-FEM, developed over the past two decades by a large community, have proven its efficiency to handle evolving discontinuities in a variety of fracture analysis. Since this method enables to describe the crack and its propagation independently of the mesh of the structure, a simple hierarchical mesh refinement procedure can be applied. Automatic adaptive re-meshing is a valuable method for elastic-plastic crack propagation analysis since it permits a locally fine mesh and then an accurate description of physical quantities in a limited area around the crack front. This is particularly important when local fracture criteria are concerned. Moreover local refinement saves computational effort, particularly when the propagation path is not a priori known. In the present work, it is shown that both methods combine with minimal effort: the kinematic continuity relations and the field transfer process, needed for history-dependent material, must include in a proper way the enrichment of the model. If this requirement is not fulfilled, numerical error may be introduced. Implementation of this combined X-FEM/AMR approach in the finit elements code Cast3M is presented in detail. In particular, an innovative field transfer strategy is proposed in 2D and 3D. Numerical applications of crack propagation in elastic-plastic media demonstrate accuracy, robustness and efficiency of the technique. Moreover, an experimental study has been conducted on a example propagation with notable impact of confined plasticity. This study provides experimental data to compare with the numerical results obtained with the developed method. This validates our modelization choices. It also is the opportunity to test the developed method robustness on a realistic case of utilization. This study showed the interest of the proposed modelization taking into account plasticity induced crack closure during the fatigue propagation

Les algorithmes numériques basés sur la méthode des éléments finis seront spécialisés dans l’analyse, la conception et l’optimisation de capteurs et d’actionneurs (S-A), ainsi que dans leur application aux structures intelligentes. Les S-A basés sur des actifs tangibles peuvent coupler plusieurs domaines, tels que les domaines mécanique, électrique, magnétique et thermique. Ils sont utilisés dans de nombreuses applications, notamment dans les structures intelligentes, la surveillance des dommages ou l’aérodynamique. Malgré l’expérience considérable de ces études, les étapes abordées consistent d’abord à développer une formulation thermodynamiquement cohérente à l’échelle macro pour introduire des modèles de plasticité; deuxièmement, fournir les outils permettant de prendre en compte les hétérogénéités des modèles multi-échelles pour les matériaux intelligents. L’objectif principal est la mise au point d’un code informatique de recherche permettant de simuler et d’étudier les performances, non seulement des S-A eux-mêmes, mais également des structures intelligentes dans lesquelles ces S-A seront montés
Numerical algorithms based on the Finite Element Method will be specialized for Analysis, Design, and Optimization of Sensors and Actuators (S-A) and their Application to Smart Structures. The S-A based on tangible assets can couple several fields, such as mechanical, electrical, magnetic, and thermal. They are used in many applications, particularly in smart structures, damage monitoring, or aerodynamics. Despite the considerable experience in these studies, the steps addressed are first to develop a thermodynamically consistent formulation for macro-scale to introduce plasticity models; second, to provide the tools to take into account the heterogeneities of multi-scale models for smart materials. The main objective is the development of a research computer code to simulate and study the performance, not only of the S-A themselves but also of the smart structures in which these S-A will be mounted

This diploma thesis deals with problem of design and calculation of membrane structure of stadium roof. This is a complex engineering problem, which includes many partial problems: finding of initial form of membrane, statically and architecturally suitable arrangement of catenaries, economical solution of boundary conditions (foundations). All components affect each other and cannot be dealt without mutual coordination. It always greatly depends on the experience and intuition of engineer who design such structure. Task which cannot be resolved according to the theory of the first order. Equilibrium forces on the deformed structure, which in many projected structures gives satisfactory results, did not correspond to reality. It is therefore necessary to consider equilibrium of forces on the deformed structure according to the theory of large deformations. Diploma thesis was entered with regard to the intention of the companies Ing. Software Dlubal s.r.o. and FEM consulting s.r.o., working together to develop software RFEM. These companies plan to complement this program system with a module MEMBRANE for searching of initial shapes of membrane structures. This work is a contribution to the creation of this module.

Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.

In this dissertation an approach is presented for the three-dimensional electrical resistivity tomography (ERT) using unstructured discretizations. The geoelectrical forward problem is solved by the finite element method using tetrahedral meshes with linear and quadratic shape functions. Unstructured meshes are suitable for modelling domains of arbitrary geometry (e.g., complicated topography). Furthermore, the best trade-off between accuracy and numerical effort can be achieved due to the capability of problem-adapted mesh refinement. Unstructured discretizations also allow the consideration of spatial extended finite electrodes. Due to a corresponding extension of the forward operator using the complete electrode model, known from medical impedance tomography, a study about the influence of such electrodes to geoelectrical measurements is given. Based on the forward operator, the so-called triple-grid-technique is developed to solve the geoelectrical inverse problem. Due to unstructured discretization, the ERT can be applied by using a resolution dependent parametrization on arbitrarily shaped two-dimensional and three-dimensional domains. A~Gauss-Newton method is used with inexact line search to fit the data within error bounds. A global regularization scheme is applied using special smoothness constraints. Furthermore, an advanced regularization scheme for the ERT is presented based on unstructured meshes, which is able to include a-priori information into the inversion and significantly improves the resulting ERT images. Structural information such as material interfaces known from other geophysical techniques are incorporated as allowed sharp resistivity contrasts. Model weighting functions can define individually the allowed deviation of the final resistivity model from given start or reference values. As a consequent further development the region concept is presented where the parameter domain is subdivided into lithological or geological regions with individual inversion and regularization parameters. All used techniques and concepts are part of the open source C++ library GIMLi, which has been developed during this thesis as an advanced tool for the method-independent solution of the inverse problem.

The goal of the current study was to develop a computational framework for modelling the coupled fluid-structure interaction problem of squeeze films often encountered in MEMS devices. Vibratory MEMS devices such as gyroscopes, RF switches, and 2D resonators often have a thin plate like structure vibrating transversely to a Fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping to the vibrating plate. For accurate modelling of the squeeze film effect, one must account for the coupled fluid-structure interaction. The majority of prior works attempting to address the coupled problem either approximate the mode shape of the vibrating plate or resort to cumbersome iterative solution strategies to address the problem in an indirect way. In the current work, we discuss the development of a fully coupled finite element based numerical scheme to solve the 2D Reynolds equation coupled with the 3D plate elasticity equation in a single step. The squeeze film solver so developed has been implemented into a commercial FEA package NISA as part of its Micro-Systems module. Further, extending on a prior analytical work, the effect of variable ow boundaries for an all sides clamped plate on squeeze film parameters has been thoroughly investigated. The developed FEM based numerical scheme has been used to validate the results of the prior analytical study. The developed numerical scheme models the 2D Reynolds equation thus limiting the model to account for the effects of the fluid volume strictly confined between the structure and the substrate. To study the effect of surrounding fluid volume ANSYS FLOTRAN simulations have been performed by numerically solving the full 3D Navier Stokes equation in the extended fluid domain for the different flow boundary scenarios. Cut-off frequencies are established beyond which one can consider a 2D fluid domain without considerable loss of accuracy. First, a displacement based finite element formulation is presented for the 2D Reynolds equation coupled with the 3D elasticity equation. Both lower order 8 node and higher order 27 node 3D elements are developed. Only a single type of 3D element is used for modelling along with a 2D fluid layer represented by the \wet" face of the 3D structural domain. The results from our numerical model are compared with experimental data from literature for a MEMS cantilever. The results from the 27 node displacement based elements show good agreement with published experimental data. The results from the lower order 8 node displacement based elements however show huge errors even for relatively fine meshes due to locking issues in modelling high aspect ratio structures. This limits the implementation of the displacement based solver in commercial FE packages where the available mesh generators are generally restricted to lower order 3D elements. In order to overcome the limitations faced by lower order elements (primarily locking issues) in modelling high aspect ratio MEMS geometries, a coupled hybrid formulation is developed next. A thorough performance study is presented considering both the hybrid and displacement based elements for lower order 8 node and higher order 27 node ele- ments. The optimal element choice for modelling squeeze film geometries is determined based on the comparative studies. The effect of element aspect ratio for hybrid and displacement based elements are studied and the superiority of hybrid formulation over displacement based formulations is established for lower order 8 node elements. The coupled hybrid nite element formulation developed for lower order elements is implemented in the commercial FEA package NISA. The implementation scheme to integrate the developed coupled hybrid 8 node squeeze film solver into the commercial FEA package is discussed. The pre-integration analysis and subsequent requirement gaps are first investigated. Based on the gap analysis, certain GUI modifications are undertaken and parser programs are developed to re-format data according to NISA input requirements. Certain special features are included in the package to aid in post processing data analysis by MEMS designers such as \frequency sweep" and \node of interest" selection. As a case study for validation, we also present the modelling of a MEMS cantilever and show that the simulation results from our software are in good agreement with experimental data reported in the literature. Finally as a case study, an extension of a prior analytical work, which studies the effect of varying flow boundaries on squeeze film parameters, is discussed. Explanations are provided for the findings reported in the prior analytical work. The concept of using variation in flow boundaries as a frequency tuning tool is introduced. The analytical results are validated with the coupled numerical scheme discussed before, by considering imposed mode shape for an all sides clamped plate as prescribed displacement to the fluid domain. The simulated results are used to study the intricacies in squeeze film damping and stiffness variations with respect to spatial changes in the fluid flow boundary conditions. In particular, it has been shown that the boundary venting conditions can be used effectively to tune the dynamic response of a micromechanical structure over a fairly large range of frequencies and somewhat smaller range of squeeze film damping. Next, the effect of the surrounding fluid volume for various venting conditions is studied. ANSYS FLOTRAN is used to solve for the full 3D Navier Stokes equation over the extended fluid domain. Results from the extended domain study are used to determine cut-off frequencies beyond which one need not resort to an extended mesh study, and yet be within 5% accuracy of the full extended mesh model.

The goal of the current study was to develop a computational framework for modelling the coupled fluid-structure interaction problem of squeeze films often encountered in MEMS devices. Vibratory MEMS devices such as gyroscopes, RF switches, and 2D resonators often have a thin plate like structure vibrating transversely to a Fixed substrate, and are generally not perfectly vacuum packed. This results in a thin air film being trapped between the vibrating plate and the fixed substrate which behaves like a squeeze film offering both stiffness and damping to the vibrating plate. For accurate modelling of the squeeze film effect, one must account for the coupled fluid-structure interaction. The majority of prior works attempting to address the coupled problem either approximate the mode shape of the vibrating plate or resort to cumbersome iterative solution strategies to address the problem in an indirect way. In the current work, we discuss the development of a fully coupled finite element based numerical scheme to solve the 2D Reynolds equation coupled with the 3D plate elasticity equation in a single step. The squeeze film solver so developed has been implemented into a commercial FEA package NISA as part of its Micro-Systems module. Further, extending on a prior analytical work, the effect of variable ow boundaries for an all sides clamped plate on squeeze film parameters has been thoroughly investigated. The developed FEM based numerical scheme has been used to validate the results of the prior analytical study. The developed numerical scheme models the 2D Reynolds equation thus limiting the model to account for the effects of the fluid volume strictly confined between the structure and the substrate. To study the effect of surrounding fluid volume ANSYS FLOTRAN simulations have been performed by numerically solving the full 3D Navier Stokes equation in the extended fluid domain for the different flow boundary scenarios. Cut-off frequencies are established beyond which one can consider a 2D fluid domain without considerable loss of accuracy. First, a displacement based finite element formulation is presented for the 2D Reynolds equation coupled with the 3D elasticity equation. Both lower order 8 node and higher order 27 node 3D elements are developed. Only a single type of 3D element is used for modelling along with a 2D fluid layer represented by the \wet" face of the 3D structural domain. The results from our numerical model are compared with experimental data from literature for a MEMS cantilever. The results from the 27 node displacement based elements show good agreement with published experimental data. The results from the lower order 8 node displacement based elements however show huge errors even for relatively fine meshes due to locking issues in modelling high aspect ratio structures. This limits the implementation of the displacement based solver in commercial FE packages where the available mesh generators are generally restricted to lower order 3D elements. In order to overcome the limitations faced by lower order elements (primarily locking issues) in modelling high aspect ratio MEMS geometries, a coupled hybrid formulation is developed next. A thorough performance study is presented considering both the hybrid and displacement based elements for lower order 8 node and higher order 27 node ele- ments. The optimal element choice for modelling squeeze film geometries is determined based on the comparative studies. The effect of element aspect ratio for hybrid and displacement based elements are studied and the superiority of hybrid formulation over displacement based formulations is established for lower order 8 node elements. The coupled hybrid nite element formulation developed for lower order elements is implemented in the commercial FEA package NISA. The implementation scheme to integrate the developed coupled hybrid 8 node squeeze film solver into the commercial FEA package is discussed. The pre-integration analysis and subsequent requirement gaps are first investigated. Based on the gap analysis, certain GUI modifications are undertaken and parser programs are developed to re-format data according to NISA input requirements. Certain special features are included in the package to aid in post processing data analysis by MEMS designers such as \frequency sweep" and \node of interest" selection. As a case study for validation, we also present the modelling of a MEMS cantilever and show that the simulation results from our software are in good agreement with experimental data reported in the literature. Finally as a case study, an extension of a prior analytical work, which studies the effect of varying flow boundaries on squeeze film parameters, is discussed. Explanations are provided for the findings reported in the prior analytical work. The concept of using variation in flow boundaries as a frequency tuning tool is introduced. The analytical results are validated with the coupled numerical scheme discussed before, by considering imposed mode shape for an all sides clamped plate as prescribed displacement to the fluid domain. The simulated results are used to study the intricacies in squeeze film damping and stiffness variations with respect to spatial changes in the fluid flow boundary conditions. In particular, it has been shown that the boundary venting conditions can be used effectively to tune the dynamic response of a micromechanical structure over a fairly large range of frequencies and somewhat smaller range of squeeze film damping. Next, the effect of the surrounding fluid volume for various venting conditions is studied. ANSYS FLOTRAN is used to solve for the full 3D Navier Stokes equation over the extended fluid domain. Results from the extended domain study are used to determine cut-off frequencies beyond which one need not resort to an extended mesh study, and yet be within 5% accuracy of the full extended mesh model.

Dissertação de Mestrado Integrado em Engenharia Electrotécnica e de Computadores apresentada à Faculdade de Ciências e Tecnologia
Esta dissertação apresenta uma estratégia de controlo preditivo aplicada a um gerador de indução duplamente alimentado (DFIG) ligado a uma rede dc, adequada para geração distribuída e em ambiente de micro-rede. A topologia de ligação da DFIG à rede dc é obtida através da substituição de um dos inversores de fonte de tensão por um retificador a díodos. Contudo a inclusão do retificador a díodos origina uma ondulação no binário, caracterizada por uma componente que oscila a uma frequência seis vezes superior à frequência do estator. Esta componente harmónica tem efeitos negativos sobre os componentes mecânicos do sistema, e como tal, são necessários esforços para eliminar essas oscilações no binário.As estratégias de controlo clássicas, baseadas na orientação de campo, abordam esta questão através da inclusão de controladores ressonantes, ou através da decomposição e supressão desta componente harmónica em referenciais múltiplos. No entanto, estes métodos apresentam desvantagens inerentes, tais como: grande esforço de sintonização, resposta dinâmica inferior e dificuldade de incluir restrições no sistema. Além disso, a existência de múltiplas malhas de controlo dita o uso de uma separação elevada nas larguras de banda do sistema de controlo e que a estabilidade do sistema está fortemente dependente da largura de banda da malha interna.A utilização de controlo preditivo baseado em modelos (MPC) no sistema de controlo proposto, consegue evitar todas as dificuldades associadas ao controlo vetorial, e é capaz de praticamente eliminar as oscilações de baixa frequência presentes no binário. Atendendo que as estratégias de controlo preditivo são baseadas em modelos discretos, o seu desempenho é fortemente dependente da precisão dos parâmetros do modelo, assim como da correcta estimação destes parâmetros. Por outro lado, a complexidade do modelo discreto deve também ser minimizada, por forma a tornar o algoritmo viável para uso prático. Como tal, também é fornecida uma comparação do desempenho do sistema, quando as diferentes técnicas de discretização são usadas, designadamente o método de Euler e a expansão em série de Taylor.
This work presents a predictive control strategy applied to a doubly-fed induction generator (DFIG) connected to a dc microgrid, suitable for distributed generation purposes and microgrid environment. The topology of connecting the DFIG to the dc grid consists in the replacement of one voltage source inverter by a diode rectifier. However, the inclusion of the diode rectifier gives rise to a large torque ripple, characterized by a component oscillating at six times the stator frequency. This harmonic component has negative effects on the mechanical components of the drive system and as such, efforts are needed to eliminate those torque oscillations.Classical control strategies, based on field orientation try to address this issue by the inclusion of resonant controllers, or by decomposing and suppressing this harmonic component in multiple reference frames. However, those methods have inherent disadvantages, such as: great tuning effort, inferior dynamic response and difficulty to include restrictions in the system. Furthermore, the existence of multiple control loops dictates that separate bandwidth for them must be ensured, as the stability of the system is closely related to the bandwidth of the inner loop. The use of model predictive control (MPC) in the proposed control system system avoids all the difficulties associated with vector control and is able to practically fully eliminate the low-frequency torque oscillations.Attending that predictive control strategies are based in discrete models, their performance is heavily dependent on the model parameters accuracy and of a correct parameter estimation. On the other hand, the complexity of the discrete model must also be minimized, to make the algorithm feasible for practical use. As such, a comparison is also provided on the steady-state and dynamic performance of the system, when the forward Euler and Taylor series expansion discretization methods are used.

Im Bereich der industriellen Metallurgie und Kristallzüchtung treten bei zahlreichen Anwendungen, wo magnetische Wechselfelder zur induktiven Beeinflussung von leitfähigen Werkstoffen eingesetzt werden, auch Strömungen mit freier Oberfläche auf. Das Anwendungsspektrum reicht dabei vom einfachen Aufschmelzen eines Metalls in einem offenen Tiegel bis hin zur vollständigen Levitation. Auch der sogenannte RGS-Prozess, ein substratbasiertes Kristallisationsverfahren zur Herstellung siliziumbasierter Dünnschichtmaterialien, ist dafür ein Beispiel. Um bei solchen Prozessen die Interaktion von Magnetfeld und Strömung zu untersuchen, ist die numerische Simulationen ein wertvolles Hilfsmittel. Für beliebige dreidimensionale Probleme werden entsprechende Berechnungen bisher durch eine externe Kopplung kommerzieller Programme realisiert, die für Magnetfeld und Strömung jeweils unterschiedliche numerische Techniken nutzen. Diese Vorgehensweise ist jedoch im Allgemeinen mit unnötigem Rechenaufwand verbunden. In dieser Arbeit wird ein neu entwickelter Methodenapparat auf Basis der FVM vorgestellt, mit welchem sich diese Art von Berechnungen effizient durchführen lassen. Mit der Implementierung dieser Methoden in foam-extend, einer erweiterten Version der quelloffenen Software OpenFOAM, ist daraus ein leistungsfähiges Werkzeug in Form einer freien Simulationsplattform entstanden, welches sich durch einen modularen Aufbau leicht erweitern lässt. Mit dieser Plattform wurden in foam-extend auch erstmalig dreidimensionale Induktionsprozesse im Frequenzraum gelöst.