500 Naturwissenschaften und Mathematik
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- 2022 (17) (remove)
Hitze in der Stadt Jena
(2022)
Die vorliegende Arbeit befasst sich mit den spezifischen Faktoren und Wechselwirkungen des städtischen Klimas und Strategien zur Prävention und Kompensation lokaler Klimaveränderungen. Problematische Merkmale des Stadtklimas werden sich infolge des Klimawandels stärker ausprägen. Insbesondere die Hitzebelastung wird zunehmen und die Lebensbedingungen in der Stadt negativ beeinflussen. Infolge höherer Temperaturen in Städten und einer höheren Temperaturdifferenz zum Umland verändern sich Windströme und die Wasserbilanz. Es sind Strategien notwendig, um den Schadstoffausstoß, die Flächeninanspruchnahme, die Abfallproduktion und den Wasser-, Energie- und Ressourcenverbrauch zu verringern, um sowohl langfristig den Klimawandel als auch dessen bereits unvermeidbaren Auswirkungen auf Städte zu begrenzen.
Beispielhaft untersucht die Arbeit das Stadtklima, dessen zukünftige Veränderungen infolge des Klimawandels, bauliche Maßnahmen und Anpassungsstrategien der Stadt Jena. Jena ist die zweitgrößte Stadt im Bundesland Thüringen und gehört heute zu den wärmsten und trockensten Großstädten Deutschlands.
Die Ergebnisse der Arbeit werden anschließend anhand eines städtebaulichen Konzepts und Entwurfs angewendet. Das Bachstraßenareal liegt in der Innenstadt, dem am stärksten von Hitze betroffenen Stadtteil. Als ehemaliger Hauptstandort des Jenaer Universitätsklinikums, soll es zu einem nachhaltigen Wissenschaftscampus der Lebenswissenschaften umgebaut werden, wobei ein Großteil der denkmalgeschützten, ehemaligen Klinikgebäude erhalten bleibt. Der Fokus liegt dabei auf der Umsetzung der zuvor formulierten, nachhaltigen Strategien zur Verbesserung des lokalen Stadtklimas und einer Abschwächung der Auswirkungen des Klimawandels auf den besonders stark betroffenen Innenstadtbereich Jenas.
Tropical coral reefs, one of the world’s oldest ecosystems which support some of the highest levels of biodiversity on the planet, are currently facing an unprecedented ecological crisis during this massive human-activity-induced period of extinction. Hence, tropical reefs symbolically stand for the destructive effects of human activities on nature [4], [5]. Artificial reefs are excellent examples of how architectural design can be combined with ecosystem regeneration [6], [7], [8]. However, to work at the interface between the artificial and the complex and temporal nature of natural systems presents a challenge, i.a. in respect to the B-rep modelling legacy of computational modelling.
The presented doctorate investigates strategies on how to apply digital practice to realise what is an essential bulwark to retain reefs in impossibly challenging times. Beyond the main question of integrating computational modelling and high precision monitoring strategies in artificial coral reef design, this doctorate explores techniques, methods, and linking frameworks to support future research and practice in ecology led design contexts.
Considering the many existing approaches for artificial coral reefs design, one finds they often fall short in precisely understanding the relationships between architectural and ecological aspects (e.g. how a surface design and material composition can foster coral larvae settlement, or structural three-dimensionality enhance biodiversity) and lack an integrated underwater (UW) monitoring process. Such a process is necessary in order to gather knowledge about the ecosystem and make it available for design, and to learn whether artificial structures contribute to reef regeneration or rather harm the coral reef ecosystem.
For the research, empirical experimental methods were applied: Algorithmic coral reef design, high precision UW monitoring, computational modelling and simulation, and validated through parallel real-world physical experimentation – two Artificial Reef Prototypes (ARPs) in Gili Trawangan, Indonesia (2012–today). Multiple discrete methods and sub techniques were developed in seventeen computational experiments and applied in a way in which many are cross valid and integrated in an overall framework that is offered as a significant contribution to the field. Other main contributions include the Ecosystem-aware design approach, Key Performance Indicators (KPIs) for coral reef design, algorithmic design and fabrication of Biorock cathodes, new high precision UW monitoring strategies, long-term real-world constructed experiments, new digital analysis methods and two new front-end web-based tools for reef design and monitoring reefs. The methodological framework is a finding of the research that has many technical components that were tested and combined in this way for the very first time.
In summary, the thesis responds to the urgency and relevance in preserving marine species in tropical reefs during this massive extinction period by offering a differentiated approach towards artificial coral reefs – demonstrating the feasibility of digitally designing such ‘living architecture’ according to multiple context and performance parameters. It also provides an in-depth critical discussion of computational design and architecture in the context of ecosystem regeneration and Planetary Thinking. In that respect, the thesis functions as both theoretical and practical background for computational design, ecology and marine conservation – not only to foster the design of artificial coral reefs technically but also to provide essential criteria and techniques for conceiving them.
Keywords: Artificial coral reefs, computational modelling, high precision underwater monitoring, ecology in design.
Im Rahmen dieser Arbeit wird das Charakterisieren struktureller Veränderungen zementgebundener Baustoffe durch zwei auf dem Ultraschall-Transmissionsverfahren beruhenden Methoden der zerstörungsfreien Prüfung (ZfP) mit mechanischen Wellen vorgenommen.
Zur kontinuierlichen Charakterisierung der Erstarrung und Erhärtung frischer zementgebundener Systeme wird ein auf Ultraschallsensoren für Longitudinal- und Scherwellen basierendes Messsystem in Kombination mit zugehörigen Verfahrensweisen zur Datenauswertung konzipiert, charakterisiert und angewandt. Gegenüber der bislang üblichen alleinigen Bewertung der Verfestigung anhand indirekter Ultraschallparameter wie Ausbreitungsgeschwindigkeit, Signalenergie oder Frequenzgehalt der Longitudinalwelle lässt sich damit eine direkte, sensible Erfassung der sich während der Strukturbildung entwickelnden dynamischen elastischen Eigenschaften auf der Basis primärer physikalischer Werkstoffparameter erreichen. Insbesondere Scherwellen und der dynamische Schubmodul sind geeignet, den graduellen Übergang zum Festkörper mit Überschreiten der Perkolationsschwelle sensibel und unabhängig vom Luftgehalt zu erfassen. Die zeitliche Entwicklung der dynamischen elastischen Eigenschaften, die Strukturbildungsraten sowie die daraus extrahierten diskreten Ergebnisparameter ermöglichen eine vergleichende quantitative Charakterisierung der Strukturbildung zementgebundener Baustoffe aus mechanischer Sicht. Dabei lassen sich typische, oft unvermeidbare Unterschiede in der Zusammensetzung der Versuchsmischungen berücksichtigen.
Der Einsatz laserbasierter Methoden zur Anregung und Erfassung von mechanischen Wellen und deren Kombination zu Laser-Ultraschall zielt darauf ab, die mit der Anwendung des konventionellen Ultraschall-Transmissionsverfahrens verbundenen Nachteile zu eliminieren. Diese resultieren aus der Sensorgeometrie, der mechanischen Ankopplung und bei einer Vielzahl von Oberflächenpunkten aus einem hohen prüftechnischen Aufwand. Die laserbasierte, interferometrische Erfassung mechanischer Wellen ist gegenüber Ultraschallsensoren rauschbehaftet und vergleichsweise unsensibel. Als wesentliche Voraussetzung der scannenden Anwendung von Laser-Ultraschall auf zementgebundene Baustoffe erfolgen systematische experimentelle Untersuchungen zur laserinduzierten ablativen Anregung. Diese sollen zum Verständnis des Anregungsmechanismus unmittelbar auf den Oberflächen von zementgebundenen Baustoffen, Gesteinskörnungen und metallischen Werkstoffen beitragen, relevante Einflussfaktoren aus den charakteristischen Materialeigenschaften identifizieren, geeignete Prozessparameter gewinnen und die Verfahrensgrenzen aufzeigen. Unter Einsatz von Longitudinalwellen erfolgt die Anwendung von Laser-Ultraschall zur zeit- und ortsaufgelösten Charakterisierung der Strukturbildung und Homogenität frischer sowie erhärteter Proben zementgebundener Baustoffe. Während der Strukturbildung wird erstmals eine simultane berührungslose Erfassung von Longitudinal- und Scherwellen vorgenommen. Unter Anwendung von tomographischen Methoden (2D-Laufzeit¬tomo¬graphie) werden überlagerungsfreie Informationen zur räumlichen Verteilung struktureller Gefügeveränderungen anhand der longitudinalen Ausbreitungsgeschwindigkeit bzw. des relativen dynamischen Elastizitätsmoduls innerhalb von virtuellen Schnittebenen geschädigter Probekörper gewonnen. Als beton-schädigende Mechanismen werden exemplarisch der kombinierte Frost-Tausalz-Angriff sowie die Alkali-Kieselsäure-Reaktion (AKR) herangezogen.
Die im Rahmen dieser Arbeit entwickelten Verfahren der zerstörungsfreien Prüfung bieten erweiterte Möglichkeiten zur Charakterisierung zementgebundener Baustoffe und deren strukturellen Veränderungen und lassen sich zielgerichtet in der Werkstoffentwicklung, bei der Qualitätssicherung sowie zur Analyse von Schadensprozessen und -ursachen einsetzen.
In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as ’classical’ approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 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 the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.
The detailed structural analysis of thin-walled circular pipe members often requires the use of a shell or solid-based finite element method. Although these methods provide a very good approximation of the deformations, they require a higher degree of discretization which causes high computational costs. On the other hand, the analysis of thin-walled circular pipe members based on classical beam theories is easy to implement and needs much less computation time, however, they are limited in their ability to approximate the deformations as they cannot consider the deformation of the cross-section.
This dissertation focuses on the study of the Generalized Beam Theory (GBT) which is both accurate and efficient in analyzing thin-walled members. This theory is based on the separation of variables in which the displacement field is expressed as a combination of predetermined deformation modes related to the cross-section, and unknown amplitude functions defined on the beam's longitudinal axis. Although the GBT was initially developed for long straight members, through the consideration of complementary deformation modes, which amend the null transverse and shear membrane strain assumptions of the classical GBT, problems involving short members, pipe bends, and geometrical nonlinearity can also be analyzed using GBT. In this dissertation, the GBT formulation for the analysis of these problems is developed and the application and capabilities of the method are illustrated using several numerical examples. Furthermore, the displacement and stress field results of these examples are verified using an equivalent refined shell-based finite element model.
The developed static and dynamic GBT formulations for curved thin-walled circular pipes are based on the linear kinematic description of the curved shell theory. In these formulations, the complex problem in pipe bends due to the strong coupling effect of the longitudinal bending, warping and the cross-sectional ovalization is handled precisely through the derivation of the coupling tensors between the considered GBT deformation modes. Similarly, the geometrically nonlinear GBT analysis is formulated for thin-walled circular pipes based on the nonlinear membrane kinematic equations. Here, the initial linear and quadratic stress and displacement tangent stiffness matrices are built using the third and fourth-order GBT deformation mode coupling tensors.
Longitudinally, the formulation of the coupled GBT element stiffness and mass matrices are presented using a beam-based finite element formulation. Furthermore, the formulated GBT elements are tested for shear and membrane locking problems and the limitations of the formulations regarding the membrane locking problem are discussed.
Isogeometric analysis (IGA) is a numerical method for solving partial differential equations (PDEs), which was introduced with the aim of integrating finite element analysis with computer-aided design systems. The main idea of the method is to use the same spline basis functions which describe the geometry in CAD systems for the approximation of solution fields in the finite element method (FEM). Originally, NURBS which is a standard technology employed in CAD systems was adopted as basis functions in IGA but there were several variants of IGA using other technologies such as T-splines, PHT splines, and subdivision surfaces as basis functions. In general, IGA offers two key advantages over classical FEM: (i) by describing the CAD geometry exactly using smooth, high-order spline functions, the mesh generation process is simplified and the interoperability between CAD and FEM is improved, (ii) IGA can be viewed as a high-order finite element method which offers basis functions with high inter-element continuity and therefore can provide a primal variational formulation of high-order PDEs in a straightforward fashion. The main goal of this thesis is to further advance isogeometric analysis by exploiting these major advantages, namely precise geometric modeling and the use of smooth high-order splines as basis functions, and develop robust computational methods for problems with complex geometry and/or complex multi-physics.
As the first contribution of this thesis, we leverage the precise geometric modeling of isogeometric analysis and propose a new method for its coupling with meshfree discretizations. We exploit the strengths of both methods by using IGA to provide a smooth, geometrically-exact surface discretization of the problem domain boundary, while the Reproducing Kernel Particle Method (RKPM) discretization is used to provide the volumetric discretization of the domain interior. The coupling strategy is based upon the higher-order consistency or reproducing conditions that are directly imposed in the physical domain. The resulting coupled method enjoys several favorable features: (i) it preserves the geometric exactness of IGA, (ii) it circumvents the need for global volumetric parameterization of the problem domain, (iii) it achieves arbitrary-order approximation accuracy while preserving higher-order smoothness of the discretization. Several numerical examples are solved to show the optimal convergence properties of the coupled IGA–RKPM formulation, and to demonstrate its effectiveness in constructing volumetric discretizations for complex-geometry objects.
As for the next contribution, we exploit the use of smooth, high-order spline basis functions in IGA to solve high-order surface PDEs governing the morphological evolution of vesicles. These governing equations are often consisted of geometric PDEs, high-order PDEs on stationary or evolving surfaces, or a combination of them. We propose an isogeometric formulation for solving these PDEs. In the context of geometric PDEs, we consider phase-field approximations of mean curvature flow and Willmore flow problems and numerically study the convergence behavior of isogeometric analysis for these problems. As a model problem for high-order PDEs on stationary surfaces, we consider the Cahn–Hilliard equation on a sphere, where the surface is modeled using a phase-field approach. As for the high-order PDEs on evolving surfaces, a phase-field model of a deforming multi-component vesicle, which consists of two fourth-order nonlinear PDEs, is solved using the isogeometric analysis in a primal variational framework. Through several numerical examples in 2D, 3D and axisymmetric 3D settings, we show the robustness of IGA for solving the considered phase-field models.
Finally, we present a monolithic, implicit formulation based on isogeometric analysis and generalized-alpha time integration for simulating hydrodynamics of vesicles according to a phase-field model. Compared to earlier works, the number of equations of the phase-field model which need to be solved is reduced by leveraging high continuity of NURBS functions, and the algorithm is extended to 3D settings. We use residual-based variational multi-scale method (RBVMS) for solving Navier–Stokes equations, while the rest of PDEs in the phase-field model are treated using a standard Galerkin-based IGA. We introduce the resistive immersed surface (RIS) method into the formulation which can be employed for an implicit description of complex geometries using a diffuse-interface approach. The implementation highlights the robustness of the RBVMS method for Navier–Stokes equations of incompressible flows with non-trivial localized forcing terms including bending and tension forces of the vesicle. The potential of the phase-field model and isogeometric analysis for accurate simulation of a variety of fluid-vesicle interaction problems in 2D and 3D is demonstrated.