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The imperative to transform current energy provisions is widely acknowledged. However, scant attention has hitherto been directed toward rural municipalities and their innate resources, notably biogenic resources. In this paper, a methodological framework is developed to interconnect resources from waste, wastewater, and agricultural domains for energy utilization. This entails cataloging existing resources, delineating their potential via quantitative assessments utilizing diverse technologies, and encapsulating them in a conceptual model. The formulated models underwent iterative evaluation with engagement from diverse stakeholders. Consequently, 3 main concepts, complemented by 72 sub-concepts, were delineated, all fostering positive contributions to climate protection and providing heat supply in the rural study area. The outcomes’ replicability is underscored by the study area’s generic structure and the employed methodology. Through these inquiries, a framework for the requisite energy transition, with a pronounced emphasis on the coupling of waste, wastewater, and agriculture sectors in rural environments, is robustly analyzed.
The study presents a Machine Learning (ML)-based framework designed to forecast the stress-strain relationship of arc-direct energy deposited mild steel. Based on microstructural characteristics previously extracted using microscopy and X-ray diffraction, approximately 1000 new parameter sets are generated by applying the Latin Hypercube Sampling Method (LHSM). For each parameter set, a Representative Volume Element (RVE) is synthetically created via Voronoi Tessellation. Input raw data for ML-based algorithms comprises these parameter sets or RVE-images, while output raw data includes their corresponding stress-strain relationships calculated after a Finite Element (FE) procedure. Input data undergoes preprocessing involving standardization, feature selection, and image resizing. Similarly, the stress-strain curves, initially unsuitable for training traditional ML algorithms, are preprocessed using cubic splines and occasionally Principal Component Analysis (PCA). The later part of the study focuses on employing multiple ML algorithms, utilizing two main models. The first model predicts stress-strain curves based on microstructural parameters, while the second model does so solely from RVE images. The most accurate prediction yields a Root Mean Squared Error of around 5 MPa, approximately 1% of the yield stress. This outcome suggests that ML models offer precise and efficient methods for characterizing dual-phase steels, establishing a framework for accurate results in material analysis.
Diese Arbeit soll einen Beitrag zum Neuen Steuerungsmodell der Öffentlichen Verwaltung auf staatlicher Ebene in Deutschland leisten. Sie dient der Untersuchung zum Aufbau eines ökonomischen Modells zur Koordination von Dienstliegenschaften auf staatlicher Ebene.
Die Untersuchung der Dienstliegenschaften zeigt, dass diese eine interne Dienstbarkeit des Staates als Wirtschaftssubjekt an den Staat als Hoheitsträger fingieren.
Die Untersuchung der Liegenschaftsverwaltung belegt, dass sie vor allem ein Controlling-Instrument für den Informationsfluss zu Entscheidungen über Dienstliegenschaften zwischen dem Hoheitsträger und dem Wirtschaftssubjekt darstellt.
Die Untersuchung der Transaktionskosten beweist, dass eine Koordination am effizientesten über die eigene Organisation mittels dezentraler Aufgabenkonzentration in Form eines SSC erreicht werden kann.
Die Untersuchung der Handlungs- und Verfügungsrechte ergab, dass die Verfügungsrechte an den Dienstliegenschaften weiter den Ressorts bzw. Nutzern obliegen. Allein das Handlungsrecht der Aufgabenwahrnehmung ist an die Liegenschaftsverwaltung übergegangen.
Die Untersuchung der Prinzipal-Agent-Verhältnisse teilt der Liegenschaftsverwaltung die Rolle eines Erfüllungsgehilfen des Wirtschaftssubjektes zu. Die monetäre Abwicklung der Ge-schäfte zwischen dem Wirtschaftssubjekt und dem Hoheitsträger obliegt als zuarbeitende Organisationseinheit ohne eigene Entscheidungsgewalt der Liegenschaftsverwaltung.
Aus diesen Thesen ergeben sich monetäre Handlungsmöglichkeiten, die in den Aufbau des Modells einfließen. Es rückt das Wirtschaftssubjekt als Entscheidungsträger über den Ressourceneinsatz in den Mittelpunkt der Betrachtung. Der Hoheitsträger ist hierbei nur der Forderungsberechtigte an das Wirtschaftssubjekt und die Liegenschaftsverwaltung dessen immobilienwirtschaftlicher Vertreter.
Diese Konstellation berücksichtigend erfolgt dem Credo des NPM gemäß die Beschreibung des Modells und des institutionellen Arrangements nach den gängigen Modellen aus der Privatwirtschaft. Anhand der Untersuchungsergebnisse wird eine Liegenschaftsverwaltung skizziert, welche einerseits den tatsächlichen betriebswirtschaftlichen Anforderungen der Immobilienwirtschaft und andererseits den Gegebenheiten des haushaltswirtschaftlichen Umfeldes der öffentlichen Verwaltung gerecht werden kann.
Das aufgebaute Realmodell dient gleichzeitig dem Vergleich mit dem bestehenden und in der Praxis angewandten Mieter-Vermieter-Modell als Idealmodell. Der Vergleich zeigt, dass sich aus der Untersuchung zivilrechtlicher Institutionen zwar kein schuldrechtliches, wohl aber ein dingliches Recht ableiten lässt. Damit einher geht die Vermutung, dass es sich bei dem Mieter-Vermieter-Modell im staatlichen Bereich um einen Fall von Modellplatonismus handelt.
Structures under wind action can exhibit various aeroelastic interaction phenomena, which can lead to destructive and catastrophic events. Such unstable interaction can be beneficially used for small-scale aeroelastic energy harvesting. Proper understanding and prediction of fluid−structure interactions (FSI) phenomena are therefore crucial in many engineering fields. This research intends to develop coupled FSI models to extend the applicability of Vortex Particle Methods (VPM) for numerically analysing the complex FSI of thin-walled flexible structures under steady and fluctuating incoming flows. In this context, the flow around deforming thin bodies is analysed using the two-dimensional and pseudo-three-dimensional implementations of VPM. The structural behaviour is modelled and analysed using the Finite Element Method. The partitioned coupling approach is considered because of the flexibility of using different mathematical procedures for solving fluid and solid mechanics. The developed coupled models are validated with several benchmark FSI problems in the literature. Finally, the models are applied to several fundamental and application field of FSI problems of different thin-walled flexible structures irrespective of their size.
Biomembranes are selectively permeable barriers that separate the internal components of the cell from its surroundings. They have remarkable mechanical behavior which is characterized by many phenomena, but most noticeably their fluid-like in-plane behavior and solid-like out-of-plane behavior. Vesicles have been studied in the context of discrete models, such as Molecular Dynamics, Monte Carlo methods, Dissipative Particle Dynamics, and Brownian Dynamics. Those methods, however, tend to have high computational costs, which limited their uses for studying atomistic details. In order to broaden the scope of this research, we resort to the continuum models, where the atomistic details of the vesicles are neglected, and the focus shifts to the overall morphological evolution. Under the umbrella of continuum models, vesicles morphology has been studied extensively. However, most of those studies were limited to the mechanical response of vesicles by considering only the bending energy and aiming for the solution by minimizing the total energy of the system. Most of the literature is divided between two geometrical representation methods; the sharp interface methods and the diffusive interface methods. Both of those methods track the boundaries and interfaces implicitly. In this research, we focus our attention on solving two non-trivial problems. In the first one, we study a constrained Willmore problem coupled with an electrical field, and in the second one, we investigate the hydrodynamics of a vesicle doublet suspended in an external viscous fluid flow.
For the first problem, we solve a constrained Willmore problem coupled with an electrical field using isogeometric analysis to study the morphological evolution of vesicles subjected to static electrical fields. The model comprises two phases, the lipid bilayer, and the electrolyte. This two-phase problem is modeled using the phase-field method, which is a subclass of the diffusive interface methods mentioned earlier. The bending, flexoelectric, and dielectric energies of the model are reformulated using the phase-field parameter. A modified Augmented-Lagrangian (ALM) approach was used to satisfy the constraints while maintaining numerical stability and a relatively large time step. This approach guarantees the satisfaction of the constraints at each time step over the entire temporal domain.
In the second problem, we study the hydrodynamics of vesicle doublet suspended in an external viscous fluid flow. Vesicles in this part of the research are also modeled using the phase-field model. The bending energy and energies associated with enforcing the global volume and area are considered. In addition, the local inextensibility condition is ensured by introducing an additional equation to the system. To prevent the vesicles from numerically overlapping, we deploy an interaction energy definition to maintain a short-range repulsion between the vesicles. The fluid flow is modeled using the incompressible Navier-Stokes equations and the vesicle evolution in time is modeled using two advection equations describing the process of advecting each vesicle by the fluid flow. To overcome the velocity-pressure saddle point system, we apply the Residual-Based Variational MultiScale (RBVMS) method to the Navier-Stokes equations and solve the coupled systems using isogeometric analysis. We study vesicle doublet hydrodynamics in shear flow, planar extensional flow, and parabolic flow under various configurations and boundary conditions.
The results reveal several interesting points about the electrodynamics and hydrodynamics responses of single vesicles and vesicle doublets. But first, it can be seen that isogeometric analysis as a numerical tool has the ability to model and solve 4th-order PDEs in a primal variational framework at extreme efficiency and accuracy due to the abilities embedded within the NURBS functions without the need to reduce the order of the PDE by creating an intermediate environment. Refinement whether by knot insertion, order increasing or both is far easier to obtain than traditional mesh-based methods. Given the wide variety of phenomena in natural sciences and engineering that are mathematically modeled by high-order PDEs, the isogeometric analysis is among the most robust methods to address such problems as the basis functions can easily attain high global continuity.
On the applicational side, we study the vesicle morphological evolution based on the electromechanical liquid-crystal model in 3D settings. This model describing the evolution of vesicles is composed of time-dependent, highly nonlinear, high-order PDEs, which are nontrivial to solve. Solving this problem requires robust numerical methods, such as isogeometric analysis. We concluded that the vesicle tends to deform under increasing magnitudes of electric fields from the original sphere shape to an oblate-like shape. This evolution is affected by many factors and requires fine-tuning of several parameters, mainly the regularization parameter which controls the thickness of the diffusive interface width. But it is most affected by the method used for enforcing the constraints. The penalty method in presence of an electrical field tends to lock on the initial phase-field and prevent any evolution while a modified version of the ALM has proven to be sufficiently stable and accurate to let the phase-field evolve while satisfying the constraints over time at each time step. We show additionally the effect of including the flexoelectric nature of the Biomembranes in the computation and how it affects the shape evolution as well as the effect of having different conductivity ratios. All the examples were solved based on a staggered scheme, which reduces the computational cost significantly.
For the second part of the research, we consider vesicle doublet suspended in a shear flow, in a planar extensional flow, and in a parabolic flow. When the vesicle doublet is suspended in a shear flow, it can either slip past each other or slide on top of each other based on the value of the vertical displacement, that is the vertical distance between the center of masses between the two vesicles, and the velocity profile applied. When the vesicle doublet is suspended in a planar extensional flow in a configuration that resembles a junction, the time in which both vesicles separate depends largely on the value of the vertical displacement after displacing as much fluid from between the two vesicles. However, when the vesicles are suspended in a tubular channel with a parabolic fluid flow, they develop a parachute-like shape upon converging towards each other before exiting the computational domain from the predetermined outlets. This shape however is affected largely by the height of the tubular channel in which the vesicle is suspended. The velocity essential boundary conditions are imposed weakly and strongly. The weak implementation of the boundary conditions was used when the velocity profile was defined on the entire boundary, while the strong implementation was used when the velocity profile was defined on a part of the boundary. The strong implementation of the essential boundary conditions was done by selectively applying it to the predetermined set of elements in a parallel-based code. This allowed us to simulate vesicle hydrodynamics in a computational domain with multiple inlets and outlets. We also investigate the hydrodynamics of oblate-like shape vesicles in a parabolic flow. This work has been done in 2D configuration because of the immense computational load resulting from a large number of degrees of freedom, but we are actively seeking to expand it to 3D settings and test a broader set of parameters and geometrical configurations.
Care of ageing adults has become a dominant field of application for assistive robot technologies, promising support for ageing adults residing in care homes and staff, in dealing with practical routine tasks and providing social and emotional relieve. A time consuming and human intensive necessity is the maintenance of high hygiene quality in care homes. Robotic vacuum cleaners have been proven effective for doing the job elsewhere, but—in the context of care homes—are counterproductive for residents’ well-being and do not get accepted. This is because people with dementia manifest their agency in more implicit and emotional ways, while making sense of the world around them. Starting from these premises, we explored how a zoomorphic designed vacuum cleaner could better accommodate the sensemaking of people with dementia. Our design reconceptualises robotic vacuum cleaners as a cat-like robot, referring to a playful behaviour and appearance to communicate a non-threatening and familiar role model. Data from an observational study shows that residents responded positively to our prototype, as most of them engaged playfully with it as if it was a pet or a cat-like toy, for example luring it with gestures. Some residents simply ignored the robot, indicating that it was not perceived as frightening or annoying. The level of activity influenced reactions; residents ignored our prototype if busy with other occupations, which proves that it did not cause significant disturbance. We further report results from focus group sessions with formal and informal caregivers who discussed a video prototype of our robot. Caregivers encouraged us to enhance the animal like characteristics (in behaviour and materiality) even further to result in richer interactions and provoke haptic pleasure but also pointed out that residents should not mistake the robot for a real cat.
Antimicrobial resistances (AMR) are ranked among the top ten threats to public health and societal development worldwide. Toilet wastewater contained in domestic wastewater is a significant source of AMR entering the aquatic environment. The current commonly implemented combined sewer systems at times cause overflows during rain events, resulting in the discharge of untreated wastewater into the aquatic environment, thus promoting AMR. In this short research article, we describe an approach to transform combined sewer systems into source separation-modified combined sewer systems that separately treat toilet wastewater. We employ simulations for demonstrating that source separation-modified combined sewer systems reduce the emission of AMR- causing substances by up to 11.5 logarithm levels. Thus, source separation- modified combined sewer systems are amongst the most effective means of combating AMR.
KEYWORDS
Vertical green system for gray water treatment: Analysis of the VertiKKA-module in a field test
(2022)
This work presents a modular Vertical Green System (VGS) for gray water treatment, developed at the Bauhaus-Universität Weimar. The concept was transformed into a field study with four modules built and tested with synthetic gray water. Each module set contains a small and larger module with the same treatment substrate and was fed hourly. A combination of lightweight structural material and biochar of agricultural residues and wood chips was used as the treatment substrate. In this article, we present the first 18 weeks of operation. Regarding the treatment efficiency, the parameters chemical oxygen demand (COD), total phosphorous (TP), ortho-phosphate (ortho-P), total bound nitrogen (TNb), ammonium nitrogen (NH4-N), and nitrate nitrogen (NO3-N) were analyzed and are presented in this work. The results of the modules with agricultural residues are promising. Up to 92% COD reduction is stated in the data. The phosphate and nitrogen fractions are reduced significantly in these modules. By contrast, the modules with wood chips reduce only 67% of the incoming COD and respectively less regarding phosphates and the nitrogen fraction.
Aktuell findet aufgrund gesellschaftspolitischer Forderungen in vielen Industriezweigen ein Umdenken in Richtung Effizienz und Ökologie aber auch Digitalisierung und Industrie 4.0 statt. In dieser Hinsicht steht die Bauindustrie, im Vergleich zu Industrien wie IT, Automobil- oder Maschinenbau, noch am Anfang.
Dabei sind die Potentiale zur Einsparung und Optimierung gerade in der Bauindustrie aufgrund der großen Mengen an zu verarbeiteten Materialien besonders hoch. Die internationale Ressourcen- und Klimadebatte führt verstärkt dazu, dass auch in der Zement- und Betonherstellung neue Konzepte erstellt und geprüft werden. Einerseits erfolgt intensive Forschung und Entwicklung im Bereich alternativer, klimafreundlicher Zemente. Andererseits werden auch auf Seiten der Betonherstellung innovative materialsparende Konzepte geprüft, wie die aktuelle Entwicklung von 3D-Druck mit Beton zeigt.
Aufgrund der hohen Anforderungen an Konstruktion, Qualität und Langlebigkeit von Bauwerken, besitzen Betonfertigteile oftmals Vorteile gegenüber Ortbeton. Die hohe Oberflächenqualität und Dauerhaftigkeit aber auch die Gleichmäßigkeit und witterungsunabhängige Herstellung sind Merkmale, die im Zusammenhang mit Betonfertigteilen immer wieder erwähnt werden. Dabei ist es essenziell, dass auch der Betonherstellungsprozess im Fertigteilwerk kritisch hinterfragt wird, damit eine effizientere und nachhaltigere Produktion von Betonfertigteilen möglich wird.
Bei der Herstellung von Betonteilen im Fertigteilwerk liegt ein besonderer Fokus auf der Optimierung der Frühfestigkeitsentwicklung. Hohe Frühfestigkeiten sind Voraussetzung für einen hochfrequenten Schalungszyklus, was Arbeiten im 2- bzw. 3-Schichtbetrieb ermöglicht. Oft werden zur Sicherstellung hoher Frühfestigkeiten hochreaktive Zemente in Kombination mit hohen Zementgehalten im Beton und/oder einer Wärmebehandlung eingesetzt. Unter dieser Prämisse ist eine ökologisch nachhaltige Betonproduktion mit verminderter CO2 Bilanz nicht möglich.
In der vorliegenden Arbeit wird ein neues Verfahren zur Beschleunigung von Beton eingeführt. Hierbei werden die Bestandteile Zement und Wasser (Zementsuspension) mit Ultraschall vorbehandelt. Ausgangspunkt der Arbeit sind vorangegangene Untersuchungen zum Einfluss von Ultraschall auf die Hydration von Zement bzw. dessen Hauptbestandteil Tricalciumsilikat (C3S), die im Rahmen dieser Arbeit weiter vertieft werden. Darüber hinaus wird die Produktion von Beton mit Ultraschall im Technikumsmaßstab betrachtet. Die so erlangten Erfahrungen dienten dazu, das Ultraschall-Betonmischsystem weiterzuentwickeln und erstmalig zur industriellen Betonproduktion zu nutzen.
In der vorliegenden Arbeit werden die Auswirkungen von Ultraschall auf die Hydratation von C3S zunächst weitergehend und grundlegend untersucht. Dies erfolgte mittels Messung der elektrischen Leitfähigkeit, Analyse der Ionenkonzentration (ICP-OES), Thermoanalyse, Messung der BET-Oberfläche sowie einer optischen Auswertung mittels Rasterelektronenmikroskopie (REM). Der Fokus liegt auf den ersten Stunden der Hydratation, also der Zeit, die durch die Ultraschallbehandlung am stärksten beeinflusst wird.
In den Untersuchungen zeigt sich, dass die Beschleunigungswirkung von Ultraschall in verdünnten C3S Suspensionen (w/f-Wert = 50) stark von der Portlanditkonzentration der Lösung abhängt. Je niedriger die Portlanditkonzentration, desto größer ist die Beschleunigung. Ergänzende Untersuchungen der Ionenkonzentration der Lösung sowie Untersuchungen am hydratisierten C3S zeigen, dass unmittelbar nach der Beschallung (nach ca. 15 Minuten Hydratation) erste Hydratphasen vorliegen. Die durch Ultraschall initiiere Beschleunigung ist in den ersten 24 Stunden am stärksten und klingt dann sukzessive ab. Die Untersuchungen schließen mit Experimenten an C3S-Pasten (w/f-Wert = 0,50), die die Beobachtungen an den verdünnten Suspensionen bestätigen und infolge der Beschallung ein früheres Auftreten und einen größeren Anteil an C-S-H Phasen zeigen. Es wird gefolgert, dass die unmittelbar infolge von Ultraschall erzeugten C-S-H Phasen als Kristallisationskeim während der folgenden Reaktion dienen und daher Ultraschall als in-situ Keimbildungstechnik angesehen werden kann. Optisch zeigt sich, dass die C-S-H Phasen der beschallten Pasten nicht nur viel früher auftreten, sondern kleiner sind und fein verteilt über die Oberfläche des C3S vorliegen. Auch dieser Effekt wird als vorteilhaft für den sich anschließenden regulären Strukturaufbau angesehen.
Im nächsten Schritt wird daher der Untersuchungsfokus vom Modellsystem mit C3S auf Portlandzement erweitert. Hierbei wird der Frage nachgegangen, wie sich eine Änderung der Zusammensetzung der Zementsuspension (w/z-Wert, Fließmittelmenge) beziehungsweise eine Änderung des Ultraschallenergieeintrag auf die Fließeigenschaften und das Erhärtungsverhalten auswirken.
Um den Einfluss verschiedener Faktoren gleichzeitig zu betrachten, werden mit Hilfe von statistischen Versuchsplänen Modelle erstellt, die das Verhalten der einzelnen Faktoren beschreiben. Zur Beschreibung der Fließeigenschaften wurde das Setzfließ- und Ausbreitmaß von Zementsuspensionen herangezogen. Die Beschleunigung der Erhärtung wurde mit Hilfe der Ermittlung des Zeitpunkts des normalen Erstarrens der Zementsuspension bestimmt.
Die Ergebnisse dieser Untersuchungen zeigen deutlich, dass die Fließeigenschaften und der Erstarrungsbeginn nicht linear mit steigendem Ultraschall-Energieeintrag verändert werden. Es zeigt sich, dass es besonders bei den Verarbeitungseigenschaften der Portlandzementsuspensionen zur Ausbildung eines spezifischen Energieeintrages kommt, bis zu welchem das Setzfließ- und das Ausbreitmaß erhöht werden. Bei Überschreiten dieses Punktes, der als kritischer Energieeintrag definiert wurde, nimmt das Setzfließ- und Ausbreitmaß wieder ab. Das Auftreten dieses Punktes ist im besonderen Maße abhängig vom w/z-Wert. Mit sinkendem w/z-Wert wird der Energieeintrag, der eine Verbesserung der Fließeigenschaften hervorruft, reduziert. Bei sehr niedrigen w/z-Werten (< 0,35), kann keine Verbesserung mehr beobachtet werden.
Wird Fließmittel vor der Beschallung zur Zementsuspension zugegeben, können die Eigenschaften der Zementsuspension maßgeblich beeinflusst werden. In beschallten Suspensionen mit Fließmittel, konnte in Abhängigkeit des Energieeintrages die fließmittelbedingte Verzögerung des Erstarrungsbeginns deutlich reduziert werden. Weiterhin zeigt sich, dass der Energieeintrag, der notwendig ist um den Erstarrungsbeginn um einen festen Betrag zu reduzieren, bei Suspensionen mit Fließmittel deutlich reduziert ist.
Auf Grundlage der Beobachtungen an Zementsuspensionen wird der Einfluss von Ultraschall in einen dispergierenden und einen beschleunigenden Effekt unterteilt. Bei hohen w/z-Werten dominiert der dispergierende Einfluss von Ultraschall und der Erstarrungsbeginn wird moderat verkürzt. Bei niedrigeren w/z-Werten der Zementsuspension, dominiert der beschleunigende Effekt wobei kein oder sogar ein negativer Einfluss auf die Verarbeitungseigenschaften beobachtet werden kann.
Im nächsten Schritt werden die Untersuchungen auf den Betonmaßstab mit Hilfe einer Technikumsanlage erweitert und der Einfluss eines zweistufigen Mischens (also dem Herstellen einer Zementsuspension im ersten Schritt und dem darauffolgenden Vermischen mit der Gesteinskörnung im zweiten Schritt) mit Ultraschall auf die Frisch- und Festbetoneigenschaften betrachtet. Durch die Anlagentechnik, die mit der Beschallung größerer Mengen Zementsuspension einhergeht, kommen weitere Einflussfaktoren auf die Zementsuspension hinzu (z. B. Pumpgeschwindigkeit, Temperatur, Druck). Im Rahmen der Untersuchungen wurde eine Betonrezeptur mit und ohne Ultraschall hergestellt und die Frisch- und Festbetoneigenschaften verglichen. Darüber hinaus wurde ein umfangreiches Untersuchungsprogramm zur Ermittlung wesentlicher Dauerhaftigkeitsparameter durchgeführt. Aufbauend auf den Erfahrungen mit der Technikumsanlage wurde das Ultraschall-Vormischsystem in mehreren Stufen weiterentwickelt und abschließend in einem Betonwerk zur Betonproduktion verwendet.
Die Untersuchungen am Beton zeigen eine deutliche Steigerung der Frühdruckfestigkeiten des Portlandzementbetons. Hierbei kann die zum Entschalen von Betonbauteilen notwendige Druckfestigkeit von 15 MPa deutlich früher erreicht werden. Das Ausbreitmaß der Betone (w/z-Wert = 0,47) wird infolge der Beschallung leicht reduziert, was sich mit den Ergebnissen aus den Untersuchungen an reinen Zementsuspensionen deckt. Bei Applikation eines Überdruckes in der Beschallkammer oder einer Kühlung der Suspension während der Beschallung, kann das Ausbreitmaß leicht gesteigert werden. Allerdings werden die hohen Frühdruckfestigkeiten der ungekühlten beziehungsweise drucklosen Variante nicht mehr erreicht.
In den Untersuchungen kann gezeigt werden, dass das Potential durch die Ultraschall-Beschleunigung genutzt werden kann, um entweder die Festigkeitsklasse des Zementes leitungsneutral zu reduzieren (von CEM I 52,5 R auf CEM I 42,5 R) oder eine 4-stündige Wärmebehandlung vollständig zu substituieren. Die Dauerhaftigkeit der Betone wird dabei nicht negativ beeinflusst. In den Untersuchungen zum Sulfat-, Karbonatisierung-, Chlorideindring- oder Frost/Tauwiderstand kann weder ein positiver noch ein negativer Einfluss durch die Beschallung abgeleitet werden. Ebenso kann in einer Untersuchung zur Alkali-Kieselsäure-Reaktion kein negativer Einfluss durch die Ultraschallbehandlung beobachtet werden.
In den darauf aufbauenden Untersuchungen wird die Anlagentechnik weiterentwickelt, um die Ultraschallbehandlung stärker an eine reale Betonproduktion anzupassen. In der ersten Iterationsstufe wird das in den Betonuntersuchungen verwendete Anlagenkonzept 1 modifiziert (von der In-line-Beschallung zur Batch-Beschallung) und als Analgenkonzept 2 für weitere Untersuchungen genutzt. Hierbei wird eine neue Betonrezeptur mit höherem w/z-Wert (0,52) verwendet, wobei die Druckfestigkeiten ebenfalls deutlich gesteigert werden können. Im Gegensatz zum ersten Beton, wird das Ausbreitmaß dieser Betonzusammensetzung gesteigert, was zur Reduktion von Fließmittel genutzt wird. Dies deckt sich ebenfalls mit den Beobachtungen an reinen Portlandzementsuspensionen, wo eine deutliche Verbesserung der Fließfähigkeit bei höheren w/z-Werten beschrieben wird.
Für diese Betonrezeptur wird ein Vergleich mit einem kommerziell erhältlichen Erhärtungsbeschleuniger (synthetische C-S-H-Keime) angestellt. Hierbei zeigt sich, dass die Beschleunigungswirkung beider Technologien vergleichbar ist. Eine Kombination beider Technologien führt zu einer weiteren deutlichen Steigerung der Frühfestigkeiten, so dass hier von einem synergistischen Effekt ausgegangen werden kann.
In der letzten Iterationsstufe, dem Anlagenkonzept 3, wird beschrieben, wie das Mischsystem im Rahmen einer universitären Ausgründung signifikant weiterentwickelt wird und erstmals in einem Betonwerk zur Betonproduktion verwendet wird. Bei den Überlegungen zur Weiterentwicklung des Ultraschall-Mischsystems wird der Fokus auf die Praktikabilität gelegt und gezeigt, dass das ultraschallgestütze Mischsystem die Druckfestigkeitsentwicklung auch im Werksmaßstab deutlich beschleunigen kann. Damit ist die Voraussetzung für eine ökologisch nachhaltige Optimierung eines Fertigteilbetons unter realen Produktionsbedingungen geschaffen worden.
Inhaltlich beschäftigt sich die Arbeit, die im Rahmen des Promotionsstudiengangs Kunst und Gestaltung an der Bauhaus-Universität entstand, mit der Erforschung sozio-interaktiver Potentiale der Videotelefonie im Kontext von Nähe und Verbundenheit mit Fokus auf Eigenbild, Embodiment sowie den Rederechtswechsel.
Die Videotelefonie als Kommunikationsform hat sich – und darauf deuten die Erfahrungen der Co- vid-19-Pandemie hin – im lebensweltlichen Alltag der Menschen etabliert und wird dort in naher Zukunft nicht mehr wegzudenken sein. Auf Basis ihrer Möglichkeiten und Errungenschaften ist es inzwischen Realität und Lebenswirklichkeit, dass die Kommunikation sowohl im privaten als auch im geschäftlichen Kontext mittels verschiedenster Kanäle stattfindet. Der Videotelefonie kommt hierbei als solche nicht nur eine tragende Funktion, sondern auch eine herausragende Rolle bei der vermeintlichen Reproduktion der Face-to-Face-Kommunikation im digitalen Raum zu und wird wie selbstverständlich zum zwischenmenschlichen Austausch genutzt. Just an diesem Punkt knüpft die Forschungsarbeit an. Zentral stand dabei das Vorhaben einer dezidierte Untersuchung des Forschungsgegenstandes Videotelefonie, sowohl aus Kultur- als auch Technikhistorischer, aber auch Medien-, Wahrnehmungs- wie Kommunikations- theoretischer Perspektive, indem analytische und phänosemiotische Perspektiven miteinander in Beziehung gesetzt werden (z.B. Wahrnehmungsbedingungen, Interaktionsmerkmale, realisierte Kommunikationsprozesse etc.). Damit verbundenes, wünschenswertes Ziel war es, eine möglichst zeitgemäße wie relevante Forschungsfrage zu adressieren, die neben den kulturellen Technisierungs- und Mediatisierungstendenzen in institutionellen und privaten Milieus ebenfalls eine conditio sine qua non der pandemischen (Massen-)Kommunikation entwirft.
Die Arbeit ist damit vor allem im Bereich des Produkt- und Interactiondesigns zu verorten. Darüber hinaus hatte sie das Ziel der Darlegung und Begründung der Videotelefonie als eigenständige Kommunikationsform, welche durch eigene, kommunikative Besonderheiten, die sich in ihrer jeweiligen Ingebrauchnahme sowie durch spezielle Wahrnehmungsbedingungen äußern, und die die Videotelefonie als »Rederechtswechselmedium« avant la lettre konsolidieren, gekennzeichnet ist. Dabei sollte der Beweis erbracht werden, dass die Videotelefonie nicht als Schwundstufe einer Kommunikation Face-to-Face, sondern als ein eigenständiges Mediatisierungs- und Kommunikationsereignis zu verstehen sei. Und eben nicht als eine beliebige – sich linear vom Telefon ausgehende – entwickelte Form der audio-visuellen Fernkommunikation darstellt, sondern die gestalterische (Bewegtbild-)Technizität ein eigenständiges Funktionsmaß offeriert, welches wiederum ein innovatives Kommunikationsmilieu im Kontext einer Rederechtswechsel-Medialität stabilisiert.
The reduction of the cement clinker content is an important prerequisite for the improvement of the CO2-footprint of concrete. Nevertheless, the durability of such concretes must be sufficient to guarantee a satisfactory service life of structures. Salt frost scaling resistance is a critical factor in this regard, as it is often diminished at increased clinker substitution rates. Furthermore, only insufficient long-term experience for such concretes exists. A high salt frost scaling resistance thus cannot be achieved by applying only descriptive criteria, such as the concrete composition. It is therefore to be expected, that in the long term a performance based service life prediction will replace the descriptive concept.
To achieve the important goal of clinker reduction for concretes also in cold and temperate climates it is important to understand the underlying mechanisms for salt frost scaling. However, conflicting damage theories dominate the current State of the Art. It was consequently derived as the goal of this thesis to evaluate existing damage theories and to examine them experimentally. It was found that only two theories have the potential to describe the salt frost attack satisfactorily – the glue spall theory and the cryogenic suction theory.
The glue spall theory attributes the surface scaling to the interaction of an external ice layer with the concrete surface. Only when moderate amounts of deicing salt are present in the test solution the resulting mechanical properties of the ice can cause scaling. However, the results in this thesis indicate that severe scaling also occurs at deicing salt levels, at which the ice is much too soft to damage concrete. Thus, the inability of the glue spall theory to account for all aspects of salt frost scaling was shown.
The cryogenic suction theory is based on the eutectic behavior of salt solutions, which consist of two phases – water ice and liquid brine – between the freezing point and the eutectic temperature. The liquid brine acts as an additional moisture reservoir, which facilitates the growth of ice lenses in the surface layer of the concrete. The experiments in this thesis confirmed, that the ice formation in hardened cement paste increases due to the suction of brine at sub-zero temperatures. The extent of additional ice formation was influenced mainly by the porosity and by the chloride binding capacity of the hardened cement paste.
Consequently, the cryogenic suction theory plausibly describes the actual generation of scaling, but it has to be expanded by some crucial aspects to represent the salt frost scaling attack completely. The most important aspect is the intensive saturation process, which is ascribed to the so-called micro ice lens pump. Therefore a combined damage theory was proposed, which considers multiple saturation processes. Important aspects of this combined theory were confirmed experimentally.
As a result, the combined damage theory constitutes a good basis to understand the salt frost scaling attack on concrete on a fundamental level. Furthermore, a new approach was identified, to account for the reduced salt frost scaling resistance of concretes with reduced clinker content.
For the safe and efficient operation of dams, frequent monitoring and maintenance are required. These are usually expensive, time consuming, and cumbersome. To alleviate these issues, we propose applying a wave-based scheme for the location and quantification of damages in dams.
To obtain high-resolution “interpretable” images of the damaged regions, we drew inspiration from non-linear full-multigrid methods for inverse problems and applied a new cyclic multi-stage full-waveform inversion (FWI) scheme. Our approach is less susceptible to the stability issues faced by the standard FWI scheme when dealing with ill-posed problems. In this paper, we first selected an optimal acquisition setup and then applied synthetic data to demonstrate the capability of our approach in identifying a series of anomalies in dams by a mixture of reflection and transmission tomography. The results had sufficient robustness, showing the prospects of application in the field of non-destructive testing of dams.
A safe and economic structural design based on the semi-probabilistic concept requires statistically representative safety elements, such as characteristic values, design values, and partial safety factors. Regarding climate loads, the safety levels of current design codes strongly reflect experiences based on former measurements and investigations assuming stationary conditions, i.e. involving constant frequencies and intensities. However, due to climate change, occurrence of corresponding extreme weather events is expected to alter in the future influencing the reliability and safety of structures and their components. Based on established approaches, a systematically refined data-driven methodology for the determination of design parameters considering nonstationarity as well as standardized targets of structural reliability or safety, respectively, is therefore proposed. The presented procedure picks up fundamentals of European standardization and extends them with respect to nonstationarity by applying a shifting time window method. Taking projected snow loads into account, the application of the method is exemplarily demonstrated and various influencing parameters are discussed.
Finite Element Simulations of dynamically excited structures are mainly influenced by the mass, stiffness, and damping properties of the system, as well as external loads. The prediction quality of dynamic simulations of vibration-sensitive components depends significantly on the use of appropriate damping models. Damping phenomena have a decisive influence on the vibration amplitude and the frequencies of the vibrating structure. However, developing realistic damping models is challenging due to the multiple sources that cause energy dissipation, such as material damping, different types of friction, or various interactions with the environment.
This thesis focuses on thermoelastic damping, which is the main cause of material damping in homogeneous materials. The effect is caused by temperature changes due to mechanical strains. In vibrating structures, temperature gradients arise in adjacent tension and compression areas. Depending on the vibration frequency, they result in heat flows, leading to increased entropy and the irreversible transformation of mechanical energy into thermal energy.
The central objective of this thesis is the development of efficient simulation methods to incorporate thermoelastic damping in finite element analyses based on modal superposition. The thermoelastic loss factor is derived from the structure's mechanical mode shapes and eigenfrequencies. In subsequent analyses that are performed in the time and frequency domain, it is applied as modal damping.
Two approaches are developed to determine the thermoelastic loss in thin-walled plate structures, as well as three-dimensional solid structures. The realistic representation of the dissipation effects is verified by comparing the simulation results with experimentally determined data. Therefore, an experimental setup is developed to measure material damping, excluding other sources of energy dissipation.
The three-dimensional solid approach is based on the determination of the generated entropy and therefore the generated heat per vibration cycle, which is a measure for thermoelastic loss in relation to the total strain energy. For thin plate structures, the amount of bending energy in a modal deformation is calculated and summarized in the so-called Modal Bending Factor (MBF). The highest amount of thermoelastic loss occurs in the state of pure bending. Therefore, the MBF enables a quantitative classification of the mode shapes concerning the thermoelastic damping potential.
The results of the developed simulations are in good agreement with the experimental results and are appropriate to predict thermoelastic loss factors. Both approaches are based on modal superposition with the advantage of a high computational efficiency. Overall, the modeling of thermoelastic damping represents an important component in a comprehensive damping model, which is necessary to perform realistic simulations of vibration processes.
Design-related reassessment of structures integrating Bayesian updating of model safety factors
(2022)
In the semi-probabilistic approach of structural design, the partial safety factors are defined by considering some degree of uncertainties to actions and resistance, associated with the parameters’ stochastic nature. However, uncertainties for individual structures can be better examined by incorporating measurement data provided by sensors from an installed health monitoring scheme. In this context, the current study proposes an approach to revise the partial safety factor for existing structures on the action side, γE by integrating Bayesian model updating. A simple numerical example of a beam-like structure with artificially generated measurement data is used such that the influence of different sensor setups and data uncertainties on revising the safety factors can be investigated. It is revealed that the health monitoring system can reassess the current capacity reserve of the structure by updating the design safety factors, resulting in a better life cycle assessment of structures. The outcome is furthermore verified by analysing a real life small railway steel bridge ensuring the applicability of the proposed method to practical applications.
Bolted connections are widely employed in structures like transmission poles, wind turbines, and television (TV) towers. The behaviour of bolted connections is often complex and plays a significant role in the overall dynamic characteristics of the structure. The goal of this work is to conduct a fatigue lifecycle assessment of such a bolted connection block of a 193 m tall TV tower, for which 205 days of real measurement data have been obtained from the installed monitoring devices. Based on the recorded data, the best-fit stochastic wind distribution for 50 years, the decisive wind action, and the locations to carry out the fatigue analysis have been decided. A 3D beam model of the entire tower is developed to extract the nodal forces corresponding to the connection block location under various mean wind speeds, which is later coupled with a detailed complex finite element model of the connection block, with over three million degrees of freedom, for acquiring stress histories on some pre-selected bolts. The random stress histories are analysed using the rainflow counting algorithm (RCA) and the damage is estimated using Palmgren-Miner's damage accumulation law. A modification is proposed to integrate the loading sequence effect into the RCA, which otherwise is ignored, and the differences between the two RCAs are investigated in terms of the accumulated damage.
Material failure can be tackled by so-called nonlocal models, which introduce an intrinsic length scale into the formulation and, in the case of material failure, restore the well-posedness of the underlying boundary value problem or initial boundary value problem. Among nonlocal models, peridynamics (PD) has attracted a lot of attention as it allows the natural transition from continuum to discontinue and thus allows modeling of discrete cracks without the need to describe and track the crack topology, which has been a major obstacle in traditional discrete crack approaches. This is achieved by replacing the divergence of the Cauchy stress tensor through an integral over so-called bond forces, which account for the interaction of particles. A quasi-continuum approach is then used to calibrate the material parameters of the bond forces, i.e., equating the PD energy with the energy of a continuum. One major issue for the application of PD to general complex problems is that they are limited to fairly simple material behavior and pure mechanical problems based on explicit time integration. PD has been extended to other applications but losing simultaneously its simplicity and ease in modeling material failure. Furthermore, conventional PD suffers from instability and hourglass modes that require stabilization. It also requires the use of constant horizon sizes, which drastically reduces its computational efficiency. The latter issue was resolved by the so-called dual-horizon peridynamics (DH-PD) formulation and the introduction of the duality of horizons.
Within the nonlocal operator method (NOM), the concept of nonlocality is further extended and can be considered a generalization of DH-PD. Combined with the energy functionals of various physical models, the nonlocal forms based on the dual-support concept can be derived. In addition, the variation of the energy functional allows implicit formulations of the nonlocal theory. While traditional integral equations are formulated in an integral domain, the dual-support approaches are based on dual integral domains. One prominent feature of NOM is its compatibility with variational and weighted residual methods. The NOM yields a direct numerical implementation based on the weighted residual method for many physical problems without the need for shape functions. Only the definition of the energy or boundary value problem is needed to drastically facilitate the implementation. The nonlocal operator plays an equivalent role to the derivatives of the shape functions in meshless methods and finite element methods (FEM). Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease by a series of matrix multiplications. In addition, NOM can be used to derive many nonlocal models in strong form.
The principal contributions of this dissertation are the implementation and application of NOM, and also the development of approaches for dealing with fractures within the NOM, mostly for dynamic fractures. The primary coverage and results of the dissertation are as follows:
-The first/higher-order implicit NOM and explicit NOM, including a detailed description of the implementation, are presented. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combining with the method of weighted residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. For the sake of conciseness, the implementation in this chapter is focused on linear elastic solids only, though the NOM can handle more complex nonlinear problems. An explicit nonlocal operator method for the dynamic analysis of elasticity solid problems is also presented. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The explicit scheme comprises the Verlet-velocity algorithm. The NOM can be very flexible and efficient for solving partial differential equations (PDEs). It's also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Several numerical examples are presented to show the capabilities of this method.
-A nonlocal operator method for the dynamic analysis of (thin) Kirchhoff plates is proposed. The nonlocal Hessian operator is derived from a second-order Taylor series expansion. NOM is higher-order continuous, which is exploited for thin plate analysis that requires $C^1$ continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
-A nonlocal fracture modeling is developed and applied to the simulation of quasi-static and dynamic fractures using the NOM. The phase field's nonlocal weak and associated strong forms are derived from a variational principle. The NOM requires only the definition of energy. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems, while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.
The aim of this study is controlling of spurious oscillations developing around discontinuous solutions of both linear and non-linear wave equations or hyperbolic partial differential equations (PDEs). The equations include both first-order and second-order (wave) hyperbolic systems. In these systems even smooth initial conditions, or smoothly varying source (load) terms could lead to discontinuous propagating solutions (fronts). For the first order hyperbolic PDEs, the concept of central high resolution schemes is integrated with the multiresolution-based adaptation to capture properly both discontinuous propagating fronts and effects of fine-scale responses on those of larger scales in the multiscale manner. This integration leads to using central high resolution schemes on non-uniform grids; however, such simulation is unstable, as the central schemes are originally developed to work properly on uniform cells/grids. Hence, the main concern is stable collaboration of central schemes and multiresoltion-based cell adapters. Regarding central schemes, the considered approaches are: 1) Second order central and central-upwind schemes; 2) Third order central schemes; 3) Third and fourth order central weighted non-oscillatory schemes (central-WENO or CWENO); 4) Piece-wise parabolic methods (PPMs) obtained with two different local stencils. For these methods, corresponding (nonlinear) stability conditions are studied and modified, as well. Based on these stability conditions several limiters are modified/developed as follows: 1) Several second-order limiters with total variation diminishing (TVD) feature, 2) Second-order uniformly high order accurate non-oscillatory (UNO) limiters, 3) Two third-order nonlinear scaling limiters, 4) Two new limiters for PPMs. Numerical results show that adaptive solvers lead to cost-effective computations (e.g., in some 1-D problems, number of adapted grid points are less than 200 points during simulations, while in the uniform-grid case, to have the same accuracy, using of 2049 points is essential). Also, in some cases, it is confirmed that fine scale responses have considerable effects on higher scales.
In numerical simulation of nonlinear first order hyperbolic systems, the two main concerns are: convergence and uniqueness. The former is important due to developing of the spurious oscillations, the numerical dispersion and the numerical dissipation. Convergence in a numerical solution does not guarantee that it is the physical/real one (the uniqueness feature). Indeed, a nonlinear systems can converge to several numerical results (which mathematically all of them are true). In this work, the convergence and uniqueness are directly studied on non-uniform grids/cells by the concepts of local numerical truncation error and numerical entropy production, respectively. Also, both of these concepts have been used for cell/grid adaptations. So, the performance of these concepts is also compared by the multiresolution-based method. Several 1-D and 2-D numerical examples are examined to confirm the efficiency of the adaptive solver. Examples involve problems with convex and non-convex fluxes. In the latter case, due to developing of complex waves, proper capturing of real answers needs more attention. For this purpose, using of method-adaptation seems to be essential (in parallel to the cell/grid adaptation). This new type of adaptation is also performed in the framework of the multiresolution analysis.
Regarding second order hyperbolic PDEs (mechanical waves), the regularization concept is used to cure artificial (numerical) oscillation effects, especially for high-gradient or discontinuous solutions. There, oscillations are removed by the regularization concept acting as a post-processor. Simulations will be performed directly on the second-order form of wave equations. It should be mentioned that it is possible to rewrite second order wave equations as a system of first-order waves, and then simulated the new system by high resolution schemes. However, this approach ends to increasing of variable numbers (especially for 3D problems).
The numerical discretization is performed by the compact finite difference (FD) formulation with desire feature; e.g., methods with spectral-like or optimized-error properties. These FD methods are developed to handle high frequency waves (such as waves near earthquake sources). The performance of several regularization approaches is studied (both theoretically and numerically); at last, a proper regularization approach controlling the Gibbs phenomenon is recommended.
At the end, some numerical results are provided to confirm efficiency of numerical solvers enhanced by the regularization concept. In this part, shock-like responses due to local and abrupt changing of physical properties, and also stress wave propagation in stochastic-like domains are studied.
In this work, the degradation performance for the photocatalytic oxidation of eight micropollutants (amisulpride, benzotriazole, candesartan, carbamazepine, diclofenac, gabapentin, methlybenzotriazole, and metoprolol) within real secondary effluent was investigated using three different reactor designs. For all reactor types, the influence of irradiation power on its reaction rate and energetic efficiency was investigated. Flat cell and batch reactor showed almost similar substance specific degradation behavior. Within the immersion rotary body reactor, benzotriazole and methylbenzotriazole showed a significantly lower degradation affinity. The flat cell reactor achieved the highest mean degradation rate, with half time values ranging from 5 to 64 min with a mean of 18 min, due to its high catalysts surface to hydraulic volume ratio. The EE/O values were calculated for all micro-pollutants as well as the mean degradation rate constant of each experimental step. The lowest substance specific energy per order (EE/O) values of 5 kWh/m3 were measured for benzotriazole within the batch reactor. The batch reactor also reached the lowest mean values (11.8–15.9 kWh/m3) followed by the flat cell reactor (21.0–37.0 kWh/m3) and immersion rotary body reactor (23.9–41.0 kWh/m3). Catalyst arrangement and irradiation power were identified as major influences on the energetic performance of the reactors. Low radiation intensities as well as the use of submerged catalyst arrangement allowed a reduction in energy demand by a factor of 3–4. A treatment according to existing treatment goals of wastewater treatment plants (80% total degradation) was achieved using the batch reactor with a calculated energy demand of 7000 Wh/m3.
The Finite Element Method (FEM) is widely used in engineering for solving Partial Differential Equations (PDEs) over complex geometries. To this end, it is required to provide the FEM software with a geometric model that is typically constructed in a Computer-Aided Design (CAD) software. However, FEM and CAD use different approaches for the mathematical description of the geometry. Thus, it is required to generate a mesh, which is suitable for FEM, based on the CAD model. Nonetheless, this procedure is not a trivial task and it can be time consuming. This issue becomes more significant for solving shape and topology optimization problems, which consist in evolving the geometry iteratively. Therefore, the computational cost associated to the mesh generation process is increased exponentially for this type of applications.
The main goal of this work is to investigate the integration of CAD and CAE in shape and topology optimization. To this end, numerical tools that close the gap between design and analysis are presented. The specific objectives of this work are listed below:
• Automatize the sensitivity analysis in an isogeometric framework for applications in shape optimization. Applications for linear elasticity are considered.
• A methodology is developed for providing a direct link between the CAD model and the analysis mesh. In consequence, the sensitivity analysis can be performed in terms of the design variables located in the design model.
• The last objective is to develop an isogeometric method for shape and topological optimization. This method should take advantage of using Non-Uniform Rational B-Splines (NURBS) with higher continuity as basis functions.
Isogeometric Analysis (IGA) is a framework designed to integrate the design and analysis in engineering problems. The fundamental idea of IGA is to use the same basis functions for modeling the geometry, usually NURBS, for the approximation of the solution fields. The advantage of integrating design and analysis is two-fold. First, the analysis stage is more accurate since the system of PDEs is not solved using an approximated geometry, but the exact CAD model. Moreover, providing a direct link between the design and analysis discretizations makes possible the implementation of efficient sensitivity analysis methods. Second, the computational time is significantly reduced because the mesh generation process can be avoided.
Sensitivity analysis is essential for solving optimization problems when gradient-based optimization algorithms are employed. Automatic differentiation can compute exact gradients, automatically by tracking the algebraic operations performed on the design variables. For the automation of the sensitivity analysis, an isogeometric framework is used. Here, the analysis mesh is obtained after carrying out successive refinements, while retaining the coarse geometry for the domain design. An automatic differentiation (AD) toolbox is used to perform the sensitivity analysis. The AD toolbox takes the code for computing the objective and constraint functions as input. Then, using a source code transformation approach, it outputs a code for computing the objective and constraint functions, and their sensitivities as well. The sensitivities obtained from the sensitivity propagation method are compared with analytical sensitivities, which are computed using a full isogeometric approach.
The computational efficiency of AD is comparable to that of analytical sensitivities. However, the memory requirements are larger for AD. Therefore, AD is preferable if the memory requirements are satisfied. Automatic sensitivity analysis demonstrates its practicality since it simplifies the work of engineers and designers.
Complex geometries with sharp edges and/or holes cannot easily be described with NURBS. One solution is the use of unstructured meshes. Simplex-elements (triangles and tetrahedra for two and three dimensions respectively) are particularly useful since they can automatically parameterize a wide variety of domains. In this regard, unstructured Bézier elements, commonly used in CAD, can be employed for the exact modelling of CAD boundary representations. In two dimensions, the domain enclosed by NURBS curves is parameterized with Bézier triangles. To describe exactly the boundary of a two-dimensional CAD model, the continuity of a NURBS boundary representation is reduced to C^0. Then, the control points are used to generate a triangulation such that the boundary of the domain is identical to the initial CAD boundary representation. Thus, a direct link between the design and analysis discretizations is provided and the sensitivities can be propagated to the design domain.
In three dimensions, the initial CAD boundary representation is given as a collection of NURBS surfaces that enclose a volume. Using a mesh generator (Gmsh), a tetrahedral mesh is obtained. The original surface is reconstructed by modifying the location of the control points of the tetrahedral mesh using Bézier tetrahedral elements and a point inversion algorithm. This method offers the possibility of computing the sensitivity analysis using the analysis mesh. Then, the sensitivities can be propagated into the design discretization. To reuse the mesh originally generated, a moving Bézier tetrahedral mesh approach was implemented.
A gradient-based optimization algorithm is employed together with a sensitivity propagation procedure for the shape optimization cases. The proposed shape optimization approaches are used to solve some standard benchmark problems in structural mechanics. The results obtained show that the proposed approach can compute accurate gradients and evolve the geometry towards optimal solutions. In three dimensions, the moving mesh approach results in faster convergence in terms of computational time and avoids remeshing at each optimization step.
For considering topological changes in a CAD-based framework, an isogeometric phase-field based shape and topology optimization is developed. In this case, the diffuse interface of a phase-field variable over a design domain implicitly describes the boundaries of the geometry. The design variables are the local values of the phase-field variable. The descent direction to minimize the objective function is found by using the sensitivities of the objective function with respect to the design variables. The evolution of the phase-field is determined by solving the time dependent Allen-Cahn equation.
Especially for topology optimization problems that require C^1 continuity, such as for flexoelectric structures, the isogeometric phase field method is of great advantage. NURBS can achieve the desired continuity more efficiently than the traditional employed functions. The robustness of the method is demonstrated when applied to different geometries, boundary conditions, and material configurations. The applications illustrate that compared to piezoelectricity, the electrical performance of flexoelectric microbeams is larger under bending. In contrast, the electrical power for a structure under compression becomes larger with piezoelectricity.