O trabalho aborda o estudo e o desenvolvimento de um interferômetro sensor de alta tensão, baseado em célula Pockels (modulador eletro-óptico) na topologia reflexiva (\"double pass\") e que é parte integrante de um Transformador de Potencial Óptico (TPO), que utiliza sistema interferométrico de luz branca (WLI-White Light Interferometry), que está sendo desenvolvido pelo grupo do Laboratório de Sensores Ópticos (LSO) do PEA-EPUSP, e é capaz de medir diretamente tensões presentes em sistema elétrico de potência (SEP) classe 69kVRMS. Para desenvolver o tema proposto foi feita uma revisão da literatura baseada em livros, artigos e teses para identificar topologias em moduladores eletro-ópticos transmissiva (\"single pass\") e reflexiva (\"double pass\") para definir o tipo de modulador mais adequado para a aplicação em questão. A partir dos estudos e implementações realizadas, verificou-se um enorme potencial para o desenvolvimento e aplicação da topologia \"double pass\" no sensor interferométrico da célula de alta tensão do TPO. A topologia mostrou-se vantajosa em relação aos protótipos dos TPOs desenvolvidos anteriormente, a partir de características tais como: a facilidade de recurso de alinhamento do feixe de luz, construção e reprodução relacionados ao cristal eletro-óptico, diminuição do número de componentes ópticos volumétricos e aumento da rigidez dielétrica da célula sensora. Simulações computacionais foram realizadas mediante a aplicação do método dos elementos finitos (MEF) que contribuíram para o auxílio do projeto da célula sensora, particularmente, para estimativa do valor da voltagem de meia onda, V?, parâmetro importante para o projeto do TPO. Um protótipo do TPO com célula sensora de alta tensão reflexiva foi implementado e testado no laboratório de alta tensão do IEEUSP a partir de ensaios com tensões nominais de 69kVrms a 60Hz e máxima de 140kVrms a 60 Hz. Como resultado deste trabalho, amplia-se o conhecimento e domínio das técnicas de construção de interferômetros sensores de alta tensão na topologia reflexiva aplicadas a TPOs. / This work describes the study and development of a high-voltage interferometer sensor based on Pockels cell (electro-optical modulator) in the reflective topology (double pass), which is part of an optical potential transformer (OPT) using a white light interferometry system (WLI) being developed by the Optical Sensors Laboratory (LSO) group from PEA-EPUSP, which is able to directly measure power electrical system (PES) voltages for the 69kVrms class. To develop the work, a bibliographic review was made on books, papers and theses in order to identify electro-optical modulators related to transmissive (single pass) and reflective (double pass) topologies aiming at defining the most appropriate modulator type for the present application. From the studies and implementations performed, it was realized that there is a huge potential for the development and application of \'double pass\' topology in the OPT high-voltage interferometric sensor. This topology showed to be advantageous compared to previously developed OPT prototypes for characteristics such as: ease of beam alignment feature, construction and reproduction related to the electro optical crystals, decrease of volumetric optical components number and increase of the sensor cell dielectric strength. Computer simulations were performed by applying the Finite Element Method (FEM) that contributed to the sensor cell design, particularly in estimating the half-wave voltage value, V?. The OPT with the reflective high-voltage sensing cell was implemented and tested at the high voltage laboratory of IEE-USP for the 69kVrms at 60Hz nominal voltage and the 140kVrms at 60Hz maximum voltage. As a result of this work, nationwide expertise over the techniques of construction of high-voltage interferometer sensors in reflective topology applied to OPTs was achieved and knowledge was broadened.

When simulating mechanical systems the flexibility of the components often has to be taken into account. This is particularly important for simulations when high detailed information is demanded, e.g. to calculate stresses. To this end the Finite Element Method (FEM) is often used. However the models can become very large, containing millions of degrees of freedom. Solving large linear systems are computationally demanding. Therefore ways of reducing the problem is often sought. These reduction does, however, remove much of the details that was to be investigated. In this thesis this problem is addressed by creating a reduction scheme, using Proper Orthogonal Decomposition (POD), that significantly reduces a problem but still captures much of the details. A novel method for enriching regular POD-based model reduction methods with hierarchically determined enrichment POD-modes is developed. The method is proposed and validated in a FEM application towards dynamical simulation. The enriched method is compared against a regular POD reduction technique. An numerical study is made of a model example of linear elasticity in a gearwheel. The numerical study suggests that the error of displacements is around ten times smaller, on average, when using the enriched basis compared to a reference basis of equal dimensionality consisting of only regular POD modes. Also it is shown that local quantities as the von Mises stress in a gearwheel tooth is preserved much better using the enriched basis. An a posteriori error estimate is proposed and proved for the static case, showing that the error is bound. / När man simulerar mekaniska system så måste man ofta ta hänsyn till de ingående komponenternas flexibilitet. Detta är särskilt viktigt då man gör simuleringar med krav på hög detaljkännedom, såsom mätningar av spänningar i kugghjul etc. Till detta ändamål används ofta en Finit Element Metod (FEM). Dock kan modellerna ofta bli väldigt stora, med över en miljon frihetsgrader. Att lösa linjära system av den storleken är beräkningsmässigt krävande. Därför är det naturligt att försöka reducera problemen. Reduktion innebär dock att information försvinner, i synnerhet de detaljer som skulle beräknas. I detta examensarbete så behandlas problemet genom att skapa en ny metod för reducering av stora finita element modeller. Metoden bygger på tidigare kunskap om Proper Orthogonal Decomposition (POD) som ett sätt att reducera modeller. Den nya metoden reducerar finita ellement modeller samtidigt som den bibehåller hög detalj. En ny metod utvecklas för att berika en vanlig POD-baserad modellreduktion med hjälp av hieraktiskt bestämda berikningsmoder. Metoden beskrivs och testas i en dynamisk FEM-applikation av elasticitet i ett kugghjul i 2 dimensioner. Metoden för berikning jämförs numeriskt med en metod som använder vanlig POD-reduktion. Körningar visar att felet i den berikade metoden är omkring 10 gånger mindre, i genomsnitt, jämfört med en vanlig metod. Det visas också att spänningar bevaras på ett mycket bra sätt med den nya berikningsmetoden. Dessutom så formuleras och bevisas ett a posteriori estimat för statiska lastfall, vilket innebär att felet i metoden är bundet.

Lineare hyperbolische partielle Differentialgleichungen in homogenen Medien, beispielsweise die Wellengleichung, die die Ausbreitung und die Streuung akustischer Wellen beschreibt, können im Zeitbereich mit Hilfe von Randintegralgleichungen formuliert werden. Im ersten Hauptteil dieser Arbeit stellen wir eine effiziente Möglichkeit vor, numerische Approximationen solcher Gleichungen zu implementieren, wenn das Huygens-Prinzip nicht gilt. Wir nutzen die Faltungsquadraturmethode für die Zeitdiskretisierung und eine Galerkin-Randelement-Methode für die Raumdiskretisierung. Mit der Faltungsquadraturmethode geht eine diskrete Faltung der Faltungsgewichte mit der Randdichte einher. Bei Gültigkeit des Huygens-Prinzips konvergieren die Gewichte exponentiell gegen null, sofern der Index hinreichend groß ist. Im gegenteiligen Fall, das heißt bei geraden Raumdimensionen oder wenn Dämpfungseffekte auftreten, kann kein Verschwinden der Gewichte beobachtet werden. Das führt zu Schwierigkeiten bei der effizienten numerischen Behandlung. Im ersten Hauptteil dieser Arbeit zeigen wir, dass die Kerne der Faltungsgewichte in gewisser Weise die Fundamentallösung im Zeitbereich approximieren und dass dies auch zutrifft, wenn beide bezüglich der räumlichen Variablen abgeleitet werden. Da die Fundamentallösung zudem für genügend große Zeiten, etwa nachdem die Wellenfront vorbeigezogen ist, glatt ist, schließen wir Gleiches auch in Bezug auf die Faltungsgewichte, die wir folglich mit hoher Genauigkeit und wenigen Interpolationspunkten interpolieren können. Darüber hinaus weisen wir darauf hin, dass zur weiteren Einsparung von Speicherkapazitäten, insbesondere bei Langzeitexperimenten, der von Schädle et al. entwickelte schnelle Faltungsalgorithmus eingesetzt werden kann. Wir diskutieren eine effiziente Implementierung des Problems und zeigen Ergebnisse eines numerischen Langzeitexperimentes. Im zweiten Hauptteil dieser Arbeit beschäftigen wir uns mit Transmissionsproblemen der Wellengleichung im Freiraum. Solche Probleme werden gewöhnlich derart behandelt, dass der Freiraum, wenn nötig durch Einführen eines künstlichen Randes, in ein unbeschränktes Außengebiet und ein beschränktes Innengebiet geteilt wird mit dem Ziel, eventuelle Inhomogenitäten oder Nichtlinearitäten des Materials vollständig im Innengebiet zu konzentrieren. Wir werden eine Lösungsstrategie vorstellen, die es erlaubt, die aus der Teilung resultierenden Teilprobleme so weit wie möglich unabhängig voneinander zu behandeln. Die Kopplung der Teilprobleme erfolgt über Transmissionsbedingungen, die auf dem ihnen gemeinsamen Rand vorgegeben sind. Wir diskutieren ein Kopplungsverfahren, das auf verschiedene Diskretisierungsschemata für das Innen- und das Außengebiet zurückgreift. Wir werden insbesondere ein explizites Verfahren im Innengebiet einsetzen, im Gegensatz zum Außengebiet, bei dem wir ein auf ein Mehrschrittverfahren beruhendes Faltungsquadraturverfahren nutzen. Die Kopplung erfolgt nach der Strategie von Johnson und Nédélec, bei der die direkte Randintegralmethode zum Einsatz kommt. Diese Strategie führt auf ein unsymmetrische System. Wir analysieren das diskrete Problem hinsichtlich Stabilität und Konvergenz und unterstreichen die Einsatzfähigkeit des Kopplungsalgorithmus mit der Durchführung numerischer Experimente.

We consider the reaction-diffusion-advection (RDA) equations resulting in air pollution mod- eling problems. We employ the finite element method (FEM) for solving the RDA equations in two dimensions. Linear triangular finite elements are used in the discretization of problem domains. The instabilities occuring in the solution when the standard Galerkin finite element method is used, in advection or reaction dominated cases, are eliminated by using an adap- tive stabilized finite element method. In transient problems the unconditionally stable Crank- Nicolson scheme is used for the temporal discretization. The stabilization is also applied for reaction or advection dominant case in the time dependent problems. It is found that the stabilization in FEM makes it possible to solve RDA problems for very small diffusivity constants. However, for transient RDA problems, although the stabilization improves the solution for the case of reaction or advection dominance, it is not that pronounced as in the steady problems. Numerical results are presented in terms of graphics for some test steady and unsteady RDA problems. Solution of an air pollution model problem is also provided.

Die vorliegende Arbeit beschäftigt sich mit der zweidimensionalen Simulation der Rissausbreitung mit Hilfe der adaptiven Finite-Elemente-Methode. Das Ziel war die Entwicklung von Algorithmen zur effizienten und automatisierten Modellierung des Risswachstums. Das zugrunde liegende Konzept besteht in der vollständigen Integration aller Teilschritte der Risswachstumssimulation in ein einziges FE-Programm. Während der gesamten Simulation erfolgt durch den Einsatz eines fehlergesteuerten h-adaptiven Verfahrens die automatische Anpassung der FE-Diskretisierung an das gestellte Rissproblem. Die Simulation der spröden Rissausbreitung erfolgt auf Basis der linear-elastischen Bruchmechanik. Die dafür benötigten Spannungsintensitätsfaktoren werden mit Hilfe des J-Integrals in Form der Interaction-Integral-Technik ermittelt. Die Simulation des duktilen Versagens in der Prozesszone an der Rissspitze wird mit Hilfe des Schädigungsmodells von Rousselier beschrieben. Das Kriterium für duktiles Risswachstum basiert auf der Auswertung des akustischen Tensors an der Rissspitze und legt den Beginn der makroskopischen Rissausbreitung mit dem Einsetzen der Lokalisierung fest.

Im Vortrag wird das Vorgehen zur Konstruktionsoptimierung mittels parametrischer FE-Simulation beschrieben. Die einzelnen Schritte werden dargestellt und am Beispiel eines Übertragungselements für Klauenkupplungen erläutert. Zunächst wird der Optimierungsgegenstand vorgestellt und die Festlegung der Entwurfsvariablen und Zielfunktionen beschrieben. Im Anschluss werden die Erstellung des FE-Modells und die Durchführung der Optimierungsrechnung schrittweise erläutert. Abschließend folgen ein Vergleich verschiedener Optimierungsmethoden und die Zusammenfassung. Als Software wurden ANSYS und Autodesk Inventor verwendet.

Detta examensarbete har utförts i samarbete med Fagerström Industrikonsult AB i Helsingborg. Fagerström Industrikonsult AB är ett ingenjörsföretag som har specialiserat sig på mekaniska och mekatroniska produkter inom flera branchområden. Ett av företagets tidigare projekt, som bland annat bygger på tryckbärande kärl och som kommer återanvändas för ett nytt projekt, är i behov av en uppdaterad analys mot utmattningsbrott.För att en tryckbärande utrustning skall kunna säljas och användas inom Europa, måste tillverkarna följa det Europeiska direktivet 97/23/EG, även kallat PED-direktiv. Detta direktiv sätter regler för konstruktion, tillverkning, märkning och kontroll. I Sverige finns denna beskrivning i Arbetsmiljöverkets författnings-samling (AFS 1999:4 2011). För att uppfylla alla de konstruktionsmässiga och tillverkningsmässiga krav på tryckkärlet som ställs i PED direktivet, så måste harmoniserade standarder användas. I detta arbete används tryckkärlsstandarden (SS-EN 13445-3: 2014) som sätter regler för design och verifiering av tryckbärande anordningar.Ett av projekten som finansierats av den Europeiska kommissionen, visade att 25% av alla tryckbärande anordningars haverier beror på utmattning. Tryckkärl är den typ av tryckbärande anordning, som är mest utsatt för skador orsakade av utmattning. Utmattningsbrott har varit känt sedan början på 1800-talet och man har länge studerat detta fenomen. Man har efter lång tids arbete hittat metodik för att ta fram analytiska modeller och prediktionstekniker samt säkra och noggranna livslängdsberäkningar för stålkonstruktioner. Fagerström Industrikonsult AB söker idag en metod för att utföra utmattningsanalys på tryckkärl i enlighet med tryckkärlsstandarden där linjärstatisk analys utförs med finita elementmetoden. Företaget eftersträvar också mer kunskap inom ämnet för att ge konstruktörerna bättre kännedom om utmattningsproblematiken samt ge möjlighet att redan i konstruktionsstadiet kunna sätta rimliga krav på tillverkning ur mekaniskt utmattningsperspektiv. / This master thesis has been carried out in collaboration with Fagerström Industrikonsult AB in Helsingborg. Fagerström Industrikonsult AB is an engineering company, specialized in mechanical and mechatronic products across a wide range of industry segments. One of the company's previous project, which is among other sub-products based on pressurized vessels, and that will be reused for a new project, needs an updated analysis against fatigue failure.In order to sell or use a pressurized equipment in Europe, the manufacturers must comply with the European Directive 97/23/EC, also called PED-directive. This directive sets the rules for design, production, marking and inspections. In Sweden, this directive is described in “Arbetsmiljöverkets Författningssamling” (AFS 1999:4 2011). In order to meet all the design and manufacturing requirements for pressure vessels that are required by the PED Directive, it is required to use harmonized standards. In this thesis, pressure vessel standard (SS-EN 13445-3: 2014) is used, which sets the rules for design and verification of pressure vessel.One of the projects funded by the European Commission, showed that 25 % of all pressure equipment failure are caused by fatigue. Pressure vessel is one type of these pressure equipment, which is most vulnerable to damage caused by fatigue. Fatigue failure has been known since the beginning of 19th century and this phenomenon has been studied for a long time. Under this extensive period of time, methods have been succefully developed for analytical models and prediction techniques as well as safe and accurate life calculations for steel structures. Fagerström Industrikonsult AB is today seeking a method to perform fatigue analysis of pressure vessels in accordance with European pressure vessel standard, where the linear static analysis is performed using the finite element method. The company is also pursuing more knowledge of the subject so its designers have more understanding of fatigue phenomena in order to be able to set reasonable requirements during design stage for production and in order to prevent this phenomena.

The thesis examines the fatigue life of weld ends, where very little usable research previously has been conducted, and often the weld ends are the critical parts of the weld. It is essential knowing the fatigue life of welds to be able to use them most efficiently.The report is divided into two parts; in the first the different calculation methods used today at Toyota Material Handling are examined and compared. Based on the results from the analysis and what is used mostly today, the effective notch approach is the method used in part two.To validate the calculation methods and models used, fatigue testing of the welded test specimens was conducted together with a stress test. New modelling methods of the weld ends that coincide with the test results were made in the finite element software Abaqus. A new way of modelling the weld ends for the effective notch method is also proposed. By using a notch radius of 0.2 mm and rounded weld ends the calculated fatigue life better matches the life of the real weld ends.

Numerical analysis of multi-field problems in porous and fractured media is an important subject for various geotechnical engineering tasks such as the management of geo-resources (e.g. engineering of geothermal, oil and gas reservoirs) as well as waste management. For practical usage, e.g. for geothermal, simulation tools are required which take into account both coupled thermo-hydro-mechanical (THM) processes and the uncertainty of geological data, i.e. the model parametrization. For modeling fractured rocks, equivalent porous medium or multiple continuum model approaches are often only the way currently due to difficulty to handle geomechanical discontinuities. However, they are not applicable for prediction of flow and transport in subsurface systems where a few fractures dominates the system behavior. Thus modeling coupled problems in discretely fractured porous media is desirable for more precise analysis. The subject of this work is developing a framework of the finite element method (FEM) for modeling coupled THM problems in discretely fractured and non-fractured porous media including thermal water flow, advective-diffusive heat transport, and thermoporoelasticity. Pre-existing fractures are considered. Systems of discretely fractured porous media can be considered as a problem of interacted multiple domains, i.e. porous medium domain and discrete fracture domain, for hydraulic and transport processes, and a discontinuous problem for mechanical processes. The FEM is required to take into account both kinds of the problems. In addition, this work includes developing a methodology for the data uncertainty using the FEM model and investigating the uncertainty impacts on evaluating coupled THM processes. All the necessary code developments in this work has been carried out with a scientific open source project OpenGeoSys (OGS). In this work, fluid flow and heat transport problems in interactive multiple domains are solved assuming continuity of filed variables (pressure and temperature) over the two domains. The assumption is reasonable if there are no infill materials in fractures. The method has been successfully applied for several numerical examples, e.g. modeling three-dimensional coupled flow and heat transport processes in discretely fractured porous media at the Gross Schoenebck geothermal site (Germany), and three-dimensional coupled THM processes in porous media at the Urach Spa geothermal site (Germany). To solve the mechanically discontinuous problems, lower-dimensional interface elements (LIEs) with local enrichments have been developed for coupled problems in a domain including pre-existing fractures. The method permits the possibility of using existing flow simulators and having an identical mesh for both processes. It enables us to formulate the coupled problems in monolithic scheme for robust computation. Moreover, it gives an advantage in practice that one can use existing standard FEM codes for groundwater flow and easily make a coupling computation between mechanical and hydraulic processes. Example of a 2D fluid injection problem into a single fracture demonstrated that the proposed method can produce results in strong agreement with semi-analytical solutions. An uncertainty analysis of THM coupled processes has been studied for a typical geothermal reservoir in crystalline rock based on the Monte-Carlo method. Fracture and matrix are treated conceptually as an equivalent porous medium, and the model is applied to available data from the Urach Spa and Falkenberg sites (Germany). Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. Two reservoir modes (undisturbed and stimulated) are considered to construct a stochastic model for permeability distribution. We found that the most significant factors in the analysis are permeability and heat capacity. The study demonstrates the importance of taking parameter uncertainties into account for geothermal reservoir evaluation in order to assess the viability of numerical modeling.

Distributionsförluster är en viktig faktor i fjärrenergisystem. Genom att optimera förluster i sådana system, kan både ekonomiska och miljömässiga aspekter uppfyllas. Tyvärr finns det ringa information om rörförluster i fjärrkylasystem. Föreliggande studie fokuserar på förluster i ett fjärrkylanät genom att både använda ett R-nätverk och FEM simuleringsmodeller. Ett R-nätverksmodell bestående av termiska konduktanser har utvecklats genom analytiska ekvationer och simuleringar med FEM har utfört för validering av modellen. Därefter har ett fjärrkylanätverk som konstrueras i Gävle, analyserats. Undersökningen omfattar 15 olika rördiametrar i tre utföranden (dubbelrör med två symmetriska och en osymmetrisk värmeisolering) och i tre förläggningsdjup (0,8; 2 och 4 meter) för en säsong om 7 månader (April t o m Oktober). Särskilt utreds ökningen av temperaturen hos framledningsmediet, där matningsrören förlagts i en å mitt i staden om en sträcka av 1 km. Den maximala förlusten under säsongen, bland alla rörkonfigurationer, motsvarar 2 % av den totala levererade energin. Slutligen konstateras att kombinationen av isolerad framledningsrör och oisolerade returrör verkar som en gångbar investering, ekonomiskt och tekniskt, men kan inte användas i hela nätet eftersom stora delar har redan byggts med oisolerade plaströr. R-nätverksmodellen, som visades vara effektiv och pålitlig i undersökningen, kan som beräkningsverktyg, framförallt för dimensionering och för att uppskatta energiförluster. / Distribution losses are a very important factor in district energy systems. By optimizing the losses in such a system, both economical and environmental aspects can be fulfilled. Unfortunately, there is few information regarding losses for district cooling systems. This study focuses on losses in district cooling networks by using both R-network and FEM simulation models. A R-network model composed of thermal conductances has been developed through analytical equations and simulations have been performed for validation. Afterwards, an in-progress construction project of a district cooling network from the city of Gävle, Sweden, is analyzed. The assessment consists of 15 pipe diameters in three configurations (two symmetric cases and one asymmetric), at three ground laying depths (0.8, 2 and 4 meters) for a duration of 7 months (April to October). A particular case in which the main distribution pipes from and to the plant are submerged in the city’s river for a distance of 1 km is investigated in order to estimate the temperature increase of the supply water. A maximum cooling loss below 2% of the total delivered energy during the season for any network configuration resulted from the calculation. Finally, the mixed pipes array seems to be a feasible investment both economically and technically but it cannot be used for the entire network spread since a part of the network has been already built with the non-insulated plastic pipes. The R-network model proved to be effective and reliable in the analysis which provides confidence that it can serve as a solid foundation for a calculation tool - primarily for design purposes and also for estimating energy loss.