TY - JOUR A1 - Legatiuk, Dmitrii T1 - Mathematical Modelling by Help of Category Theory: Models and Relations between Them JF - mathematics N2 - The growing complexity of modern practical problems puts high demand on mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice is becoming particularly important. Methods for model comparison and model choice typically used in practical applications nowadays are computationbased, and thus time consuming and computationally costly. Therefore, it is necessary to develop other approaches to working abstractly, i.e., without computations, with mathematical models. An abstract description of mathematical models can be achieved by the help of abstract mathematics, implying formalisation of models and relations between them. In this paper, a category theory-based approach to mathematical modelling is proposed. In this way, mathematical models are formalised in the language of categories, relations between the models are formally defined and several practically relevant properties are introduced on the level of categories. Finally, an illustrative example is presented, underlying how the category-theory based approach can be used in practice. Further, all constructions presented in this paper are also discussed from a modelling point of view by making explicit the link to concrete modelling scenarios. KW - Kategorientheorie KW - Modellierung KW - Modellierungsmethode KW - OA-Publikationsfonds2021 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210817-44844 UR - https://www.mdpi.com/2227-7390/9/16/1946?type=check_update&version=1 VL - 2021 IS - volume 9, issue 16, article 1946 PB - MDPI CY - Basel ER - TY - JOUR A1 - Alkam, Feras A1 - Lahmer, Tom T1 - A robust method of the status monitoring of catenary poles installed along high-speed electrified train tracks JF - Results in Engineering N2 - Electric trains are considered one of the most eco-friendly and safest means of transportation. Catenary poles are used worldwide to support overhead power lines for electric trains. The performance of the catenary poles has an extensive influence on the integrity of the train systems and, consequently, the connected human services. It became a must nowadays to develop SHM systems that provide the instantaneous status of catenary poles in- service, making the decision-making processes to keep or repair the damaged poles more feasible. This study develops a data-driven, model-free approach for status monitoring of cantilever structures, focusing on pre-stressed, spun-cast ultrahigh-strength concrete catenary poles installed along high-speed train tracks. The pro-posed approach evaluates multiple damage features in an unfied damage index, which leads to straightforward interpretation and comparison of the output. Besides, it distinguishes between multiple damage scenarios of the poles, either the ones caused by material degradation of the concrete or by the cracks that can be propagated during the life span of the given structure. Moreover, using a logistic function to classify the integrity of structure avoids the expensive learning step in the existing damage detection approaches, namely, using the modern machine and deep learning methods. The findings of this study look very promising when applied to other types of cantilever structures, such as the poles that support the power transmission lines, antenna masts, chimneys, and wind turbines. KW - Fahrleitung KW - Catenary poles KW - SHM KW - Model-free status monitoring KW - Sigmoid function KW - High-speed electric train KW - Schaden KW - OA-Publikationsfonds2021 Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20211011-45212 UR - https://www.sciencedirect.com/science/article/pii/S2590123021000906?via%3Dihub VL - 2021 IS - volume 12, article 100289 SP - 1 EP - 8 PB - Elsevier CY - Amsterdam ER - TY - THES A1 - Stang, René T1 - Methode zur Ökoeffizienzbewertung wärmetechnischer Anlagen in Gebäuden N2 - Die vorliegende Arbeit richtet sich an Ingenieur*innen und Wissenschaftler*innen der technischen Gebäudeausrüstung. Sie greift einen sich abzeichnenden Änderungsbedarf in der Umwelt- und Nachhaltigkeitsbewertung von Gebäuden und wärmetechnischen Anlagen auf. Der aktuell genutzte nicht erneuerbare Primärenergiebedarf wird insbesondere hinsichtlich künftiger politischer Klima- und Umweltschutzziele als alleinige Bewertungsgröße nicht ausreichend sein. Die mit dieser Arbeit vorgestellte Ökoeffizienzbewertungsmethode kann als geeignetes Instrument zur Lösung der Probleme beitragen. Sie ermöglicht systematische, ganzheitliche Bewertungen und reproduzierbare Vergleiche wärmetechnischer Anlagen bezüglich ihrer ökologischen und ökonomischen Nachhaltigkeit. Die wesentlichsten Neuentwicklungen sind die spezifische Umweltleistung, in Erweiterung zum genutzten Primärenergiefaktor, und der Ökoeffizienzindikator UWI. KW - Energiewirtschaft KW - Nachhaltigkeit KW - Primärenergie KW - erneuerbare Energie KW - Wärmebedarf KW - Nachhaltigkeitsbewertung KW - Ökobilanz KW - Ökoeffizienz KW - Primärenergiefaktor KW - Umweltleistung Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20211119-45280 SN - 978-3-18-300623-6 (print) PB - VDI Verlag CY - Düsseldorf ER - TY - THES A1 - Ren, Huilong T1 - Dual-horizon peridynamics and Nonlocal operator method N2 - 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. KW - Peridynamik KW - Variational principle KW - weighted residual method KW - gradient elasticity KW - phase field fracture method KW - smoothed particle hydrodynamics KW - numerical methods KW - PDEs Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210412-44039 ER - TY - THES A1 - Ruhland, Grit T1 - FOLGELANDSCHAFT. Eine Untersuchung der Auswirkungen des Uranbergbaus auf die Landschaft um Gera/Ronneburg. N2 - Das Kernthema dieser Arbeit ist die Beschäftigung mit den Folgen des Uranbergbaus in dem Gebiet um die ehemalige Abbauregion der Wismut SAG/SDAG in Ronneburg (Ostthüringen). Dieses Thema wird unter historischen, sozialen, kulturanthropologischen und künstlerischen Aspekten betrachtet und in den Zusammenhang mit den weltweiten Voraussetzungen der Nuklearindustrie und Auswirkungen des Uranbergbaus und seiner Folgen gestellt. Die Arbeit legt dar, wie eine Uranbergbaufolgelandschaft entsteht und welches Wissen ist für ein angemessenes Verständnis des Phänomens wichtig ist. Es wird untersucht, ob Kunst bezüglich der Uranbergbaufolgelandschaft einen relevanten Beitrag leisten kann bzw. in welcher Form dies versucht wurde, bzw. stellte Arbeiten vor, die verwandete Themen bearbeitet haben. In Kombination dieser beiden Hauptaspekte geht die Arbeit der Frage nach, welche Faktoren die Uranbergbaufolgelandschaft prägen und ob es sinnvolle Beteiligungsfelder für künstlerisches Forschen oder Handeln gibt sowie welche Bedingungen hierfür erfüllt werdenmüssten. Die Kernthese der Arbeit ist, dass künstlerische Arbeiten im Themenfeld des Uranbergbaus unter bestimmten Bedingungen relevante Beiträge leisten können. N2 - This thesis is exploring the consequences of uranium mining in the area around the former mining region of the Wismut SAG / SDAG in Ronneburg (East Thuringia), East Germany. The topic is viewed from historical, social, cultural-anthropological and artistic aspects and placed in the context of the worldwide requirements of the nuclear industry and the effects of uranium mining and its consequences. The thesis explains how a uranium mining landscape is created and what knowledge is important for an adequate understanding of the phenomenon. It is examined whether art can make a relevant contribution in dealing with the uranium mining landscape. It discusses artworks that have dealt with related topics. In combination of these two main aspects, the thesis investigates the question which factors shape the uranium mining landscape and whether there are meaningful fields of participation for artistic research and which conditions would have to be met for this. The core thesis of the work is that artistic work in the field of uranium mining can make relevant contributions under certain conditions. It also contains field research, interviews and the description and application of a method called "random-structured landscape observation". KW - Uranbergbau KW - Nachbergbau KW - Geiger-Müller-Zählrohr KW - Kerntechnische Industrie KW - Nuclear Art KW - Environmental Art KW - Künstlerische Forschung KW - Artistic Research KW - Geigerzähler KW - Nuklearindustrie KW - Atomindustrie Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210906-44953 ER - TY - JOUR A1 - Kleiner, Florian T1 - Optimization and semi-automatic evaluation of a frosting process for a soda lime silicate glass based on phosphoric acid JF - International Journal of Applied Glass Science N2 - Chemical glass frosting processes are widely used to create visual attractive glass surfaces. A commonly used frosting bath mainly contains ammonium bifluoride (NH4HF2) mixed with hydrochloric acid (HCl). The frosting process consists of several baths. Firstly, the preliminary bath to clean the object. Secondly, the frosting bath which etches the rough light scattering structure into the glass surface. Finally, the washing baths to clean the frosted object. This is where the constituents of the preceding steps accumulate and have to be filtered from the sewage. In the present contribution, phosphoric acid (H3PO4) was used as a substitute for HCl to reduce the amount of ammonium (NH4+) and chloride (Cl−) dissolved in the waste water. In combination with magnesium carbonate (MgCO3), it allows the precipitation of ammonium within the sewage as ammonium magnesium phosphate (MgNH4PO4). However, a trivial replacement of HCl by H3PO4 within the frosting process causes extensive frosting errors, such as inhomogeneous size distributions of the structures or domains that are not fully covered by these structures. By modifying the preliminary bath composition, it was possible to improve the frosting result considerably. To determine the optimal composition of the preliminary bath, a semi-automatic evaluation method has been developed. This method renders the objective comparison of the resulting surface quality possible. KW - Silicatglas KW - Mattieren KW - Ätzen KW - automated quality control KW - etching KW - glass frosting KW - phosphoric acid Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210701-44548 UR - https://ceramics.onlinelibrary.wiley.com/doi/10.1111/ijag.15866 SP - 1 EP - 8 PB - John Wiley & Sons ER - TY - CHAP A1 - Kleiner, Florian A1 - Rößler, Christiane T1 - Utilizing Modern FIB/SEM Technology and EDS for 3D Imaging of Hydrated Alite and its Pore Space T2 - ERICA-CASH II Final Converence N2 - The exploration of cementitious materials using scanning electron microscopes (SEM) is mainly done using fractured or polished surfaces. This leads to high-resolution 2D-images that can be combined using EDX and EBSD to unveil details of the microstructure and composition of materials. Nevertheless, this does not provide a quantitative insight into the three-dimensional fine structure of for example C-S-H phases. The focused ion beam (FIB) technology can cut a block of material in thin layers of less than 10 nm. This gives us a volume of 1000 μm³ with a voxel resolution of down to 4 x 4 x 10 nm³. The results can be combined with simultaneously acquired EDX data to improve image segmentation. Results of the investigation demonstrate that it is possible to obtain close-to-native 3D-visualisation of the spatial distribution of unreacted C3S, C-S-H and CH. Additionally, an optimized preparation method allows us to quantify the fine structure of C-S-H phases (length, aspect ratio, …) and the pore space. KW - Rasterelektronenmikroskop KW - Alit KW - SEM KW - Focussed Ion Beam KW - EDX KW - energy dispersive X-ray spectroscopy KW - alite Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210702-44555 ER - TY - THES A1 - Alkam, Feras T1 - Vibration-based Monitoring of Concrete Catenary Poles using Bayesian Inference N2 - This work presents a robust status monitoring approach for detecting damage in cantilever structures based on logistic functions. Also, a stochastic damage identification approach based on changes of eigenfrequencies is proposed. The proposed algorithms are verified using catenary poles of electrified railways track. The proposed damage features overcome the limitation of frequency-based damage identification methods available in the literature, which are valid to detect damage in structures to Level 1 only. Changes in eigenfrequencies of cantilever structures are enough to identify possible local damage at Level 3, i.e., to cover damage detection, localization, and quantification. The proposed algorithms identified the damage with relatively small errors, even at a high noise level. KW - Parameteridentifikation KW - Bayesian Inference, Uncertainty Quantification KW - Inverse Problems KW - Damage Identification KW - Concrete catenary pole KW - SHM KW - Inverse Probleme KW - Bayes’schen Inferenz KW - Unschärfequantifizierung KW - Schadenerkennung KW - Oberleitungsmasten Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210526-44338 UR - https://asw-verlage.de/katalog/vibration_based_monitoring_of_co-2363.html VL - 2021 PB - Bauhaus-Universitätsverlag CY - Weimar ER - TY - THES A1 - Goswami, Somdatta T1 - Phase field modeling of fracture with isogeometric analysis and machine learning methods N2 - This thesis presents the advances and applications of phase field modeling in fracture analysis. In this approach, the sharp crack surface topology in a solid is approximated by a diffusive crack zone governed by a scalar auxiliary variable. The uniqueness of phase field modeling is that the crack paths are automatically determined as part of the solution and no interface tracking is required. The damage parameter varies continuously over the domain. But this flexibility comes with associated difficulties: (1) a very fine spatial discretization is required to represent sharp local gradients correctly; (2) fine discretization results in high computational cost; (3) computation of higher-order derivatives for improved convergence rates and (4) curse of dimensionality in conventional numerical integration techniques. As a consequence, the practical applicability of phase field models is severely limited. The research presented in this thesis addresses the difficulties of the conventional numerical integration techniques for phase field modeling in quasi-static brittle fracture analysis. The first method relies on polynomial splines over hierarchical T-meshes (PHT-splines) in the framework of isogeometric analysis (IGA). An adaptive h-refinement scheme is developed based on the variational energy formulation of phase field modeling. The fourth-order phase field model provides increased regularity in the exact solution of the phase field equation and improved convergence rates for numerical solutions on a coarser discretization, compared to the second-order model. However, second-order derivatives of the phase field are required in the fourth-order model. Hence, at least a minimum of C1 continuous basis functions are essential, which is achieved using hierarchical cubic B-splines in IGA. PHT-splines enable the refinement to remain local at singularities and high gradients, consequently reducing the computational cost greatly. Unfortunately, when modeling complex geometries, multiple parameter spaces (patches) are joined together to describe the physical domain and there is typically a loss of continuity at the patch boundaries. This decrease of smoothness is dictated by the geometry description, where C0 parameterizations are normally used to deal with kinks and corners in the domain. Hence, the application of the fourth-order model is severely restricted. To overcome the high computational cost for the second-order model, we develop a dual-mesh adaptive h-refinement approach. This approach uses a coarser discretization for the elastic field and a finer discretization for the phase field. Independent refinement strategies have been used for each field. The next contribution is based on physics informed deep neural networks. The network is trained based on the minimization of the variational energy of the system described by general non-linear partial differential equations while respecting any given law of physics, hence the name physics informed neural network (PINN). The developed approach needs only a set of points to define the geometry, contrary to the conventional mesh-based discretization techniques. The concept of `transfer learning' is integrated with the developed PINN approach to improve the computational efficiency of the network at each displacement step. This approach allows a numerically stable crack growth even with larger displacement steps. An adaptive h-refinement scheme based on the generation of more quadrature points in the damage zone is developed in this framework. For all the developed methods, displacement-controlled loading is considered. The accuracy and the efficiency of both methods are studied numerically showing that the developed methods are powerful and computationally efficient tools for accurately predicting fractures. T3 - ISM-Bericht // Institut für Strukturmechanik, Bauhaus-Universität Weimar - 2021,1 KW - Phasenfeldmodell KW - Neuronales Netz KW - Sprödbruch KW - Isogeometric Analysis KW - Physics informed neural network KW - phase field KW - deep neural network KW - brittle fracture Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210304-43841 ER - TY - JOUR A1 - Staubach, Patrick A1 - Machacek, Jan A1 - Skowronek, Josefine A1 - Wichtmann, Torsten T1 - Vibratory pile driving in water-saturated sand: Back-analysis of model tests using a hydro-mechanically coupled CEL method JF - Soils and Foundations N2 - The development of a hydro-mechanically coupled Coupled-Eulerian–Lagrangian (CEL) method and its application to the back-analysisof vibratory pile driving model tests in water-saturated sand is presented. The predicted pile penetration using this approachis in good agreement with the results of the model tests as well as with fully Lagrangian simulations. In terms of pore water pressure, however, the results of the CEL simulation show a slightly worse accordance with the model tests compared to the Lagrangian simulation. Some shortcomings of the hydro-mechanically coupled CEL method in case of frictional contact problems and pore fluids with high bulk modulus are discussed. Lastly, the CEL method is applied to the simulation of vibratory driving of open-profile piles under partially drained conditions to study installation-induced changes in the soil state. It is concluded that the proposed method is capable of realistically reproducing the most important mechanisms in the soil during the driving process despite its addressed shortcomings. KW - Plastische Deformation KW - Vibratory pile driving KW - Coupled-Eulerian–Lagrangian KW - Hydro-mechanically coupled KW - Hypoplasticity KW - Relative acceleration KW - Large deformation KW - Deformationsverhalten KW - Plastizität KW - OA-Publikationsfonds2020 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210203-43571 UR - https://www.sciencedirect.com/science/article/pii/S0038080620337586?via%3Dihub VL - 2021 IS - Volume 61, Issue 1 SP - 144 EP - 159 PB - Elsevier, Science Direct CY - Amsterdam ER -