500 Naturwissenschaften und Mathematik
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Recent years have seen a gradual shift in focus of international policies from a national and regional perspective to that of cities, a shift which is closely related to the rapid urbanization of developing countries. As revealed in the 2011 Revision of the World Urbanization Prospects published by the United Nations, 51% of the global population (approximately 3.6 billion people) lives in cities. The report predicts that by 2050, the world’s urban population will increase by 2.3 billion, making up 68% of the population. The growth of urbanization in the next few decades is expected to primarily come from developing countries, one third of which will be in China and India.
With rapid urbanization and the ongoing growth of mega cities, cities must become increasingly resilient and intelligent to cope with numerous challenges and crises like droughts and floods arising from extreme climate, destruction brought by severe natural disasters, and aggregated social contradictions resulting from economic crises. All cities face the urban development dynamics and uncertainties arising from these problems. Under such circumstances, cities are considered the critical path from crisis to prosperity, so scholars and organizations have proposed the construction of “resilient cities.” On the one hand, this theory emphasizes cities’ defenses and buffering capacity against disasters, crises and uncertainties, as well as recovery after destruction; on the other hand, it highlights the learning capacity of urban systems, identification of opportunities amid challenges, and maintenance of development vitality. Some scholars even believe that urban resilience is a powerful supplement to sustainable development. Hence, resilience assessment has become the latest and most important perspective for evaluating the development and crisis defense capacity of cities.
Rather than a general abstract concept, urban resilience is a comprehensive measurement of a city’s level of development. The dynamic development of problems is reflected through quantitative indicators and appraisal systems not only from the perspective of academic research, but also governmental policy, so as to scientifically guide development, and measure and compare cities’ development levels. Although international scholars have proposed
quantitative methods for urban resilience assessment, they are however insufficiently systematic and regionally adaptive for China’s current urban development needs. On the basis of comparative study on European and North American resilient city theories, therefore, this paper puts forwards a theoretical framework for resilient city systems consistent with China’s national conditions in light of economic development pressure, natural resource depletion, pollution, and other salient development crises in China. The key factors influencing urban resilience are taken into full consideration; expert appraisal is conducted based on the Delphi Method and the analytic hierarchy process (AHP) to design an extensible and updatable resilient city evaluation system which is sufficiently systematic, geographically adaptable, and sustainable for China’s current urban development needs. Finally, Changsha is taken as the main case for empirical study on comprehensive evaluation of similar cities in Central China to improve the indicator system.
A categorical perspective towards aerodynamic models for aeroelastic analyses of bridge decks
(2019)
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.
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.
The K-nearest neighbors (KNN) machine learning algorithm is a well-known non-parametric classification method. However, like other traditional data mining methods, applying it on big data comes with computational challenges. Indeed, KNN determines the class of a new sample based on the class of its nearest neighbors; however, identifying the neighbors in a large amount of data imposes a large computational cost so that it is no longer applicable by a single computing machine. One of the proposed techniques to make classification methods applicable on large datasets is pruning. LC-KNN is an improved KNN method which first clusters the data into some smaller partitions using the K-means clustering method; and then applies the KNN for each new sample on the partition which its center is the nearest one. However, because the clusters have different shapes and densities, selection of the appropriate cluster is a challenge. In this paper, an approach has been proposed to improve the pruning phase of the LC-KNN method by taking into account these factors. The proposed approach helps to choose a more appropriate cluster of data for looking for the neighbors, thus, increasing the classification accuracy. The performance of the proposed approach is evaluated on different real datasets. The experimental results show the effectiveness of the proposed approach and its higher classification accuracy and lower time cost in comparison to other recent relevant methods.
Material failure can be tackled by so-called nonlocal models, which introduce an intrinsic length scale into the formulation and, in the case of material failure, restore the well-posedness of the underlying boundary value problem or initial boundary value problem. Among nonlocal models, peridynamics (PD) has attracted a lot of attention as it allows the natural transition from continuum to discontinue and thus allows modeling of discrete cracks without the need to describe and track the crack topology, which has been a major obstacle in traditional discrete crack approaches. This is achieved by replacing the divergence of the Cauchy stress tensor through an integral over so-called bond forces, which account for the interaction of particles. A quasi-continuum approach is then used to calibrate the material parameters of the bond forces, i.e., equating the PD energy with the energy of a continuum. One major issue for the application of PD to general complex problems is that they are limited to fairly simple material behavior and pure mechanical problems based on explicit time integration. PD has been extended to other applications but losing simultaneously its simplicity and ease in modeling material failure. Furthermore, conventional PD suffers from instability and hourglass modes that require stabilization. It also requires the use of constant horizon sizes, which drastically reduces its computational efficiency. The latter issue was resolved by the so-called dual-horizon peridynamics (DH-PD) formulation and the introduction of the duality of horizons.
Within the nonlocal operator method (NOM), the concept of nonlocality is further extended and can be considered a generalization of DH-PD. Combined with the energy functionals of various physical models, the nonlocal forms based on the dual-support concept can be derived. In addition, the variation of the energy functional allows implicit formulations of the nonlocal theory. While traditional integral equations are formulated in an integral domain, the dual-support approaches are based on dual integral domains. One prominent feature of NOM is its compatibility with variational and weighted residual methods. The NOM yields a direct numerical implementation based on the weighted residual method for many physical problems without the need for shape functions. Only the definition of the energy or boundary value problem is needed to drastically facilitate the implementation. The nonlocal operator plays an equivalent role to the derivatives of the shape functions in meshless methods and finite element methods (FEM). Based on the variational principle, the residual and the tangent stiffness matrix can be obtained with ease by a series of matrix multiplications. In addition, NOM can be used to derive many nonlocal models in strong form.
The principal contributions of this dissertation are the implementation and application of NOM, and also the development of approaches for dealing with fractures within the NOM, mostly for dynamic fractures. The primary coverage and results of the dissertation are as follows:
-The first/higher-order implicit NOM and explicit NOM, including a detailed description of the implementation, are presented. The NOM is based on so-called support, dual-support, nonlocal operators, and an operate energy functional ensuring stability. The nonlocal operator is a generalization of the conventional differential operators. Combining with the method of weighted residuals and variational principles, NOM establishes the residual and tangent stiffness matrix of operate energy functional through some simple matrix without the need of shape functions as in other classical computational methods such as FEM. NOM only requires the definition of the energy drastically simplifying its implementation. For the sake of conciseness, the implementation in this chapter is focused on linear elastic solids only, though the NOM can handle more complex nonlinear problems. An explicit nonlocal operator method for the dynamic analysis of elasticity solid problems is also presented. The explicit NOM avoids the calculation of the tangent stiffness matrix as in the implicit NOM model. The explicit scheme comprises the Verlet-velocity algorithm. The NOM can be very flexible and efficient for solving partial differential equations (PDEs). It's also quite easy for readers to use the NOM and extend it to solve other complicated physical phenomena described by one or a set of PDEs. Several numerical examples are presented to show the capabilities of this method.
-A nonlocal operator method for the dynamic analysis of (thin) Kirchhoff plates is proposed. The nonlocal Hessian operator is derived from a second-order Taylor series expansion. NOM is higher-order continuous, which is exploited for thin plate analysis that requires $C^1$ 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 time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.
-A nonlocal fracture modeling is developed and applied to the simulation of quasi-static and dynamic fractures using the NOM. The phase field's nonlocal weak and associated strong forms are derived from a variational principle. The NOM requires only the definition of energy. We present both a nonlocal implicit phase field model and a nonlocal explicit phase field model for fracture; the first approach is better suited for quasi-static fracture problems, while the key application of the latter one is dynamic fracture. To demonstrate the performance of the underlying approach, several benchmark examples for quasi-static and dynamic fracture are solved.
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.
The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood. Reducing the discretization size while keep- ing the neighborhood size will often require extra consideration. Peridy- namic (PD) is a newly developed numerical method with nonlocal nature. Its straightforward integral form equation of motion allows simulating dy- namic problems without any extra consideration required. The formation of crack and its propagation is known as natural to peridynamic. This means that discontinuity is a result of the simulation and does not demand any post-processing. As with other nonlocal methods, PD is considered an expensive method. The refinement of the nodal spacing while keeping the neighborhood size (i.e., horizon radius) constant, emerges to several nonphysical phenomena.
This research aims to reduce the peridynamic computational and imple- mentation costs. A novel refinement approach is introduced. The pro- posed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. It will be shown that no ghost forces will be created when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamic and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. Further development of the method for higher dimensions proves to have a direct relationship with the mesh sensitivity of the PD. A method for solving the mesh sensitivity of the PD is intro- duced. The application of the method will be examined by solving a crack propagation problem similar to those reported in the literature.
New software architecture is proposed considering both academic and in- dustrial use. The available simulation tools for employing PD will be collected, and their advantages and drawbacks will be addressed. The challenges of implementing any node base nonlocal methods while max- imizing the software flexibility to further development and modification
will be discussed and addressed. A software named Relation-Based Sim- ulator (RBS) is developed for examining the proposed architecture. The exceptional capabilities of RBS will be explored by simulating three dis- tinguished models. RBS is available publicly and open to further develop- ment. The industrial acceptance of the RBS will be tested by targeting its performance on one Mac and two Linux distributions.
The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood. Reducing the discretization size while keep- ing the neighborhood size will often require extra consideration. Peridynamic (PD) is a newly developed numerical method with nonlocal nature. Its straightforward integral form equation of motion allows simulating dynamic problems without any extra consideration required. The formation of crack and its propagation is known as natural to peridynamic. This means that discontinuity is a result of the simulation and does not demand any post-processing. As with other nonlocal methods, PD is considered an expensive method. The refinement of the nodal spacing while keeping the neighborhood size (i.e., horizon radius) constant, emerges to several nonphysical phenomena.
This research aims to reduce the peridynamic computational and imple- mentation costs. A novel refinement approach is introduced. The pro- posed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. It will be shown that no ghost forces will be created when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamic and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. Further development of the method for higher dimensions proves to have a direct relationship with the mesh sensitivity of the PD. A method for solving the mesh sensitivity of the PD is intro- duced. The application of the method will be examined by solving a crack propagation problem similar to those reported in the literature.
New software architecture is proposed considering both academic and in- dustrial use. The available simulation tools for employing PD will be collected, and their advantages and drawbacks will be addressed. The challenges of implementing any node base nonlocal methods while max- imizing the software flexibility to further development and modification will be discussed and addressed. A software named Relation-Based Sim- ulator (RBS) is developed for examining the proposed architecture. The exceptional capabilities of RBS will be explored by simulating three distinguished models. RBS is available publicly and open to further develop- ment. The industrial acceptance of the RBS will be tested by targeting its performance on one Mac and two Linux distributions.
Self-healing materials have recently become more popular due to their capability to autonomously and autogenously repair the damage in cementitious materials. The concept of self-healing gives the damaged material the ability to recover its stiffness. This gives a difference in comparing with a material that is not subjected to healing. Once this material is damaged, it cannot sustain loading due to the stiffness degradation. Numerical modeling of self-healing materials is still in its infancy. Multiple experimental researches were conducted in literature to describe the behavior of self-healing of cementitious materials. However, few numerical investigations were undertaken.
The thesis presents an analytical framework of self-healing and super healing materials based on continuum damage-healing mechanics. Through this framework, we aim to describe the recovery and strengthening of material stiffness and strength. A simple damage healing law is proposed and applied on concrete material. The proposed damage-healing law is based on a new time-dependent healing variable. The damage-healing model is applied on isotropic concrete material at the macroscale under tensile load. Both autonomous and autogenous self-healing mechanisms are simulated under different loading conditions. These two mechanisms are denoted in the present work by coupled and uncoupled self-healing mechanisms, respectively. We assume in the coupled self-healing that the healing occurs at the same time with damage evolution, while we assume in the uncoupled self-healing that the healing occurs when the material is deformed and subjected to a rest period (damage is constant). In order to describe both coupled and uncoupled healing mechanisms, a one-dimensional element is subjected to different types of loading history.
In the same context, derivation of nonlinear self-healing theory is given, and comparison of linear and nonlinear damage-healing models is carried out using both coupled and uncoupled self-healing mechanisms. The nonlinear healing theory includes generalized nonlinear and quadratic healing models. The healing efficiency is studied by varying the values of the healing rest period and the parameter describing the material characteristics. In addition, theoretical formulation of different self-healing variables is presented for both isotropic and anisotropic maerials. The healing variables are defined based on the recovery in elastic modulus, shear modulus, Poisson's ratio, and bulk modulus. The evolution of the healing variable calculated based on cross-section as function of the healing variable calculated based on elastic stiffness is presented in both hypotheses of elastic strain equivalence and elastic energy equivalence. The components of the fourth-rank healing tensor are also obtained in the case of isotropic elasticity, plane stress and plane strain.
Recent research revealed that self-healing presents a crucial solution also for the strengthening of the materials. This new concept has been termed ``Super Healing``. Once the stiffness of the material is recovered, further healing can result as a strengthening material. In the present thesis, new theory of super healing materials is defined in isotropic and anisotropic cases using sound mathematical and mechanical principles which are applied in linear and nonlinear super healing theories. Additionally, the link of the proposed theory with the theory of undamageable materials is outlined. In order to describe the super healing efficiency in linear and nonlinear theories, the ratio of effective stress to nominal stress is calculated as function of the super healing variable. In addition, the hypotheses of elastic strain and elastic energy equivalence are applied. In the same context, new super healing matrix in plane strain is proposed based on continuum damage-healing mechanics.
In the present work, we also focus on numerical modeling of impact behavior of reinforced concrete slabs using the commercial finite element package Abaqus/Explicit. Plain and reinforced concrete slabs of unconfined compressive strength 41 MPa are simulated under impact of ogive-nosed hard projectile. The constitutive material modeling of the concrete and steel reinforcement bars is performed using the Johnson-Holmquist-2 damage and the Johnson-Cook plasticity material models, respectively. Damage diameters and residual velocities obtained by the numerical model are compared with the experimental results and effect of steel reinforcement and projectile diameter is studied.
This paper presents the development of an assessment scheme for a visual qualitative evaluation of nailed connections in existing structures, such as board trusses. In terms of further use and preservation, a quick visual inspection will help to evaluate the quality of a structure regarding its load-bearing capacity and deformation behaviour. Tests of old and new nailed joints in combination with a rating scheme point out the correlation between the load-bearing capacity and condition of a joint. Old joints of comparatively good condition tend to exhibit better results than those of poor condition. Moreover, aged joints are generally more load-bearing than newly assembled ones.
As machine vision-based inspection methods in the field of Structural Health Monitoring (SHM) continue to advance, the need for integrating resulting inspection and maintenance data into a centralised building information model for structures notably grows. Consequently, the modelling of found damages based on those images in a streamlined automated manner becomes increasingly important, not just for saving time and money spent on updating the model to include the latest information gathered through each inspection, but also to easily visualise them, provide all stakeholders involved with a comprehensive digital representation containing all the necessary information to fully understand the structure’s current condition, keep track of any progressing deterioration, estimate the reduced load bearing capacity of the damaged element in the model or simulate the propagation of cracks to make well-informed decisions interactively and facilitate maintenance actions that optimally extend the service life of the structure. Though significant progress has been recently made in information modelling of damages, the current devised methods for the geometrical modelling approach are cumbersome and time consuming to implement in a full-scale model. For crack damages, an approach for a feasible automated image-based modelling is proposed utilising neural networks, classical computer vision and computational geometry techniques with the aim of creating valid shapes to be introduced into the information model, including related semantic properties and attributes from inspection data (e.g., width, depth, length, date, etc.). The creation of such models opens the door for further possible uses ranging from more accurate structural analysis possibilities to simulation of damage propagation in model elements, estimating deterioration rates and allows for better documentation, data sharing, and realistic visualisation of damages in a 3D model.
Broadband dielectric measurement methods based on vector network analyzer coupled with coaxial transmission line cell (CC) and open-ended coaxial probe (OC) are simply reviewed, by which the dielectric behaviors in the frequency range of 1 MHz to 3 GHz of two practical geomaterials are investigated. Kaolin after modified compaction with different water contents is measured by using CC. The results are consistent with previous study on standardized compacted kaolin and suggest that the dielectric properties at frequencies below 100 MHz are not only a function of water content but also functions of other soil state parameters including dry density. The hydration process of a commercial grout is monitored in real time by using OC. It is found that the time dependent dielectric properties can accurately reveal the different stages of the hydration process. These measurement results demonstrate the practicability of the introduced methods in determining dielectric properties of soft geomaterials.
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.
This study permits a reliability analysis to solve the mechanical behaviour issues existing in the current structural design of fabric structures. Purely predictive material models are highly desirable to facilitate an optimized design scheme and to significantly reduce time and cost at the design stage, such as experimental characterization.
The present study examined the role of three major tasks; a) single-objective optimization, b) sensitivity analyses and c) multi-objective optimization on proposed weave structures for woven fabric composites. For single-objective optimization task, the first goal is to optimize the elastic properties of proposed complex weave structure under unit cells basis based on periodic boundary conditions.
We predict the geometric characteristics towards skewness of woven fabric composites via Evolutionary Algorithm (EA) and a parametric study. We also demonstrate the effect of complex weave structures on the fray tendency in woven fabric composites via tightness evaluation. We utilize a procedure which does not require a numerical averaging process for evaluating the elastic properties of woven fabric composites. The fray tendency and skewness of woven fabrics depends upon the behaviour of the floats which is related to the factor of weave. Results of this study may suggest a broader view for further research into the effects of complex weave structures or may provide an alternative to the fray and skewness problems of current weave structure in woven fabric composites.
A comprehensive study is developed on the complex weave structure model which adopts the dry woven fabric of the most potential pattern in singleobjective optimization incorporating the uncertainties parameters of woven fabric composites. The comprehensive study covers the regression-based and variance-based sensitivity analyses. The second task goal is to introduce the fabric uncertainties parameters and elaborate how they can be incorporated into finite element models on macroscopic material parameters such as elastic modulus and shear modulus of dry woven fabric subjected to uni-axial and biaxial deformations. Significant correlations in the study, would indicate the need for a thorough investigation of woven fabric composites under uncertainties parameters. The study describes here could serve as an alternative to identify effective material properties without prolonged time consumption and expensive experimental tests.
The last part focuses on a hierarchical stochastic multi-scale optimization approach (fine-scale and coarse-scale optimizations) under geometrical uncertainties parameters for hybrid composites considering complex weave structure. The fine-scale optimization is to determine the best lamina pattern that maximizes its macroscopic elastic properties, conducted by EA under the following uncertain mesoscopic parameters: yarn spacing, yarn height, yarn width and misalignment of yarn angle. The coarse-scale optimization has been carried out to optimize the stacking sequences of symmetric hybrid laminated composite plate with uncertain mesoscopic parameters by employing the Ant Colony Algorithm (ACO). The objective functions of the coarse-scale optimization are to minimize the cost (C) and weight (W) of the hybrid laminated composite plate considering the fundamental frequency and the buckling load factor as the design constraints.
Based on the uncertainty criteria of the design parameters, the appropriate variation required for the structural design standards can be evaluated using the reliability tool, and then an optimized design decision in consideration of cost can be subsequently determined.
The key objective of this research is to study fracture with a meshfree method, local maximum entropy approximations, and model fracture in thin shell structures with complex geometry and topology. This topic is of high relevance for real-world applications, for example in the automotive industry and in aerospace engineering. The shell structure can be described efficiently by meshless methods which are capable of describing complex shapes as a collection of points instead of a structured mesh. In order to find the appropriate numerical method to achieve this goal, the first part of the work was development of a method based on local maximum entropy (LME)
shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method (XFEM) at a comparable computational cost. In addition, we keep the advantages of the LME shape functions,such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes
near the crack such as blending or shifting.
As extension of this method to three dimensional problems and complex thin shell structures with arbitrary crack growth is cumbersome, we developed a phase field model for fracture using LME. Phase field models provide a powerful tool to tackle moving interface problems, and have been extensively used in physics and materials science. Phase methods are gaining popularity in a wide set of applications in applied science and engineering, recently a second order phase field approximation for brittle fracture has gathered significant interest in computational fracture such that sharp cracks discontinuities are modeled by a diffusive crack. By minimizing the system energy with respect to the mechanical displacements and the phase-field, subject to an irreversibility condition to avoid crack healing, this model can describe crack nucleation, propagation, branching and merging. One of the main advantages of the phase field modeling of fractures is the unified treatment of the interfacial tracking and mechanics, which potentially leads to simple, robust, scalable computer codes applicable to complex systems. In other words, this approximation reduces considerably the implementation complexity because the numerical tracking of the fracture is not needed, at the expense of a high computational cost. We present a fourth-order phase field model for fracture based on local maximum entropy (LME) approximations. The higher order continuity of the meshfree LME approximation allows to directly solve the fourth-order phase field equations without splitting the fourth-order differential equation into two second order differential equations. Notably, in contrast to previous discretizations that use at least a quadratic basis, only linear completeness is needed in the LME approximation. We show that the crack surface can be captured more accurately in the fourth-order model than the second-order model. Furthermore, less nodes are needed for the fourth-order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.
In the last part of this research, we present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantageous over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected
pipes.
One of the most important renewable energy technologies used nowadays are wind power turbines. In this paper, we are interested in identifying the operating status of wind turbines, especially rotor blades, by means of multiphysical models. It is a state-of-the-art technology to test mechanical structures with ultrasonic-based methods. However, due to the density and the required high resolution, the testing is performed with high-frequency waves, which cannot penetrate the structure in depth. Therefore, there is a need to adopt techniques in the fields of multiphysical model-based inversion schemes or data-driven structural health monitoring. Before investing effort in the development of such approaches, further insights and approaches are necessary to make the techniques applicable to structures such as wind power plants (blades). Among the expected developments, further accelerations of the so-called “forward codes” for a more efficient implementation of the wave equation could be envisaged. Here, we employ electromagnetic waves for the early detection of cracks. Because in many practical situations, it is not possible to apply techniques from tomography (characterized by multiple sources and sensor pairs), we focus here on the question of whether the existence of cracks can be determined by using only one source for the sent waves.
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.
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.
The growing complexity of modern engineering problems necessitates development of advanced numerical methods. In particular, methods working directly with discrete structures, and thus, representing exactly some important properties of the solution on a lattice and not just approximating the continuous properties, become more and more popular nowadays. Among others, discrete potential theory and discrete function theory provide a variety of methods, which are discrete counterparts of the classical continuous methods for solving boundary value problems. A lot of results related to the discrete potential and function theories have been presented in recent years. However, these results are related to the discrete theories constructed on square lattices, and, thus, limiting their practical applicability and
potentially leading to higher computational costs while discretising realistic domains.
This thesis presents an extension of the discrete potential theory and discrete function theory to rectangular lattices. As usual in the discrete theories, construction of discrete operators is strongly influenced by a definition of discrete geometric setting. For providing consistent constructions throughout the whole thesis, a detailed discussion on the discrete geometric setting is presented in the beginning. After that, the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, which is the core of the discrete potential theory, its numerical analysis, and practical calculations are presented. By using the discrete fundamental solution of the discrete Laplace operator on a rectangular lattice, the discrete potential theory is then constructed for interior and exterior settings. Several discrete interior and exterior boundary value problems are then solved. Moreover, discrete transmission problems are introduced and several numerical examples of these problems are discussed. Finally, a discrete fundamental solution of the discrete Cauchy-Riemann operator on a rectangular lattice is constructed, and basics of the discrete function theory on a rectangular lattice are provided. This work indicates that the discrete theories provide
solution methods with very good numerical properties to tackle various boundary value problems, as well as transmission problems coupling interior and exterior problems. The results presented in this thesis provide a basis for further development of discrete theories on irregular lattices.