@phdthesis{Ashour,
  author    = {Ashour, Mohammed},
  title     = {Electromechanics and Hydrodynamics of Single Vesicles and Vesicle Doublet Using Phase-Field Isogeometric Analysis},
  doi       = {10.25643/bauhaus-universitaet.6400},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230628-64003},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {175},
  abstract  = {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.},
  subject      = {Isogeometrische Analyse},
  language  = {en}
}
@phdthesis{Chawdhury,
  author    = {Chawdhury, Samir},
  title     = {Partitioned Algorithms using Vortex Particle Methods for Fluid-Structure Interaction of Thin-walled Flexible Structures},
  publisher = {arts + science weimar GmbH},
  address   = {Weimar},
  isbn      = {978-3-95773-297-2},
  doi       = {10.25643/bauhaus-universitaet.6404},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230703-64042},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {256},
  abstract  = {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.},
  subject      = {Windenergie},
  language  = {en}
}
@phdthesis{Held,
  author    = {Held, Tobias},
  title     = {Einblick: Gestalterische Potentiale und Perspektiven der Videotelefonie im Kontext von N{\"a}he und Distanz. Eine praxis-basierte, (re-)kontextualisierende und diskursanalytische Studie.},
  doi       = {10.25643/bauhaus-universitaet.4886},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230111-48867},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {534},
  abstract  = {Inhaltlich besch{\"a}ftigt sich die Arbeit, die im Rahmen des Promotionsstudiengangs Kunst und Gestaltung an der Bauhaus-Universit{\"a}t entstand, mit der Erforschung sozio-interaktiver Potentiale der Videotelefonie im Kontext von N{\"a}he 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 M{\"o}glichkeiten und Errungenschaften ist es inzwischen Realit{\"a}t und Lebenswirklichkeit, dass die Kommunikation sowohl im privaten als auch im gesch{\"a}ftlichen Kontext mittels verschiedenster Kan{\"a}le 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 selbstverst{\"a}ndlich zum zwischenmenschlichen Austausch genutzt. Just an diesem Punkt kn{\"u}pft 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 ph{\"a}nosemiotische Perspektiven miteinander in Beziehung gesetzt werden (z.B. Wahrnehmungsbedingungen, Interaktionsmerkmale, realisierte Kommunikationsprozesse etc.). Damit verbundenes, w{\"u}nschenswertes Ziel war es, eine m{\"o}glichst zeitgem{\"a}ße 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. Dar{\"u}ber hinaus hatte sie das Ziel der Darlegung und Begr{\"u}ndung der Videotelefonie als eigenst{\"a}ndige Kommunikationsform, welche durch eigene, kommunikative Besonderheiten, die sich in ihrer jeweiligen Ingebrauchnahme sowie durch spezielle Wahrnehmungsbedingungen {\"a}ußern, 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 eigenst{\"a}ndiges 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-)Technizit{\"a}t ein eigenst{\"a}ndiges Funktionsmaß offeriert, welches wiederum ein innovatives Kommunikationsmilieu im Kontext einer Rederechtswechsel-Medialit{\"a}t stabilisiert.},
  subject      = {Videotelefonie},
  language  = {de}
}
@phdthesis{Haefner2006,
  author    = {H{\"a}fner, Stefan},
  title     = {Grid-based procedures for the mechanical analysis of heterogeneous solids},
  doi       = {10.25643/bauhaus-universitaet.858},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20070830-9185},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2006},
  abstract  = {The importance of modern simulation methods in the mechanical analysis of heterogeneous solids is presented in detail. Thereby the problem is noted that even for small bodies the required high-resolution analysis reaches the limits of today's computational power, in terms of memory demand as well as acceptable computational effort. A further problem is that frequently the accuracy of geometrical modelling of heterogeneous bodies is inadequate. The present work introduces a systematic combination and adaption of grid-based methods for achieving an essentially higher resolution in the numerical analysis of heterogeneous solids. Grid-based methods are as well primely suited for developing efficient and numerically stable algorithms for flexible geometrical modeling. A key aspect is the uniform data management for a grid, which can be utilized to reduce the effort and complexity of almost all concerned methods. A new finite element program, called Mulgrido, was just developed to realize this concept consistently and to test the proposed methods. Several disadvantages which generally result from grid discretizations are selectively corrected by modified methods. The present work is structured into a geometrical model, a mechanical model and a numerical model. The geometrical model includes digital image-based modeling and in particular several methods for the theory-based generation of inclusion-matrix models. Essential contributions refer to variable shape, size distribution, separation checks and placement procedures of inclusions. The mechanical model prepares the fundamentals of continuum mechanics, homogenization and damage modeling for the following numerical methods. The first topic of the numerical model introduces to a special version of B-spline finite elements. These finite elements are entirely variable in the order k of B-splines. For homogeneous bodies this means that the approximation quality can arbitrarily be scaled. In addition, the multiphase finite element concept in combination with transition zones along material interfaces yields a valuable solution for heterogeneous bodies. As the formulation is element-based, the storage of a global stiffness matrix is superseded such that the memory demand can essentially be reduced. This is possible in combination with iterative solver methods which represent the second topic of the numerical model. Here, the focus lies on multigrid methods where the number of required operations to solve a linear equation system only increases linearly with problem size. Moreover, for badly conditioned problems quite an essential improvement is achieved by preconditioning. The third part of the numerical model discusses certain aspects of damage simulation which are closely related to the proposed grid discretization. The strong efficiency of the linear analysis can be maintained for damage simulation. This is achieved by a damage-controlled sequentially linear iteration scheme. Finally a study on the effective material behavior of heterogeneous bodies is presented. Especially the influence of inclusion shapes is examined. By means of altogether more than one hundred thousand random geometrical arrangements, the effective material behavior is statistically analyzed and assessed.},
  subject      = {B-Spline},
  language  = {en}
}
@phdthesis{LopezZermeno,
  author    = {L{\´o}pez Zerme{\~n}o, Jorge Alberto},
  title     = {Isogeometric and CAD-based methods for shape and topology optimization: Sensitivity analysis, B{\´e}zier elements and phase-field approaches},
  doi       = {10.25643/bauhaus-universitaet.4710},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20220831-47102},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {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 B{\´e}zier 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 B{\´e}zier 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 B{\´e}zier 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 B{\´e}zier 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.},
  subject      = {CAD},
  language  = {en}
}
@phdthesis{Mthunzi,
  author    = {Mthunzi, Everett},
  title     = {Interactive Surface Environments: Design and Implementation},
  doi       = {10.25643/bauhaus-universitaet.6406},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20230704-64065},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {128},
  abstract  = {This dissertation presents three studies on the design and implementation of interactive surface environments. It puts forward approaches to engineering interactive surface prototypes using prevailing methodologies and technologies. The scholarly findings from each study have been condensed into academic manuscripts, which are conferred herewith. The first study identifies a communication gap between engineers of interactive surface systems (i.e., originators of concepts) and future developers. To bridge the gap, it explores a UML-based framework to establish a formal syntax for modeling hardware, middleware, and software of interactive surface prototypes. The proposed framework targets models-as-end-products, towards enabling a shared view of research prototypes thereby facilitating dialogue between concept originators and future developers. The second study positions itself to support developers with an open-source solution for exploiting 3D point clouds for interactive tabletop applications using CPU architectures. Given dense 3D point-cloud representations of tabletop environments, the study aims toward mitigating high computational effort by segmenting candidate interaction regions as a preprocessing step. The study contributes a robust open-source solution for reducing computational costs when leveraging 3D point clouds for interactive tabletop applications. The solution itself is flexible and adaptable to variable interactive surface applications. The third study contributes an archetypal concept for integrating mobile devices as active components in augmented tabletop surfaces. With emphasis on transparent development trails, the study demonstrates the utility of the open-source tool developed in the second study. In addition to leveraging 3D point clouds for real-time interaction, the research considers recent advances in computer vision and wireless communication to realize a modern, interactive tabletop application. A robust strategy that combines spatial augmented reality, point-cloud-based depth perception, CNN-based object detection, and Bluetooth communication is put forward. In addition to seamless communication between adhoc mobile devices and interactive tabletop systems, the archetypal concept demonstrates the benefits of preprocessing point clouds by segmenting candidate interaction regions, as suggested in the second study. Collectively, the studies presented in this dissertation contribute; 1—bridging the gap between originators of interactive surface concepts and future developers, 2— promoting the exploration of 3D point clouds for interactive surface applications using CPU-based architectures, and 3—leveraging 3D point clouds together with emerging CNN-based object detection, and Bluetooth communication technologies to advance existing surface interaction concepts.},
  subject      = {Mensch-Maschiene-Kommunikation},
  language  = {en}
}
@phdthesis{NguyenThanh,
  author    = {Nguyen-Thanh, Nhon},
  title     = {Isogeometric analysis based on rational splines over hierarchical T-mesh and alpha finite element method for structural analysis},
  issn      = {1610-7381},
  doi       = {10.25643/bauhaus-universitaet.2078},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20131125-20781},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {196},
  abstract  = {This thesis presents two new methods in finite elements and isogeometric analysis for structural analysis. The first method proposes an alternative alpha finite element method using triangular elements. In this method, the piecewise constant strain field of linear triangular finite element method models is enhanced by additional strain terms with an adjustable parameter a, which results in an effectively softer stiffness formulation compared to a linear triangular element. In order to avoid the transverse shear locking of Reissner-Mindlin plates analysis the alpha finite element method is coupled with a discrete shear gap technique for triangular elements to significantly improve the accuracy of the standard triangular finite elements. The basic idea behind this element formulation is to approximate displacements and rotations as in the standard finite element method, but to construct the bending, geometrical and shear strains using node-based smoothing domains. Several numerical examples are presented and show that the alpha FEM gives a good agreement compared to several other methods in the literature. Second method, isogeometric analysis based on rational splines over hierarchical T-meshes (RHT-splines) is proposed. The RHT-splines are a generalization of Non-Uniform Rational B-splines (NURBS) over hierarchical T-meshes, which is a piecewise bicubic polynomial over a hierarchical T-mesh. The RHT-splines basis functions not only inherit all the properties of NURBS such as non-negativity, local support and partition of unity but also more importantly as the capability of joining geometric objects without gaps, preserving higher order continuity everywhere and allow local refinement and adaptivity. In order to drive the adaptive refinement, an efficient recovery-based error estimator is employed. For this problem an imaginary surface is defined. The imaginary surface is basically constructed by RHT-splines basis functions which is used for approximation and interpolation functions as well as the construction of the recovered stress components. Numerical investigations prove that the proposed method is capable to obtain results with higher accuracy and convergence rate than NURBS results.},
  subject      = {Isogeometric analysis},
  language  = {en}
}
@phdthesis{Ren,
  author    = {Ren, Huilong},
  title     = {Dual-horizon peridynamics and Nonlocal operator method},
  doi       = {10.25643/bauhaus-universitaet.4403},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20210412-44039},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  pages     = {223},
  abstract  = {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.},
  subject      = {Peridynamik},
  language  = {en}
}
@phdthesis{Staeudel,
  author    = {St{\"a}udel, J{\"u}rgen},
  title     = {Development, Implementation and Operation of Integrated Sanitation Systems Based on Material-Flows - Integrated Sanitation in the City of Darkhan, Mongolia - A Practicable Example},
  doi       = {10.25643/bauhaus-universitaet.3179},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170512-31794},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  abstract  = {The world society faces a huge challenge to implement the human right of "access to sanitation". More and more it is accepted that the conventional approach towards providing sanitation services is not suitable to solve this problem. This dissertation examines the possibility to enhance "access to sanitation" for people who are living in areas with underdeveloped water and wastewater infrastructure systems. The idea hereby is to follow an integrated approach for sanitation, which allows for a mutual completion of existing infrastructure with resource-based sanitation systems. The notion "integrated sanitation system (iSaS)" is defined in this work and guiding principles for iSaS are formulated. Further on the implementation of iSaS is assessed at the example of a case study in the city of Darkhan in Mongolia. More than half of Mongolia's population live in settlements where yurts (tents of Nomadic people) are predominant. In these settlements (or "ger areas") sanitation systems are not existent and the hygienic situation is precarious. An iSaS has been developed for the ger areas in Darkhan and tested over more than two years. Further on a software-based model has been developed with the goal to describe and assess different variations of the iSaS. The results of the assessment of material-flows, monetary-flows and communication-flows within the iSaS are presented in this dissertation. The iSaS model is adaptable and transferable to the socio-economic conditions in other regions and climate zones.},
  subject      = {Abwasser},
  language  = {en}
}
@phdthesis{Wolff2009,
  author    = {Wolff, Thomas},
  title     = {Ein methodischer Bemessungsansatz zur Absch{\"a}tzung des Tragverhaltens von Pfahlgr{\"u}ndungen in weichem kalkigen Sedimentgestein},
  doi       = {10.25643/bauhaus-universitaet.1414},
  url       = {http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20100125-14993},
  school      = {Bauhaus-Universit{\"a}t Weimar},
  year      = {2009},
  abstract  = {In der vorliegenden Arbeit wird das Tragverhalten und das Sicherheitsniveau axial belasteter Großbohrpf{\"a}hle in den pleistoz{\"a}nen Kalkarenit der K{\"u}stenregion von Dubai untersucht. Zun{\"a}chst wird auf der Grundlage von Ergebnissen umfangreicher Baugrundanalysen und Probebelastungen das Tragverhalten detailliert beschrieben. Anschließend wird ein auf der Finiten-Elemente-Methode basierendes Strukturmodell zur Simulation des Last-Setzungsverhaltens von Großbohrpf{\"a}hlen im Sinne eines numerischen Versuchsstandes entwickelt. Um herstellungsbedingte Ver{\"a}nderungen der Baugrundeigenschaften in der Kontaktzone Pfahl-Baugrund zu ber{\"u}cksichtigen, die mit boden- und felsmechanischen Elementversuchen gew{\"o}hnlich nicht erfassbar sind, werden die Gr{\"o}ßen der relevanten konstitutiven Parameterwerte iterativ mittels inverser Optimierungsstrategien bestimmt. Abschließend wird eine methodische Vorgehensweise aufgezeigt, wie das Sicherheitsniveau axial belasteter Großbohrpf{\"a}hlen unter Ber{\"u}cksichtigung der r{\"a}umlichen Variabilit{\"a}t der Baugrundeigenschaften zuverl{\"a}ssig abgesch{\"a}tzt werden kann.},
  subject      = {Pfahl},
  language  = {de}
}