Universitätsbibliothek
Weimar Open Access

In the last two decades, Peridynamics (PD) attracts much attention in the field of fracture mechanics. One key feature of PD is the nonlocality, which is quite different from the ideas in conventional methods such as FEM and meshless method. However, conventional PD suffers from problems such as constant horizon, explicit algorithm, hourglass mode. In this thesis, by examining the nonlocality with scrutiny, we proposed several new concepts such as dual-horizon (DH) in PD, dual-support (DS) in smoothed particle hydrodynamics (SPH), nonlocal operators and operator energy functional. The conventional PD (SPH) is incorporated in the DH-PD (DS-SPH), which can adopt an inhomogeneous discretization and inhomogeneous support domains. The DH-PD (DS-SPH) can be viewed as some fundamental improvement on the conventional PD (SPH). Dual formulation of PD and SPH allows h-adaptivity while satisfying the conservations of linear momentum, angular momentum and energy. By developing the concept of nonlocality further, we introduced the nonlocal operator method as a generalization of DH-PD. Combined with energy functional of various physical models, the nonlocal forms based on dual-support concept are derived. In addition, the variation of the energy functional allows implicit formulation of the nonlocal theory. At last, we developed the higher order nonlocal operator method which is capable of solving higher order partial differential equations on arbitrary domain in higher dimensional space. Since the concepts are developed gradually, we described our findings chronologically. In chapter 2, we developed a DH-PD formulation that includes varying horizon sizes and solves the "ghost force" issue. The concept of dual-horizon considers the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly with arbitrary particle discretization. All three peridynamic formulations, namely bond based, ordinary state based and non-ordinary state based peridynamics can be implemented within the DH-PD framework. A simple adaptive refinement procedure (h-adaptivity) is proposed reducing the computational cost. Both two- and three- dimensional examples including the Kalthoff-Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. In chapter 3, a nonlocal operator method (NOM) based on the variational principle is proposed for the solution of waveguide problem in computational electromagnetic field. Common differential operators as well as the variational forms are defined within the context of nonlocal operators. The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease, which is necessary for the eigenvalue analysis of the waveguide problem. The present formulation is applied to solve 1D Schrodinger equation, 2D electrostatic problem and the differential electromagnetic vector wave equations based on electric fields. In chapter 4, a general nonlocal operator method is proposed which is applicable for solving partial differential equations (PDEs) of mechanical problems. The nonlocal operator can be regarded as the integral form, ``equivalent'' to the differential form in the sense of a nonlocal interaction model. The variation of a nonlocal operator plays an equivalent role as the derivatives of the shape functions in the meshless methods or those of the finite element method. Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease. The nonlocal operator method is enhanced here also with an operator energy functional to satisfy the linear consistency of the field. A highlight of the present method is the functional derived based on the nonlocal operator can convert the construction of residual and stiffness matrix into a series of matrix multiplications using the predefined nonlocal operators. The nonlocal strong forms of different functionals can be obtained easily via the concept of support and dual-support. Several numerical examples of different types of PDEs are presented. In chapter 5, we extended the NOM to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original NOM in chapter 3 and chapter 4, which can only achieve one-order convergence. The higher order NOM obtains all partial derivatives with specified maximal order simultaneously without resorting to shape functions. The functional based on the nonlocal operators converts the construction of residual and stiffness matrix into a series of matrix multiplication on the nonlocal operator matrix. Several numerical examples solved by strong form or weak form are presented to show the capabilities of this method. In chapter 6, the NOM proposed as a particle-based method in chapter 3,4,5, has difficulty in imposing accurately the boundary conditions of various orders. In this paper, we converted the particle-based NOM into a scheme with interpolation property. The new scheme describes partial derivatives of various orders at a point by the nodes in the support and takes advantage of the background mesh for numerical integration. The boundary conditions are enforced via the modified variational principle. The particle-based NOM can be viewed a special case of NOM with interpolation property when nodal integration is used. The scheme based on numerical integration greatly improves the stability of the method, as a consequence, the operator energy functional in particle-based NOM is not required. We demonstrated the capabilities of current method by solving the gradient solid problems and comparing the numerical results with the available exact solutions. In chapter 7, we derived the DS-SPH in solid within the framework of variational principle. The tangent stiffness matrix of SPH can be obtained with ease, and can be served as the basis for the present implicit SPH. We proposed an hourglass energy functional, which allows the direct derivation of hourglass force and hourglass tangent stiffness matrix. The dual-support is {involved} in all derivations based on variational principles and is automatically satisfied in the assembling of stiffness matrix. The implementation of stiffness matrix comprises with two steps, the nodal assembly based on deformation gradient and global assembly on all nodes. Several numerical examples are presented to validate the method.

This dissertation investigates the interactions between urban form, allocation of activities, and pedestrian movement in the context of urban planning. The ability to assess the long-term impact of urban planning decisions on what people do and how they get there is of central importance, with various disciplines addressing this topic. This study focuses on approaches proposed by urban morphologists, urban economists, and transportation planners, each aiming the attention at a different part of the form-activity-movement interaction. Even though there is no doubt about the advantages of these highly focused approaches, it remains unclear what is the cost of ignoring the effect of some interactions while considering others. The general aim of this dissertation is to empirically test the validity of the individual models and quantify the impact of this isolationist approach on their precision and bias. For this purpose, we propose a joined form-activity-movement interaction model and conduct an empirical study in Weimar, Germany. We estimate how the urban form and activities affect movement as well as how movement and urban form affect activities. By estimating these effects in isolation and simultaneously, we assess the bias of the individual models. On the one hand, the empirical study results confirm the significance of all interactions suggested by the individual models. On the other hand, we were able to show that when these interactions are estimated in isolation, the resulting predictions are biased. To conclude, we do not question the knowledge brought by transportation planners, urban morphologists, and urban economists. However, we argue that it might be of little use on its own. We see the relevance of this study as being twofold. On the one hand, we proposed a novel methodological framework for the simultaneous estimation of the form-activity-movement interactions. On the other hand, we provide empirical evidence about the strengths and limitations of current approaches.

Die Corona-Krise hat die Erosion städtischer Solidarität offen zu Tage treten lassen. Dagegen bringen Anton Brokow-Loga und Frank Eckardt in dieser Schrift die praktische Utopie einer solidarischen Postwachstumsstadt „auf den Punkt“. Vom Commoning über die Umverteilung der städtischen Flächen bis zu einer sozial-ökologischen Verkehrswende: Eine progressive Stadtpolitik für alle überwindet bisheriges Schubladendenken. Sie setzt stattdessen auf heterogene Zusammenhänge und ungewöhnliche Bündnisse. Zu dem hier umrissenen Vorhaben gehört auch, eine basisdemokratisch orientierte Stadtpolitik mit dem Ziel einer umfassenden Transformation von Stadt und Gesellschaft zu verknüpfen. Wie kann ein Blick auf die kommunale Ebene helfen, globalen Ungerechtigkeiten zu begegnen? Welchen Weg weisen munizipalistische Plattformen und Vergemeinschaftungen jenseits von Privat- oder Staatseigentum?

Housing estates were fundamentally conceived upon state socialist utopia ideas to provide standard housing for citizens. While former state socialist housing estates have been extensively researched in the field of architecture, urban and sociology studies, there is still a gap in identifying how production processes affect morphological changes during the post-socialist era. This thesis compares the processes in the production of the largest housing estates of Marzahn in GDR and Petržalka in Czechoslovakia from 1970 to 1989 through contextual analysis of primary and secondary sources, which include visual maps, diagrams from professional architecture and planning journals, government documents and textbooks, as well as academic journals, books and newspaper articles. Then it discusses how these processes inadvertently created conducive conditions affecting their development in the market economy after 1989. It then interprets the results through application of Actor-Network Theory and Historical Institutionalism, while conceptualising them through David Harvey’s dialectical utopianism theory. Harvey (2000) delineates two types of utopia, one of spatial form and one of process. The former refers to materialised ideals in physical forms whereas the latter refers to the ongoing process of spatializing. The thesis aims to show how the production of Marzahn in GDR was more path dependent on policies established in 1950s and 1960s whereas Petržalka was a product of new Czechoslovakian policies in 1970s, changing aspects of the urban planning process, a manifestation of a more emphatic technocratic thinking on a wider scale. This ultimately influences the trajectories of development after 1989, showing more effects in Petržalka.

Complex vortex flow patterns around bridge piers, especially during floods, cause scour process that can result in the failure of foundations. Abutment scour is a complex three-dimensional phenomenon that is difficult to predict especially with traditional formulas obtained using empirical approaches such as regressions. This paper presents a test of a standalone Kstar model with five novel hybrid algorithm of bagging (BA-Kstar), dagging (DA-Kstar), random committee (RC-Kstar), random subspace (RS-Kstar), and weighted instance handler wrapper (WIHWKstar) to predict scour depth (ds) for clear water condition. The dataset consists of 99 scour depth data from flume experiments (Dey and Barbhuiya, 2005) using abutment shapes such as vertical, semicircular and 45◦ wing. Four dimensionless parameter of relative flow depth (h/l), excess abutment Froude number (Fe), relative sediment size (d50/l) and relative submergence (d50/h) were considered for the prediction of relative scour depth (ds/l). A portion of the dataset was used for the calibration (70%), and the remaining used for model validation. Pearson correlation coefficients helped deciding relevance of the input parameters combination and finally four different combinations of input parameters were used. The performance of the models was assessed visually and with quantitative metrics. Overall, the best input combination for vertical abutment shape is the combination of Fe, d50/l and h/l, while for semicircular and 45◦ wing the combination of the Fe and d50/l is the most effective input parameter combination. Our results show that incorporating Fe, d50/l and h/l lead to higher performance while involving d50/h reduced the models prediction power for vertical abutment shape and for semicircular and 45◦ wing involving h/l and d50/h lead to more error. The WIHW-Kstar provided the highest performance in scour depth prediction around vertical abutment shape while RC-Kstar model outperform of other models for scour depth prediction around semicircular and 45◦ wing.