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Gegenstand dieser Arbeit ist es, Simulationsergebnisse von Pro/MECHANICA und ANSYS zu vergleichen, um somit einen Hinweis auf die Qualität der Berechnungsergebnisse von integrierten FEM-Systemen zu bekommen. Als Beispiele dienen verschiedene Bauteile aus dem Gebiet der Strukturmechanik (linear-elastischer Bereich), welche mit Pro/MECHANICA und ANSYS modelliert und berechnet werden. Abschließend erfolgt eine Gegenüberstellung der Daten aus FEM und analytischer Rechnung, sowie eine Bewertung der Ergebnisse.

Stimuli-sensitive hydrogels are polymeric materials, which are able to reversibly swell in water in response to evironmental changes. Relevant stimuli include variations of pH, temperature, concentration of specific ions etc. Stacked layers composed of multiple thin hydrogels - also referred to as hydrogel-layer composites - combine the distinct sensing properties of different hydrogels. This approach enables the development of sophisticated micro uidic devices such as bisensitive valves or uid-sensitive de ectors. In order to numerically simulate the swelling of a polyelectrolyte hydrogel in response to an ion concentration change the multifield theory is adopted. The set of partial differential equations - including the description of the chemical, the electrical and the mechanical field - are solved using the Finite Element Method. Simulations are carried out on a twodimensional domain in order to capture interactions between the different fields. In the present work, the ion transport is governed by diffusive and migrative uxes. The distribution of ions in the gel and the solution bath result in an osmotic pressure difference, which is responsible for the mechanical deformation of the hydrogel-layer composite. The realized numerical investigation gives an insight into the evolution of the displacement field, the distribution of ions and the electric potential within the bulk material and the interface between gel and solution bath. The predicted behavior of the relevant field variables is in excellent agreement with results available in the literature.

Nafion membranes, are polymeric thin films widely employed in micro-batteries and fuel cells. These devices are expected to play a key role in the next generation energy systems for use in vehicles as a replacement to combustion engines. In fact, a minimum environmental impact is guaranteed by reduced carbon dioxide emissions. It is usually complicated to investigate the behavior of thin membranes through experiments. Therefore, numerical simulations are carried out in order to enable a better understanding of the phenomena and of the multi-field couplings occurring in polymeric membranes. A continuum-based, three-dimensional and electro-chemo-mechanical (ECM) model for a hydrated polymer membrane is presented. Different effects are taken into account: (i) mechanics, (ii) water uptake, (iii) ion transport, and (iv) electrostatics. The dissipation inequality drives the choice of the suitable constitutive equations of the multi-physics theory. In the mechanical field, an additive decomposition of the deformation gradient in (i) a distortion part, related to the ion motion, and (ii) an elastic part, is assumed. The multi-field model is numerically solved within the finite element framework. Time-dependent simulations are performed by using the commercial tool COMSOL Multiphysics. Furthermore, two closed form solutions are obtained by using (i) a one-dimensional reduced model and (ii) an approach based on the bar theory with an electro-chemical distortion field.

Die Dynamik von elastischen Membranen, Kapseln und Schalen hat sich zu einem aktiven Forschungsgebiet in der simulationsgestützten Physik und Biologie entwickelt. Die dünne Oberfläche dieser elastischen Materialien ermöglicht es, sie effizient als Hyperfläche zu approximieren. Solche Oberflächen reagieren auf Dehnungen in Oberflächenrichtung und Verformungen in Normalenrichtung mit einer elastischen Kraft. Zusätzlich können Oberflächenspannungskräfte auftreten. In dieser Arbeit präsentieren wir eine neuartige Arbitrary Lagrangian-Eulerian (ALE) Methode um solche in (Navier-Stokes) Fluiden eingebetteten elastischen Schalen zu simulieren. Dadurch, dass das Gitter an die elastische Oberfläche angepasst ist, kombiniert die vorgeschlagene Methode hohe Genauigkeit mit Effizienz in der Berechnung der Lösungen. Folglich kann man die Simulationen mit einer verhältnismäßig geringen Gitterauflösung durchführen. Der Fokus dieser Arbeit liegt bei achsensymmetrischen Formen und Strömungen, wie sie bei vielen biophysikalischen Anwendungen zu finden sind. Neben einer allgemeinen dreidimensionalen Beschreibung formulieren wir achsensymmetrische Kräfte auf der Oberfläche, für welche wir eine Diskretisierung mit der Finite Differenzen Methode vorschlagen, welche an eine Finite-Elemente Methode für die umgebenden Fluide gekoppelt ist. Weiterhin entwickeln wir eine Strategie zur impliziten Kopplung der Kräfte, um Zeitschrittrestriktionen zu reduzieren. In verschiedenen numerischen Tests werden wir zeigen, dass akkurate Ergebnisse schon in einer Größenordnung von Minuten auf einer Single-Core CPU erreicht werden können. Die Methode wurde in drei aktuellen Anwendungen verwendet, wobei mindestens zwei davon nach unserer Kenntnis im Moment mit keiner anderen numerischen Methode simuliert werden können: Zunächst präsentieren wir Simulationen von biologischen Zellen, die im Zuge eines RT-DC (Real-Time Deformability Cytometry) Experiments durch einen schmalen mikrofluidischen Kanal advektiert und dabei verformt werden. Danach zeigen wir die Ergebnisse erster Simulationen der uniaxialen Kompression biologischer Zellen zwischen zwei parallelen Platten im Zuge eines AFM Experiments. Schließlich präsentieren wir Resultate erster Simulationen von neuartigen mikroschwimmenden Schalen, welche lediglich durch äußere Einflüsse (wie z.B. Ultraschall), zum Schwimmen angeregt werden können. / The dynamics of membranes, shells, and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface, which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel arbitrary Lagrangian-Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions, which are present in a wide range of biophysical problems. Next to a general three-dimensional description, we formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. Several numerical test cases show that accurate results can be achieved at computational times on the order of minutes on a single core CPU. Three state-of-the-art applications are demonstrated, where to our knowledge at least two of them cannot be simulated with any other numerical method so far. First, simulations of biological cells being advected through a microfluidic channel and therefore being deformed during an RT-DC (Real-Time Deformability Cytometry) experiment are presented. Then, the uniaxial compression of the cortex of a biological cell during an AFM experiment is investigated. Finally, we present the results of first simulations of the observed shape oscillations of novel microswimming shells which can be locomoted by exterior influences (e.g. ultrasound waves) only.

Main goals of this master thesis are following: to perform the state of the art research of overpressure constructions (especially space habitats, plane fuselages); to create an own concept of the functional inside ending (hole) in the sandwich panel for a door; to perform stress-strain analysis of this concept; to perform the design optimalization of this concept in order to minimise the weight. To solve the problems above software Ansys 17.2 is chosen, because it allows to: model the material of the honeycomb core of sandwich panel as homogenous linear orthotropic material; evaluate reserve factors of all critical limit states; perform the design optimalization; perform Monte Carlo simulation. First and second design optimalizations discover, that with defined parameters: 0,635 mm width of aluminium sandwich face sheets and inner overpressure 0,1 MPa, a creation of the model, that would be safe by changing the values of design variables is not possible. Specifically, the maximum value of shear stress on the glued areas between aluminium face sheets and honeycomb core is higher than the shear strength of the glue. Therefore, two new concepts are created. First for inner pressure 0,03 MPa and bigger width of aluminium face sheets 3,175 mm, second for inner pressure 0,02 MPa and same width of aluminium face sheets 0,635 mm. For both these concepts, an overall reserve factor is calculated. First, the value of an overall reserve factor is calculated deterministically. Secondly, the value of an overall reserve factor is calculated stochastically considering the variance of material properties of the honeycomb core ± 10 % by Monte Carlo simulation. An overall reserve factor of the concept with inner pressure 0,02 MPa is determined as 1,21. An overall reserve factor of the concept with inner pressure 0,03 MPa is determined as 1,20. The weight of the concept for inner pressure 0,03 MPa is though 4 times bigger than the weight of the concept for inner pressure 0,02 MPa. In the concept for inner pressure 0,02 MPa the maximum value of HMH stress in aluminium components is critical, stochastically considered material properties of the honeycomb core don’t have a significant influence on this value. In the concept for inner pressure 0,03 MPa the value of maximum shear stress on the glued areas between aluminium face sheets and the honeycomb core is critical, stochastically considered material properties of the honeycomb core have a significant influence on this value. In the concept for inner pressure 0,03 MPa an absolute error of overall reserve factor is 8 % (overall reserve factor calculated deterministically was 1,28) which is significant. Monte Carlo simulation is also used to find that the value of Poisson ratio XY of the honeycomb core doesn’t have statistically significant influence on all limit states. Value of the reserve factor of the honeycomb core is higher than 2 in both concepts. Monte Carlo simulation discovers that this value can be significantly lower. Using Tsai-Wu failure criteria the reserve factor in the concept for inner pressure 0,02 MPa is determined as 2,72 deterministically x 2,41 stochastically (absolute error 31 %), in the concept for inner pressure 0,03 MPa the reserve factor is determined as 6,85 deterministically x 6,17 stochastically (absolute error 68 %).

In der vorliegenden Arbeit werden verschiedene Randwertprobleme zur Beschreibung der Ausbreitung magnetotellurischer Felder mit Hilfe der Finite-Elemente-Methode numerisch gelöst. Die zwei- und dreidimensionalen Randwertprobleme zur Simulation des elektrischen oder des magnetischen Feldes, des magnetischen Vektorpotentials und des elektrischen Skalarpotentials, des magnetischen Vektorpotentials allein oder des anomalen magnetischen Vektorpotentials werden aus den Maxwell-Gleichungen hergeleitet. Auf Grundlage von Anwendung der Konvergenztheorie auf die Finite-Elemente-Lösung werden Konvergenzstudien für zweidimensionale Modelle des homogenen und des geschichteten Halbraums sowie für das dreidimensionale COMMEMI 3-D-2-Modell durchgeführt. Diese werden genutzt, um die Randwertprobleme hinsichtlich ihrer Effizienz zu bewerten. Außerdem liefern Konvergenzstudien eine Abschätzung des lokalen Fehlers der numerischen Lösung für ein realitätsnahes Modell des Vulkans Stromboli und seiner Umgebung, welches digitale Geländedaten enthält. / This thesis presents the numerical finite-element solution of different formulations of the magnetotelluric boundary value problem. Based on Maxwell\'s equations, the two-dimensional and three-dimensional boundary value problems are derived in terms of the electric or the magnetic field, the magnetic vector and the electric scalar potential, the magnetic vector potential only, or the anomalous magnetic vector potential. To evaluate their efficiency, convergence studies are performed for the two-dimensional models of the homogeneous and the layered halfspace as well as for the COMMEMI-3-D-2 model. Moreover, convergence studies yield estimates of the local error of the numerical solution for a close-to-reality model of Stromboli volcano incorporating digital terrain data.

The knowledge about the reliability of power electronics is necessary for the design of converters. Especially for offshore applications it is essential to know, which fatigue processes happen and how the lifetime can be estimated. Numerical simulation is an important tool for the development of power electronic systems. This thesis analyse the thermal and thermal-mechanical behaviour of packages for power semiconductor devices with the help of simulations. One topic is the evaluation of different thermal models. The main focus is on the description of the thermal cross-coupling between the devices and the influence to the lifetime estimation. The power module is a well established package for power semiconductor devices. It will be explained how the heating period of power cycles influences the failure mode of this package type. Additionally, it will evaluated how SiC devices and DAB substrates influence the power cycling capability. The press-pack is in focus for high power applications as the package short-circuits during an electrical failure without external auxiliary systems. However, the knowledge about the power cycling behaviour is currently limited. With the help of simulations this behaviour will be analysed and possible weak points will be also derived. In the end of the work it will be discussed, how the lifetime can be estimated with help of FEM simulations. / Für die Entwicklung von Umrichtern ist die Kenntnis über die Zuverlässigkeit der Leistungselektronik ein wichtiges Kernthema. Insbesondere für Offshore-Anwendungen ist das Wissen über die stattfindenden Ermüdungsprozesse und die Abschätzung der zu erwartenden Lebensdauer der Bauteile essentiell. Hierfür hat sich die Simulation als ein wichtiges Werkzeug für die Entwicklung und Lebensdauerbewertung von leistungselektronischen Anlagen etabliert. In der folgenden Arbeit wird das thermische und das thermisch-mechanische Verhalten der Leistungselektronik mittels Simulationen untersucht. Hierzu wird ein Vergleich zwischen verschiedenen thermischen Modellen für Leistungsbauelemente durchgeführt. Schwerpunkt ist die Beschreibung der thermischen Kopplung zwischen den Chips und deren Einfluss auf die Lebensdauerabschätzung. Ein weiterer Schwerpunkt ist das Leistungsmodul, welches sich als ein Standardgehäuse etabliert hat. Dazu wird erklärt, wie die Variation der Einschaltzeit im aktiven Lastwechseltest den Fehlermodus dieses Gehäusetyps beeinflusst. Weiterhin wird untersucht, wie SiC als Leistungshalbleiter und DAB als Substrat die Zuverlässigkeit beein- flusst. Der Press-Pack ist für Hochleistungsapplikationen von hohem Interesse, da dieses Gehäuse im elektrischen Fehlerfall ohne äußere Unterstützung kurzschliesst. Jedoch ist das Wissen über diese Gehäusetechnologie unter aktiven Lastwechselbedingungen sehr limitiert. Mit Hilfe von Simulationen wird dieses Verhalten untersucht und mögliche Schwachpunkte abgeleitet. Am Ende der Arbeit werden Möglichkeiten untersucht, wie Mithilfe von FEM Simulationen die Lebensdauer von Leistungsmodulen evaluiert werden kann.

The rise of additive manufacturing has enabled new degrees of freedom in terms of design and functionality. In this context, this contribution addresses the design and characterization of structural unit cells that are intended as building blocks of highly porous lattice structures with tailored properties. While typical lattice structures are often composed of gyroid or diamond lattices, this study presents stackable unit cells of different sizes created by a generative design approach tomeet boundary conditions such as printability and homogeneous stress distributions under a given mechanical load. Suitable laser powder bed fusion (LPBF) parameterswere determined forAlSi10Mg to ensure high resolution and process reproducibility for all considered unit cells. Stacks of unit cells were integrated into tensile and pressure test specimens for which the mechanical performance of the cells was evaluated. Experimentally measured material properties, applied process parameters, and mechanical test results were employed for calibration and validation of finite element (FE) simulations of both the LPBF process as well as the subsequent mechanical characterization. The obtained data therefore provides the basis to combine the different unit cells into tailored lattice structures and to numerically investigate the local variation of properties in the resulting structures. / Durch die Einführung der Additiven Fertigung können neue Freiheitsgrade in Bezug auf Gestaltungsfreiheit und Funktionalität erreicht werden. In diesem Zusammenhang adressiert dieser Beitrag das Design und die Charakterisierung struktureller Einheitszellen als Bausteine für hochgradig poröse Gitterstrukturen mit maßgeschneiderten Eigenschaften. Während typische Gitterstrukturen oft auf Gyroid- oder Diamantstrukturen basieren, präsentiert dieser Beitrag stapelbare Einheitszellen unterschiedlicher Größe, die durch einen generativen Designansatz erstellt wurden. Hierdurch sollen verschiedene Randbedingungen wie eine gute Druckbarkeit und homogene Spannungsverteilung unter gegebenen mechanischen Lasten erreicht werden. Um eine hohe Auflösung und Reproduzierbarkeit der Einheitszellen zu erreichen, wurden für den verwendeten Werkstoff AlSi10Mg geeignete Druckparameter für das Laserstrahlschmelzen (LPBF) ermittelt. Stapel von Einheitszellen wurden in Zug- und Druckproben integriert, anhand derer die mechanische Stabilität der Zellen ermittelt wurde. Experimentell bestimmte Materialeigenschaften, die verwendeten Prozessparameter und die Ergebnisse der mechanischen Untersuchungen wurden anschließend für die Kalibrierung und Validierung Finiter Elemente (FE) Simulationen herangezogen, wobei simulationsseitig sowohl der Prozess des Laserstrahlschmelzens als auch die nachgelagerte mechanische Charakterisierung berücksichtigt wurden. Die hier präsentierten Ergebnisse sollen als Basis sowohl für eine gezielte Anordnung der Einheitszellen zu maßgeschneiderten Gitterstrukturen dienen als auch für die numerische Auswertung der lokal variierenden Eigenschaften der somit resultierenden Strukturen.

Nowadays society strongly depends on its available resources and the long term stability of the surrounding ecosystem. Numerical modelling has become a general standard for evaluating past, current or future system states for a large number of applications supporting decision makers in proper management. In order to ensure the correct representation of the investigated processes and results of a simulation, verification examples (benchmarks), that are based on observation data or analytical solutions, are utilized to evaluate the numerical modelling tool. In many parts of the world, groundwater is an important resource for freshwater. While it is not only limited in quantity, subsurface water bodies are often in danger of contamination from various natural or anthropogenic sources. Especially in arid regions, marine saltwater intrusion poses a major threat to groundwater aquifers which mostly are the exclusive source of freshwater in these dry climates. In contrast to common numerical groundwater modelling, density-driven flow and mass transport have to be considered as vital processes in the system and in scenario simulations for fresh-saltwater interactions. In the beginning of this thesis, the capabilities of the modelling tool OpenGeoSys are verified with selected benchmarks to represent the relevant non-linear process coupling. Afterwards, variable-density application and process studies on different scales are presented. Application studies comprehend regional groundwater modelling of a coastal aquifer system extensively used for agricultural irrigation, as well as hydro-geological model development and parametrization. In two process studies, firstly, a novel method to model gelation of a solute in porous media is developed and verified on small scale laboratory observation data, and secondly, investigations of thermohaline double-diffusive Rayleigh regimes on medium scale are carried out. With the growing world population and, thus, increasing pressure on non-renewable resources, intelligent management strategies intensify demand for potent simulation tools and development of novel methods. In that way, this thesis highlights not only OpenGeoSys’ potential of density-dependent process modelling, but the comprehensive importance of variable-density flow and transport processes connecting, both, avant-garde scientific research, and real-world application challenges.:Abstract Zusammenfassung Nomenclature List of Figures List of Tables I Background and Fundamentals 1 Introduction 1.1 Motivation 1.2 Structure of the Thesis 1.3 Variable-Density Flow in Literature 2 Theory and Methods 2.1 Governing Equations 2.2 Fluid Properties 2.3 Modelling and Visualization Tools 3 Benchmarks 3.1 Steady-state Unconfined Groundwater Table 3.2 Theis Transient Pumping Test 3.3 Transient Saltwater Intrusion 3.4 Development of a Freshwater Lens II Applications 4 Extended Inverse Distance Weighting Interpolation 4.1 Motivation 4.2 Extension of IDW Method 4.3 Artificial Test and Regional Scale Application 4.4 Summary and Conclusions 5 Modelling Transient Saltwater Intrusion 5.1 Background and Motivation 5.2 Methods and Model Setup 5.3 Simulation Results and Discussion 5.4 Summary, Conclusion and Outlook 6 Gelation of a Dense Fluid 6.1 Motivation 6.2 Methods and Model Setup 6.3 Results and Conclusions 7 Delineating Double-Diffusive Rayleigh Regimes 7.1 Background and Motivation 7.2 Methods and Model Setup 7.3 Results 7.4 Conclusions and Outlook III Summary and Conclusions 8 Important Achievements 9 Conclusions and Outlook Bibliography Publications Acknowledgements Appendix