Universitätsbibliothek
Weimar Open Access

Components of structural glazing have to meet different requirements and resist various impacts, depending on the field of application. Within an international research project of the EU innovation program Horizon 2020, special glass panes with a fluid circulating in capillaries are developed exploiting solar energy. Major influences to this glazing are UV irradiation and the fluidic contact, effecting the mechanical and optical durability of the bonding material within the glass setup. Regarding to visual requirements, acrylate adhesives and EVA films are analyzed as possible bonding materials by destructive and non-destructive testing methods. Two types of specimen are presented for obtaining the mechanical behavior and the surface appearances of the bonding material.

The p-Laplace equation is a nonlinear generalization of the well-known Laplace equation. It is often used as a model problem for special types of nonlinearities, and therefore it can be seen as a bridge between very general nonlinear equations and the linear Laplace equation, too. It appears in many problems for instance in the theory of non-Newtonian fluids and fluid dynamics or in rockfill dam problems, as well as in special problems of image restoration and image processing. The aim of this thesis is to solve the p-Laplace equation for 1 < p < 2, as well as for 2 < p < 3 and to find strong solutions in the framework of Clifford analysis. The idea is to apply a hypercomplex integral operator and special function theoretic methods to transform the p-Laplace equation into a p-Dirac equation. We consider boundary value problems for the p-Laplace equation and transfer them to boundary value problems for a p-Dirac equation. These equations will be solved iteratively by applying Banach’s fixed-point principle. Applying operator-theoretical methods for the p-Dirac equation, the existence and uniqueness of solutions in certain Sobolev spaces will be proved. In addition, using a finite difference approach on a uniform lattice in the plane, the fundamental solution of the Cauchy-Riemann operator and its adjoint based on the fundamental solution of the Laplacian will be calculated. Besides, we define gener- alized discrete Teodorescu transform operators, which are right-inverse to the discrete Cauchy-Riemann operator and its adjoint in the plane. Furthermore, a new formula for generalized discrete boundary operators (analogues of the Cauchy integral operator) will be considered. Based on these operators a new version of discrete Borel-Pompeiu formula is formulated and proved. This is the basis for an operator calculus that will be applied to the numerical solution of the p-Dirac equation. Finally, numerical results will be presented showing advantages and problems of this approach.

Spätestens seit dem Herbst 2015, als fluchtbedingte Migration nach Europa und Deutschland sich immens verstärkte, ist das Thema Flucht im öffentlichen Diskurs omnipräsent. Auch in der Forschung findet die Thematik in den letzten Jahren wieder mehr Beachtung. Wenig betrachtet wird bisher jedoch die Schnittstelle von Stadt- und Migrationsforschung, insbesondere in Bezug auf den öffentlichen Raum und geschlechtsspezifische Eigenheiten, die dabei zum Tragen kommen. An dieser Stelle knüpft die Arbeit an und versucht sich der Thematik über die Frage „Wie nutzen geflüchtete Frauen öffentliche Räume in der Stadt und wie nehmen sie diese wahr?“ anzunähern. Dafür wird zunächst aus soziologischer und raumtheoretischer Perspektive der Einfluss von Machtmechanismen, weiblicher Identität und Migrations- bzw. Fluchthintergrund auf die Wahrnehmung und Nutzung von Raum betrachtet. Anschließend wird mit Hilfe von qualitativen Expertinnen-Interviews sowie in Zusammenarbeit mit geflüchteten Frauen unter Anwendung der Methode der Mental-Maps und deren Auswertung am Beispiel von Weimar untersucht, welchen Stellenwert öffentlicher Raum im Alltag der Frauen einnimmt und wie dieser perzipiert wird. Hierbei stellt sich heraus, dass öffentliche Räume für die betrachtete Zielgruppe keine wesentliche Bedeutung haben und ihr Fokus vielmehr auf halbprivaten institutionalisierten Räumen liegt. Inwieweit dies eine Besonderheit für die Gruppe geflüchteter Frauen darstellt, könnte im Abgleich mit anderen Zielgruppen in weiteren Untersuchungen betrachtet werden.

Urban planners are often challenged with the task of developing design solutions which must meet multiple, and often contradictory, criteria. In this paper, we investigated the trade-offs between social, psychological, and energy potential of the fundamental elements of urban form: the street network and the building massing. Since formal mehods to evaluate urban form from the psychological and social point of view are not readily available, we developed a methodological framework to quantify these criteria as the first contribution in this paper. To evaluate the psychological potential, we conducted a three-tiered empirical study starting from real world environments and then abstracting them to virtual environments. In each context, the implicit (physiological) response and explicit (subjective) response of pedestrians were measured. To quantify the social potential, we developed a street network centrality-based measure of social accessibility. For the energy potential, we created an energy model to analyze the impact of pure geometric form on the energy demand of the building stock. The second contribution of this work is a method to identify distinct clusters of urban form and, for each, explore the trade-offs between the select design criteria. We applied this method to two case studies identifying nine types of urban form and their respective potential trade-offs, which are directly applicable for the assessment of strategic decisions regarding urban form during the early planning stages.

Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary. This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterisation is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications.