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- 2012 (91) (remove)
Long-span cable supported bridges are prone to aerodynamic instabilities caused by wind and this phenomenon is usually a major design criterion. If the wind speed exceeds the critical flutter speed of the bridge, this constitutes an Ultimate Limit State. The prediction of the flutter boundary therefore requires accurate and robust models. This paper aims at studying various combinations of models to predict the flutter phenomenon.
Since flutter is a coupling of aerodynamic forcing with a structural dynamics problem, different types and classes of models can be combined to study the interaction. Here, both numerical approaches and analytical models are utilised and coupled in different ways to assess the prediction quality of the hybrid model. Models for aerodynamic forces employed are the analytical Theodorsen expressions for the motion-enduced aerodynamic forces of a flat plate and Scanlan derivatives as a Meta model. Further, Computational Fluid Dynamics (CFD) simulations using the Vortex Particle Method (VPM) were used to cover numerical models.
The structural representations were dimensionally reduced to two degree of freedom section models calibrated from global models as well as a fully three-dimensional Finite Element (FE) model. A two degree of freedom system was analysed analytically as well as numerically.
Generally, all models were able to predict the flutter phenomenon and relatively close agreement was found for the particular bridge. In conclusion, the model choice for a given practical analysis scenario will be discussed in the context of the analysis findings.
MODEL DESCRIBING STATIC AND DYNAMIC DISPLACEMENTS OF SILOS WALL DURING THE FLOW OF LOOSE MATERIAL
(2012)
Correct evaluation of wall displacements is a key matter when designing silos. This issue is important from both the standpoint of design engineer (load-bearing capacity of structures) and end-consumer (durability of structures). Commonplace methods of silo design mainly focus on satisfying limit states of load-bearing capacity. Current standards fail to specify methods of dynamic displacements analysis. Measurements of stressacting on silo walls prove that the actual stress is sum of static and dynamic stresses. Janssen came up with differential equation describing state of static equilibrium in cross-section of a silo. By solving the equation static stress of granular solid on silo walls can be determined. Equations of motion were determined from equilibrium equations of feature objects. General solution, describing dynamic stresses was presented as parametric model. This paper presents particular integrals of differential equation, which enable analysing displacements and vibrations for different rigidities of silo walls, types of granular solid and its flow rate.
Civil engineers take advantage of models to design reliable structures. In order to fulfill the design goal with a certain amount of confidence, the utilized models should be able to predict the probable structural behavior under the expected loading schemes. Therefore, a major challenge is to find models which provide less uncertain and more robust responses. The problem gets even twofold when the model to be studied is a global model comprised of different interacting partial models. This study aims at model quality evaluation of global models with a focus on frame-wall systems as the case study. The paper, presents the results of the first step taken toward accomplishing this goal. To start the model quality evaluation of the global frame-wall system, the main element (i.e. the wall) was studied through nonlinear static and dynamic analysis using two different modeling approaches. The two selected models included the fiber section model and the Multiple-Vertical-Line-Element-Model (MVLEM). The influence of the wall aspect ratio (H=L) and the axial load on the response of the models was studied. The results from nonlinear static and dynamic analysis of both models are presented and compared. The models resulted in quite different responses in the range of low aspect ratio walls under large axial loads due to different contribution of the shear deformations to the top displacement. In the studied cases, the results implied that careful attention should be paid to the model quality evaluation of the wall models specifically when they are supposed to be coupled to other partial models such as a moment frame or a soil-footing substructure which their response is sensitive to shear deformations. In this case, even a high quality wall model would not result in a high quality coupled system since it fails to interact properly with the rest of the system.
New foundations for geometric algebra are proposed based upon the existing isomorphisms between geometric and matrix algebras. Each geometric algebra always has a faithful real matrix representation with a periodicity of 8. On the other hand, each matrix algebra is always embedded in a geometric algebra of a convenient dimension. The geometric product is also isomorphic to the matrix product, and many vector transformations such as rotations, axial symmetries and Lorentz transformations can be written in a form isomorphic to a similarity transformation of matrices. We collect the idea that Dirac applied to develop the relativistic electron equation when he took a basis of matrices for the geometric algebra instead of a basis of geometric vectors. Of course, this way of understanding the geometric algebra requires new definitions: the geometric vector space is defined as the algebraic subspace that generates the rest of the matrix algebra by addition and multiplication; isometries are simply defined as the similarity transformations of matrices as shown above, and finally the norm of any element of the geometric algebra is defined as the nth root of the determinant of its representative matrix of order n×n. The main idea of this proposal is an arithmetic point of view consisting of reversing the roles of matrix and geometric algebras in the sense that geometric algebra is a way of accessing, working and understanding the most fundamental conception of matrix algebra as the algebra of transformations of multilinear quantities.
The Bernstein polynomials are used for important applications in many branches of Mathematics and the other sciences, for instance, approximation theory, probability theory, statistic theory, num- ber theory, the solution of the di¤erential equations, numerical analysis, constructing Bezier curves, q-calculus, operator theory and applications in computer graphics. The Bernstein polynomials are used to construct Bezier curves. Bezier was an engineer with the Renault car company and set out in the early 1960’s to develop a curve formulation which would lend itself to shape design. Engineers may …nd it most understandable to think of Bezier curves in terms of the center of mass of a set of point masses. Therefore, in this paper, we study on generating functions and functional equations for these polynomials. By applying these functions, we investigate interpolation function and many properties of these polynomials.
Monogenic functions play a role in quaternion analysis similarly to that of holomorphic functions in complex analysis. A holomorphic function with nonvanishing complex derivative is a conformal mapping. It is well-known that in Rn+1, n ≥ 2 the set of conformal mappings is restricted to the set of Möbius transformations only and that the Möbius transformations are not monogenic. The paper deals with a locally geometric mapping property of a subset of monogenic functions with nonvanishing hypercomplex derivatives (named M-conformal mappings). It is proved that M-conformal mappings orthogonal to all monogenic constants admit a certain change of solid angles and vice versa, that change can characterize such mappings. In addition, we determine planes in which those mappings behave like conformal mappings in the complex plane.
Der Nachbehandlung eines Fahrbahndeckenbetons kommt zum Erzielen eines hohen Frost-Tausalz-Widerstandes der fertigen Betondecke eine besondere Bedeutung zu. Bei der Waschbetonbauweise erfolgt die Nachbehandlung in mehreren Schritten. Eine erste Nachbehandlung gewährleistet den Verdunstungsschutz des Betons bis zum Zeitpunkt des Ausbürstens des verzögerten Oberflächenmörtels. Daran schließt sich die zweite Nachbehandlung an, in der Regel durch Aufsprühen eines flüssigen Nachbehandlungsmittels.
Der zweite Nachbehandlungsschritt ist entscheidend für den Frost-Tausalz-Widerstand der Betondecke. Im Rahmen eines Forschungsprojektes wurde daher untersucht, inwiefern durch eine Optimierung der zweiten Nachbehandlung der Frost-Tausalz-Widerstand von Waschbetonoberflächen erhöht werden kann, insbesondere bei Verwendung hüttensandhaltiger Zemente. Schon durch eine einmalige Nassnachbehandlung wurde eine deutlich höherer Widerstand der Waschbetons gegen Frost-Tausalz-Angriff erzielt.
It is well known that complex quaternion analysis plays an important role in the study of higher order boundary value problems of mathematical physics. Following the ideas given for real quaternion analysis, the paper deals with certain orthogonal decompositions of the complex quaternion Hilbert space into its subspaces of null solutions of Dirac type operator with an arbitrary complex potential. We then apply them to consider related boundary value problems, and to prove the existence and uniqueness as well as the explicit representation formulae of the underlying solutions.
Increasingly powerful hard- and software allows for the numerical simulation of complex physical phenomena with high levels of detail. In light of this development the definition of numerical models for the Finite Element Method (FEM) has become the bottleneck in the simulation process. Characteristic features of the model generation are large manual efforts and a de-coupling of geometric and numerical model. In the highly probable case of design revisions all steps of model preprocessing and mesh generation have to be repeated. This includes the idealization and approximation of a geometric model as well as the definition of boundary conditions and model parameters. Design variants leading to more resource-efficient structures might hence be disregarded due to limited budgets and constrained time frames.
A potential solution to above problem is given with the concept of Isogeometric Analysis (IGA). Core idea of this method is to directly employ a geometric model for numerical simulations, which allows to circumvent model transformations and the accompanying data losses. Basis for this method are geometric models described in terms of Non-uniform rational B-Splines (NURBS). This class of piecewise continuous rational polynomial functions is ubiquitous in computer graphics and Computer-Aided Design (CAD). It allows the description of a wide range of geometries using a compact mathematical representation. The shape of an object thereby results from the interpolation of a set of control points by means of the NURBS functions, allowing efficient representations for curves, surfaces and solid bodies alike. Existing software applications, however, only support the modeling and manipulation of the former two. The description of three-dimensional solid bodies consequently requires significant manual effort, thus essentially forbidding the setup of complex models.
This thesis proposes a procedural approach for the generation of volumetric NURBS models. That is, a model is not described in terms of its data structures but as a sequence of modeling operations applied to a simple initial shape. In a sense this describes the "evolution" of the geometric model under the sequence of operations. In order to adapt this concept to NURBS geometries, only a compact set of commands is necessary which, in turn, can be adapted from existing algorithms. A model then can be treated in terms of interpretable model parameters. This leads to an abstraction from its data structures and model variants can be set up by variation of the governing parameters.
The proposed concept complements existing template modeling approaches: templates can not only be defined in terms of modeling commands but can also serve as input geometry for said operations. Such templates, arranged in a nested hierarchy, provide an elegant model representation. They offer adaptivity on each tier of the model hierarchy and allow to create complex models from only few model parameters. This is demonstrated for volumetric fluid domains used in the simulation of vertical-axis wind turbines. Starting from a template representation of airfoil cross-sections, the complete "negative space" around the rotor blades can be described by a small set of model parameters, and model variants can be set up in a fraction of a second.
NURBS models offer a high geometric flexibility, allowing to represent a given shape in different ways. Different model instances can exhibit varying suitability for numerical analyses. For their assessment, Finite Element mesh quality metrics are regarded. The considered metrics are based on purely geometric criteria and allow to identify model degenerations commonly used to achieve certain geometric features. They can be used to decide upon model adaptions and provide a measure for their efficacy. Unfortunately, they do not reveal a relation between mesh distortion and ill-conditioning of the equation systems resulting from the numerical model.
Methods for model quality assessment are aiming to find the most appropriate model with respect to accuracy and computational effort for a structural system under investigation. Model error estimation techniques can be applied for this purpose when kinematical models are investigated. They are counted among the class of white box models, which means that the model hierarchy and therewith the best model is known. This thesis gives an overview of discretisation error estimators. Deduced from these, methods for model error estimation are presented. Their general goal is to make a prediction of the inaccuracies that are introduced using the simpler model without knowing the solution of a more complex model. This information can be used to steer an adaptive process. Techniques for linear and non-linear problems as well as global and goal-oriented errors are introduced. The estimation of the error in local quantities is realised by solving a dual problem, which serves as a weight for the primal error. So far, such techniques have mainly been applied in
material modelling and for dimensional adaptivity. Within the scope of this thesis, available model error estimators are adapted for an application to kinematical models. Their applicability is tested regarding the question of whether a geometrical non-linear calculation is necessary or not. The analysis is limited to non-linear estimators due to the structure of the underlying differential equations. These methods often involve simplification, e.g linearisations. It is investigated to which extent such assumptions lead to meaningful results, when applied to kinematical models.
The process of analysis and design in structural engineering requires the consideration of different partial models, for example loading, structural materials, structural elements, and analysis types. The various partial models are combined by coupling several of their components. Due to the large number of available partial models describing similar phenomena, many different model combinations are possible to simulate the same aspects of a structure. The challenging task of an engineer is to select a model combination that ensures a sufficient, reliable prognosis. In order to achieve this reliable prognosis of the overall structural behavior, a high individual quality of the partial models and an adequate coupling of the partial models is required. Several methodologies have been proposed to evaluate the quality of partial models for their intended application, but a detailed study of the coupling quality is still lacking. This paper proposes a new approach to assess the coupling quality of partial models in a quantitative manner. The approach is based on the consistency of the coupled data and applies for uni- and bidirectional coupled partial models. Furthermore, the influence of the coupling quality on the output quantities of the partial models is considered. The functionality of the algorithm and the effect of the coupling quality are demonstrated using an example of coupled partial models in structural engineering.
This thesis explores how architecture aids in the performance of open-ended narratives by engaging both actively and passively with memory, i.e. remembering and forgetting. I argue that architecture old and new stems from specific cultural and social forms, and is dictated by processes of remembering and forgetting. It is through interaction (between inhabitant and object) that architecture is given innate meanings within an urban environment that makes its role in the interplay one of investigative interest.
To enable the study of this performance, I develop a framework based on various theoretical paradigms to investigate three broad questions: 1) How does one study the performance of memory and forgetting through architecture in dynamic urban landscapes? 2) Is there a way to identify markers and elements within the urban environment that enable such a study? 3) What is the role that urban form plays within this framework and does the transformation of urban form imply the transformation of memory and forgetting?
The developed framework is applied to a macro (an urban level study of Bangalore, India) and micro level study (a singular or object level study of Stari Most/ Old Bridge, Mostar, BiH), to analyse the performance of remembering and forgetting in various urban spheres through interaction with architecture and form. By means of observations, archival research, qualitative mapping, drawings and narrative interviews, the study demonstrates that certain sites and characteristics of architecture enable the performance of remembering and the questioning of forgetting by embodying features that support this act.
Combining theory and empirical studies this thesis is an attempt to elucidate on the processes through which remembering and forgetting is initiated and experienced through architectural forms. The thesis argues for recognising the potential of architecture as one that embodies and supports the performance of memory and forgetting, by acting as an auratic contact zone.
The topic of structural robustness is covered extensively in current literature in structural engineering. A few evaluation methods already exist. Since these methods are based on different evaluation approaches, the comparison is difficult. But all the approaches have one in common, they need a structural model which represents the structure to be evaluated. As the structural model is the basis of the robustness evaluation, there is the question if the quality of the chosen structural model is influencing the estimation of the structural robustness index. This paper shows what robustness in structural engineering means and gives an overview of existing assessment methods. One is the reliability based robustness index, which uses the reliability indices of a intact and a damaged structure. The second one is the risk based robustness index, which estimates the structural robustness by the usage of direct and indirect risk. The paper describes how these approaches for the evaluation of structural robustness works and which parameters will be used. Since both approaches needs a structural model for the estimation of the structural behavior and the probability of failure, it is necessary to think about the quality of the chosen structural model. Nevertheless, the chosen model has to represent the structure, the input factors and reflect the damages which occur. On the example of two different model qualities, it will be shown, that the model choice is really influencing the quality of the robustness index.
In this paper experimental studies and numerical analysis carried out on reinforced concrete beam are partially reported. They aimed to apply the rigid finite element method to calculations for reinforced concrete beams using discrete crack model. Hence rotational ductility resulting from crack occurrence had to be determined. A relationship for calculating it in static equilibrium was proposed. Laboratory experiments proved that dynamic ductility is considerably smaller. Therefore scaling of the empirical parameter was carried out. Consequently a formula for its value depending on reinforcement ratio was obtained.
Schwerpunkt Entwerfen
(2012)
Entwerfen ist ein äusserst unscharfer Begriff. Mit ihm kann je nach Kontext ebenso Zeichnen, Planen, Modellieren, Projektieren oder Darstellen gemeint sein wie Erfi nden, Entwickeln, Konzipieren, Komponieren und ähnliches. Wenn Architekten vom Entwurf reden, verwenden sie das Wort meist in einer Bedeutung, die auf den kunsttheoretischen Diskurs zurückgeht, der im Florenz des 16. Jahrhunderts entstanden ist: Entwurf als disegno. Dementsprechend konnte Entwerfen in der kunsthermeneutischen Rezeption schließlich mit dem ›künstlerischen Schaff ensprozess‹ selbst synonym werden. Im Entwerfen meint man der geistigen Vermögen und Prozesse im künstlerischen Subjekt habhaft zu werden.
An diese Tradition soll hier bewusst nicht angeknüpft werden. Um das Entwerfen als Kulturtechnik in seiner historischen Bedingtheit zu beschreiben, muss es aus dem anthropozentrischen Ursprung herausgerückt werden, an den es der florentinische kunsttheoretische Diskurs versetzt hat. Statt das Entwerfen als fundamentalen Akt künstlerischen Schaff ens zu begreifen und als anthropologische Konstante der Geschichte zu entziehen, wäre eben diese Konzeption als historisches Resultat von diskursiven, technischen und institutionellen Praktiken zu befragen.
Schwerpunkt Kollektiv
(2012)
Die neuere und höchst produktive Konjunktur des »Kollektiv«-Begriffs in Soziologie und Kulturtheorie, wie sie sich insbesondere durch die Ent-faltung der Akteur-Netzwerk-Theorie herausgebildet hat, ist zunächst durch vier miteinander zusammenhängende Eigentümlichkeiten gekennzeichnet. Erstens bezeichnet das »Kollektiv« in diesem Sinne vor allem anderen eine Ansammlung von Entitäten zu einem als Ganzem operativen, möglicherweise sogar handlungs- und reflexionsfähigen Komplex. Die Operationen werden dabei erstens im »Kollektiv« und durch das »Kollektiv« ausgeführt, gleichzeitig jedoch sind sie es, die das »Kollektiv« überhaupt erst aufspannen und relationieren und so zusammenhalten und reproduzieren bzw. variieren. Das Besondere daran ist zweitens – und das unterscheidet den »Kollektiv«-Begriff etwa von demjenigen des Systems –, dass es keine Subsumption der beteiligten Entitäten unter das kollektive Gebilde gibt. Die Operationsfähigkeit und der Zusammenschluss führen weder zu einem Aufgehen des Einzelnen im Ganzen, noch zerfällt im Rückfall das Ganze in eine bloße Gesamtheit aufsummierbarer Teile und Effekte. Kurz: Das »Kollektiv« kann nicht über die Beziehung von Ganzem und Teil definiert und schon gar nicht nach einer dieser beiden Seiten hin aufgelöst werden. Drittens, und das ist der vermutlich plakativste Zug des neuen »Kollektiv«-Begriffs, umfasst das »Kollektiv« Entitäten völlig heterogener Art, genauer: Es bringt solche Gegebenheiten zusammen, die nach klassischer ontologischer Tradition verschiedenen Seinsbezirken zugerechnet worden wären. Das sind vor allem die berühmten menschlichen und nichtmenschlichen Akteure Bruno Latours, das sind also Personen und Artefakte, Kultur- und Naturdinge, Intelligibles und Sensibles, Reflexives und Irreflexives, Technisches und Ästhetisches, Bilder und Objekte oder sogar Materielles und Immaterielles wie Geister, Götter und Ahnen, so bei Descola oder Gell. Und viertens schließlich ist der »Kollektiv«-Begriff speziell ein Kontrastbegriff , der innerhalb der »neuen Soziologie« der Akteur-Netzwerk-Theorie an die Stelle des Gesellschaftsbegriff s treten soll, eben um dessen humanozentrische Prägung einerseits und seine subsumptive, generalisierende und anti-partikulare Tradition
andererseits abzustreifen.
The aim of this paper we discuss explicit series constructions for the fundamental solution of the Helmholtz operator on some important examples non-orientable conformally at manifolds. In the context of this paper we focus on higher dimensional generalizations of the Klein bottle which in turn generalize higher dimensional Möbius strips that we discussed in preceding works. We discuss some basic properties of pinor valued solutions to the Helmholtz equation on these manifolds.
Die Arbeit behandelt die Geschichte der Landesplanung in Mitteldeutschland und besteht aus zwei Teilen: den Zeiträumen der 1920 und 1990 Jahre. Dabei wird die Herausbildung der Landesplanung im mitteldeutschen Industriegebiet (um Merseburg) bzw. Thüringen behandelt. Die kognitiven, institutionellen und planerischen Grundlagen der Landesplanung werden herausgearbeitet. Dabei spielen die paradigmatischen Grundlagen (Dezentralisierung) sowie die internationalen Beziehungen (insbes. zu den USA) eine besondere Rolle. Schließlich werden das Wirken von Schlüsselpersonen (u.a. Prager, Luthardt, Langen) und die Bezüge zum Bauhaus untersucht. Die Analyse des Planwerks für Mitteldeutschland (1932) wird umfassend geführt. In der Analyse der Entstehung können erste Ansätze nicht-linearer Planung herausgearbeitet werden. Der zweite Teil der Arbeit widmet sich dem Industriellen Gartenreich, einem Projekt der Stiftung Bauhaus Dessau, das als Korrespondenzregion zur EXPO anerkannt worden war. Hier stehen das Gesamtkonzept, aber auch Projekte wie Ferropolis im Zentrum der Betrachtung. Die Analysen der Landesplanung werden in ihren Bezügen zur gesellschaftlichen und konkret wirtschaftlichen Entwicklung behandelt. Schließlich werden beide Entwicklungsphasen und deren landesplanerischen Resultate übergreifend bewertet und in einem Modell emergent-adaptiver Planung verortet und ein Ausblick auf die Entwicklung der Landesplanung als nicht-lineare Planung gegeben.
Die besondere Aggressivität von hochkonzentrierten Magnesiumsulfatlösungen bei Einwirkung auf Beton ist seit vielen Jahrzehnten bekannt. Neben dem Sulfat greift zusätzlich auch das Magnesium den Zementstein an. Bei hohen Lösungskonzentrationen nimmt der Magnesiumangriff gegenüber dem Sulfatangriff sogar eine dominante Rolle ein. Magnesiumgehalte unter 300 mg/l im Grundwasser gelten allerdings bislang als nicht angreifend. In Auslagerungs- und Laborversuchen wurde jedoch festgestellt, dass auch bei praxisrelevanten Magnesium- (<300 mg/l) und Sulfatgehalten (1.500 mg/l) das Magnesium zu einer deutlichen Verschärfung des Sulfatangriffes bei niedrigen Temperaturen führte. Diese Verschärfung trat bei Mörteln und Betonen auf, bei denen der erhöhte Sulfatwiderstand durch einen teilweisen Zementersatz mit 20 % Flugasche zu einem CEM II/A-LL erreicht werden sollte, gemäß der Flugascheregelung nach EN 206-1/DIN 1045-2.
Bei einem teilweisen Zementersatz durch 30 % Flugasche konnte auch in magnesiumhaltigen Sulfatlösungen eine deutliche Verbesserung des Sulfatwiderstandes erreicht werden. Mörtel mit HS-Zement als Bindemittel wiesen keinerlei Schäden auf. Schadensverursachend war eine Kombination mehrerer Einflüsse. Zum einen wurde der Sulfatwiderstand des Zement-Flugasche-Systems durch die unzureichende Reaktion der Flugasche infolge der niedrigen Lagerungstemperatur geschwächt. Zum anderen konnte durch die Einwirkung des Magnesiums in der Randzone vermutlich eine Destabilisierung der C-S-H-Phasen erfolgen, wodurch die Thaumasitbildung an dieser Stelle forciert wurde. Zusätzlich wurde durch den Portlanditverbrauch und die pH-Wert-Absenkung in der Randzone die puzzolanische Reaktion der Flugasche behindert.