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- 2010 (119) (remove)

Die Behandlung von geometrischen Singularitäten bei der Lösung von Randwertaufgaben der Elastostatik stellt erhöhte Anforderungen an die mathematische Modellierung des Randwertproblems und erfordert für eine effiziente Auswertung speziell angepasste Berechnungsverfahren. Diese Arbeit beschäftigt sich mit der systematischen Verallgemeinerung der Methode der komplexen Spannungsfunktionen auf den Raum, wobei der Schwerpunkt in erster Linie auf der Begründung des mathematischen Verfahrens unter besonderer Berücksichtigung der praktischen Anwendbarkeit liegt. Den theoretischen Rahmen hierfür bildet die Theorie quaternionenwertiger Funktionen. Dementsprechend wird die Klasse der monogenen Funktionen als Grundlage verwendet, um im ersten Teil der Arbeit ein räumliches Analogon zum Darstellungssatz von Goursat zu beweisen und verallgemeinerte Kolosov-Muskhelishvili Formeln zu konstruieren. Im Hinblick auf die vielfältigen Anwendungsbereiche der Methode beschäftigt sich der zweite Teil der Arbeit mit der lokalen und globalen Approximation von monogenen Funktionen. Hierzu werden vollständige Orthogonalsysteme monogener Kugelfunktionen konstruiert, infolge dessen neuartige Darstellungen der kanonischen Reihenentwicklungen (Taylor, Fourier, Laurent) definiert werden. In Analogie zu den komplexen Potenz- und Laurentreihen auf der Grundlage der holomorphen z-Potenzen werden durch diese monogenen Orthogonalreihen alle wesentlichen Eigenschaften bezüglich der hyperkomplexen Ableitung und der monogenen Stammfunktion verallgemeinert. Anhand repräsentativer Beispiele werden die qualitativen und numerischen Eigenschaften der entwickelten funktionentheoretischen Verfahren abschließend evaluiert. In diesem Kontext werden ferner einige weiterführende Anwendungsbereiche im Rahmen der räumlichen Funktionentheorie betrachtet, welche die speziellen Struktureigenschaften der monogenen Potenz- und Laurentreihenentwicklungen benötigen.

Verkehrsmengenrisiko bei PPP-Projekten im Straßensektor - Determinanten effizienter Risikoallokation
(2010)

Trotz weltweit umfangreichen Erfahrungen mit Public Private Partnership Projekten im Straßensektor bleibt der Umgang mit dem Verkehrsmengenrisiko für die Projektbeteiligten eine Herausforderung. Die Arbeit widmet sich daher der wesentlichen Fragestellung nach einer effizienten Allokation dieses Risikos, dem nicht weniger Bedeutung zukommt als für den gesamtwirtschaftlichen Erfolg eines Straßenkonzessionsprojektes eine entscheidende Rolle zu spielen. Untersucht werden zunächst die Charakteristika des Verkehrsmengenrisikos mit seinen umfänglichen Einflussfaktoren. Anschließend werden die in der Praxis zur Anwendung kommenden Vertragsmodelle zur Bewirtschaftung von Straßeninfrastruktur dargestellt und analysiert, wie in den einzelnen Modellen Verkehrsmengenrisiko auf die verschiedenen Vertragspartner verteilt wird. Auf Basis dieser Grundlagen wird ein kriteriengestützter Analyserahmen entwickelt, der die Effizienz unterschiedlicher Risikoallokationen zwischen den Vertragspartner bewertet. Dabei werden einerseits die effizienzbeeinflussenden Eigenschaften der potentiellen Risikoträger eines PPP-Projektes berücksichtigt als auch die die effizienzbeeinflussenden Wirkungen der unterschiedlichen Vertragsmodelle. Aus den Erkenntnissen dieser Analyse werden letztlich Handlungs- und Gestaltungsempfehlungen zum Umgang mit dem Verkehrsmengenrisiko abgeleitet.

We consider a structural truss problem where all of the physical model parameters are uncertain: not just the material values and applied loads, but also the positions of the nodes are assumed to be inexact but bounded and are represented by intervals. Such uncertainty may typically arise from imprecision during the process of manufacturing or construction, or round-off errors. In this case the application of the finite element method results in a system of linear equations with numerous interval parameters which cannot be solved conventionally. Applying a suitable variable substitution, an iteration method for the solution of a parametric system of linear equations is firstly employed to obtain initial bounds on the node displacements. Thereafter, an interval tightening (pruning) technique is applied, firstly on the element forces and secondly on the node displacements, in order to obtain tight guaranteed enclosures for the interval solutions for the forces and displacements.

Die vorliegende Arbeit beschäftigt sich mit der vergleichenden Analyse unterschiedlicher Berechnungsansätze zum hydraulischen Grundbruch. Diese wurden zunächst analysiert, an Beispielberechnungen angewandt und schließlich miteinander verglichen. Weiterhin wurde der Einfluss verschiedener Randbedingungen, allem voran der Baugrubenbreite, auf die Sicherheit gegen einen hydraulischen Grundbruch untersucht. Es werden Empfehlungen zur Anwendbarkeit verschiedener Näherungsansätze bei Vorhandensein bestimmter Einflussfaktoren gegeben.

In the past, several types of Fourier transforms in Clifford analysis have been studied. In this paper, first an overview of these different transforms is given. Next, a new equation in a Clifford algebra is proposed, the solutions of which will act as kernels of a new class of generalized Fourier transforms. Two solutions of this equation are studied in more detail, namely a vector-valued solution and a bivector-valued solution, as well as the associated integral transforms.

Fuzzy functions are suitable to deal with uncertainties and fuzziness in a closed form maintaining the informational content. This paper tries to understand, elaborate, and explain the problem of interpolating crisp and fuzzy data using continuous fuzzy valued functions. Two main issues are addressed here. The first covers how the fuzziness, induced by the reduction and deficit of information i.e. the discontinuity of the interpolated points, can be evaluated considering the used interpolation method and the density of the data. The second issue deals with the need to differentiate between impreciseness and hence fuzziness only in the interpolated quantity, impreciseness only in the location of the interpolated points and impreciseness in both the quantity and the location. In this paper, a brief background of the concept of fuzzy numbers and of fuzzy functions is presented. The numerical side of computing with fuzzy numbers is concisely demonstrated. The problem of fuzzy polynomial interpolation, the interpolation on meshes and mesh free fuzzy interpolation is investigated. The integration of the previously noted uncertainty into a coherent fuzzy valued function is discussed. Several sets of artificial and original measured data are used to examine the mentioned fuzzy interpolations.

In order to make control decisions, Smart Buildings need to collect data from multiple sources and bring it to a central location, such as the Building Management System (BMS). This needs to be done in a timely and automated fashion. Besides data being gathered from different energy using elements, information of occupant behaviour is also important for a building’s requirement analysis. In this paper, the parameter of Occupant Density was considered to help find behaviour of occupants towards a building space. Through this parameter, support for building energy consumption and requirements based on occupant need and demands was provided. The demonstrator presented provides information on the number of people present in a particular building space at any time, giving the space density. Such collections of density data made over a certain period of time represents occupant behaviour towards the building space, giving its usage patterns. Similarly, inventory items were tracked and monitored for moving out or being brought into a particular read zone. For both, people and inventory items, this was achieved using small, low-cost, passive Ultra-High Frequency (UHF) Radio Frequency Identification (RFID) tags. Occupants were given the tags in a form factor of a credit card to be possessed at all times. A central database was built where occupant and inventory information for a particular building space was maintained for monitoring and providing a central data access.

One of the main focuses of recent Chinese urban development is the creation and retrofitting of public spaces driven by the market force and demand. However, researches concerning human and cultural influences on shaping public spaces have been scanty. There still exist many undefined ambiguous planning aspects institutionally and legislatively. This is an explanatory research to address interactions, incorporations and interrelationship between the lived environment and its peoples. It is knowledge-seeking and normative. Theoretically, public space in a Chinese context is conceptualized; empirically, a selected case is inquired. The research has unfolded a comparatively complete understanding of China’s planning evolution and on-going practices. Data collection emphasizes the concept of ‘people’ and ‘space’. First-hand data is derived from the intensive fieldwork and observatory and participatory documentations. The ample detailed authentic empirical data empowers space syntax as a strong analysis tool in decoding how human’s activities influence the public space. Findings fall into two categories but interdependent. Firstly, it discloses the studied settlement as a generic, organic and incremental development model. Its growth and established environment is evolutionary and incremental, based on its intrinsic traditions, life values and available resources. As a self-sustaining settlement, it highlights certain vernacular traits of spatial development out of lifestyles and cultural practices. Its spatial articulation appears as a process parallel to socio-economic transitions. Secondly, crucial planning aspects are theoretically summarized to address the existing gap between current planning methodology and practicalities. It pinpoints several most significant and particular issues, namely, disintegrated land use system and urban planning; missing of urban design in the planning system, loss of a human-responsive environment resulted from standardized planning and under-estimation of heritage in urban development. The research challenges present Chinese planning laws and regulations through urban public space study; and pinpoints to yield certain growth leverage for planning and development. Thus, planning is able to empower inhabitants to make decisions along the process of shaping and sustaining their space. Therefore, it discusses not only legislative issues, concerning land use planning, urban design and heritage conservation. It leads to a pivotal proposal, i.e., the integration of human and their social spaces in formulating a new spatial strategy. It expects to inform policymakers of underpinning social values and cultural practices in reconfiguring postmodern Chinese spatiality. It propounds that social context endemic to communities shall be integrated as a crucial tool in spatial strategy design, hence to strengthen spatial attributes and improve life quality.

In this paper we present rudiments of a higher dimensional analogue of the Szegö kernel method to compute 3D mappings from elementary domains onto the unit sphere. This is a formal construction which provides us with a good substitution of the classical conformal Riemann mapping. We give explicit numerical examples and discuss a comparison of the results with those obtained alternatively by the Bergman kernel method.

In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces.

THE FOURIER-BESSEL TRANSFORM
(2010)

In this paper we devise a new multi-dimensional integral transform within the Clifford analysis setting, the so-called Fourier-Bessel transform. It appears that in the two-dimensional case, it coincides with the Clifford-Fourier and cylindrical Fourier transforms introduced earlier. We show that this new integral transform satisfies operational formulae which are similar to those of the classical tensorial Fourier transform. Moreover the L2-basis elements consisting of generalized Clifford-Hermite functions appear to be eigenfunctions of the Fourier-Bessel transform.

This paper describes the application of interval calculus to calculation of plate deflection, taking in account inevitable and acceptable tolerance of input data (input parameters). The simply supported reinforced concrete plate was taken as an example. The plate was loaded by uniformly distributed loads. Several parameters that influence the plate deflection are given as certain closed intervals. Accordingly, the results are obtained as intervals so it was possible to follow the direct influence of a change of one or more input parameters on output (in our example, deflection) values by using one model and one computing procedure. The described procedure could be applied to any FEM calculation in order to keep calculation tolerances, ISO-tolerances, and production tolerances in close limits (admissible limits). The Wolfram Mathematica has been used as tool for interval calculation.

In this dissertation, a new, unique and original biaxial device for testing unsaturated soil was designed and developed. A study on the mechanical behaviour of unsaturated sand in plane-strain conditions using the new device is presented. The tests were mainly conducted on Hostun sand specimens. A series of experiments including basic characterisation, soil water characteristic curves, and compression biaxial tests on dry, saturated, and unsaturated sand were conducted. A set of bearing capacity tests of strip model footing on unsaturated sand were performed. Additionally, since the presence of fine content (i.e., clay) influences the behavior of soils, soil water characteristic tests were also performed for sand-kaolin mixtures specimens.

Im vorliegenden Beitrag wird ein Framework für ein verteiltes dynamisches Produktmodell (FREAC) vorgestellt, welches der experimentellen Softwareentwicklung dient. Bei der Entwicklung von FREAC wurde versucht, folgende Eigenschaften umzusetzen, die bei herkömmlichen Systemen weitgehend fehlen: Erstens eine hohe Flexibilität, also eine möglichst hohe Anpassbarkeit für unterschiedliche Fachdisziplinen; Zweitens die Möglichkeit, verschiedene Tools nahtlos miteinander zu verknüpfen; Drittens die verteilte Modellbearbeitung in Echtzeit; Viertens das Abspeichern des gesamten Modell-Bearbeitungsprozesses; Fünftens eine dynamische Erweiterbarkeit sowohl für Softwareentwickler, als auch für die Nutzer der Tools. Die Bezeichnung FREAC umfasst sowohl das Framework zur Entwicklung und Pflege eines Produktmodells (FREAC-Development) als auch die entwickelten Tools selbst (FREAC-Tools).

Am 25. März 2010 veranstaltete die Professur Baubetrieb und Bauverfahren im Rahmen der jährlich stattfindenden baubetrieblichen Tagungsreihe gemeinsam mit der Arbeitsgruppe „Unikatprozesse“ in der Fachgruppe „Simulation in Produktion und Logistik“ (SPL) im Rahmen der Arbeitsgemeinschaft Simulation – ASIM einen ganztägigen Workshop mit dem Titel: „Modellierung von Prozessen zur Fertigung von Unikaten“. Viele Bauprozesse sind dadurch gekennzeichnet, dass sie Unikatcharakter besitzen. Unikate sind durch prototypische Einmaligkeit, Individualität, vielfältige Randbedingungen, einen geringen Grad an Standardisierung und Wiederholungen gekennzeichnet. Das erschwert die realitätsnahe Modellierung zur Simulation sogenannter Unikatprozesse. Dieser Besonderheit widmet sich die überwiegende Zahl der Tagungsbeiträge, die in diesem Band widergegeben sind.

Besides home entertainment and business presentations, video projectors are powerful tools for modulating images spatially as well as temporally. The re-evolving need for stereoscopic displays increases the demand for low-latency projectors and recent advances in LED technology also offer high modulation frequencies. Combining such high-frequency illumination modules with synchronized, fast cameras, makes it possible to develop specialized high-speed illumination systems for visual effects production. In this thesis we present different systems for using spatially as well as temporally modulated illumination in combination with a synchronized camera to simplify the requirements of standard digital video composition techniques for film and television productions and to offer new possibilities for visual effects generation. After an overview of the basic terminology and a summary of related methods, we discuss and give examples of how modulated light can be applied to a scene recording context to enable a variety of effects which cannot be realized using standard methods, such as virtual studio technology or chroma keying. We propose using high-frequency, synchronized illumination which, in addition to providing illumination, is modulated in terms of intensity and wavelength to encode technical information for visual effects generation. This is carried out in such a way that the technical components do not influence the final composite and are also not visible to observers on the film set. Using this approach we present a real-time flash keying system for the generation of perspectively correct augmented composites by projecting imperceptible markers for optical camera tracking. Furthermore, we present a system which enables the generation of various digital video compositing effects outside of completely controlled studio environments, such as virtual studios. A third temporal keying system is presented that aims to overcome the constraints of traditional chroma keying in terms of color spill and color dependency. ...

This paper deals with the modelling and the analysis of masonry vaults. Numerical FEM analyses are performed using LUSAS code. Two vault typologies are analysed (barrel and cross-ribbed vaults) parametrically varying geometrical proportions and constraints. The proposed model and the developed numerical procedure are implemented in a computer analysis. Numerical applications are developed to assess the model effectiveness and the efficiency of the numerical procedure. The main object of the present paper is the development of a computational procedure which allows to define 3D structural behaviour of masonry vaults. For each investigated example, the homogenized limit analysis approach has been employed to predict ultimate load and failure mechanisms. Finally, both a mesh dependence study and a sensitivity analysis are reported. Sensitivity analysis is conducted varying in a wide range mortar tensile strength and mortar friction angle with the aim of investigating the influence of the mechanical properties of joints on collapse load and failure mechanisms. The proposed computer model is validated by a comparison with experimental results available in the literature.

In recent years special hypercomplex Appell polynomials have been introduced by several authors and their main properties have been studied by different methods and with different objectives. Like in the classical theory of Appell polynomials, their generating function is a hypercomplex exponential function. The observation that this generalized exponential function has, for example, a close relationship with Bessel functions confirmed the practical significance of such an approach to special classes of hypercomplex differentiable functions. Its usefulness for combinatorial studies has also been investigated. Moreover, an extension of those ideas led to the construction of complete sets of hypercomplex Appell polynomial sequences. Here we show how this opens the way for a more systematic study of the relation between some classes of Special Functions and Elementary Functions in Hypercomplex Function Theory.

The numerical simulation of microstructure models in 3D requires, due to enormous d.o.f., significant resources of memory as well as parallel computational power. Compared to homogeneous materials, the material hetrogeneity on microscale induced by different material phases demand for adequate computational methods for discretization and solution process of the resulting highly nonlinear problem. To enable an efficient/scalable solution process of the linearized equation systems the heterogeneous FE problem will be described by a FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) discretization. The fundamental FETI-DP equation can be solved by a number of different approaches. In our approach the FETI-DP problem will be reformulated as Saddle Point system, by eliminating the primal and Lagrangian variables. For the reduced Saddle Point system, only defined by interior and dual variables, special Uzawa algorithms can be adapted for iteratively solving the FETI-DP saddle-point equation system (FETI-DP SPE). A conjugate gradient version of the Uzawa algorithm will be shown as well as some numerical tests regarding to FETI-DP discretization of small examples using the presented solution technique. Furthermore the inversion of the interior-dual Schur complement operator can be approximated using different techniques building an adequate preconditioning matrix and therewith leading to substantial gains in computing time efficiency.

Within the scheduling of construction projects, different, partly conflicting objectives have to be considered. The specification of an efficient construction schedule is a challenging task, which leads to a NP-hard multi-criteria optimization problem. In the past decades, so-called metaheuristics have been developed for scheduling problems to find near-optimal solutions in reasonable time. This paper presents a Simulated Annealing concept to determine near-optimal construction schedules. Simulated Annealing is a well-known metaheuristic optimization approach for solving complex combinatorial problems. To enable dealing with several optimization objectives the Pareto optimization concept is applied. Thus, the optimization result is a set of Pareto-optimal schedules, which can be analyzed for selecting exactly one practicable and reasonable schedule. A flexible constraint-based simulation approach is used to generate possible neighboring solutions very quickly during the optimization process. The essential aspects of the developed Pareto Simulated Annealing concept are presented in detail.

A practical framework for generating cross correlated fields with a specified marginal distribution function, an autocorrelation function and cross correlation coefficients is presented in the paper. The contribution promotes a recent journal paper [1]. The approach relies on well known series expansion methods for simulation of a Gaussian random field. The proposed method requires all cross correlated fields over the domain to share an identical autocorrelation function and the cross correlation structure between each pair of simulated fields to be simply defined by a cross correlation coefficient. Such relations result in specific properties of eigenvectors of covariance matrices of discretized field over the domain. These properties are used to decompose the eigenproblem which must normally be solved in computing the series expansion into two smaller eigenproblems. Such decomposition represents a significant reduction of computational effort. Non-Gaussian components of a multivariate random field are proposed to be simulated via memoryless transformation of underlying Gaussian random fields for which the Nataf model is employed to modify the correlation structure. In this method, the autocorrelation structure of each field is fulfilled exactly while the cross correlation is only approximated. The associated errors can be computed before performing simulations and it is shown that the errors happen especially in the cross correlation between distant points and that they are negligibly small in practical situations.

From passenger’s perspective, punctuality is one of the most important features of tram route operation. We present a stochastic simulation model with special focus on determining important factors of influence. The statistical analysis bases on large samples (sample size is nearly 2000) accumulated from comprehensive measurements on eight tram routes in Cracow. For the simulation, we are not only interested in average values but also in stochastic characteristics like the variance and other properties of the distribution. A realization of trams operations is assumed to be a sequence of running times between successive stops and times spent by tram at the stops divided in passengers alighting and boarding times and times waiting for possibility of departure . The running time depends on the kind of track separation including the priorities in traffic lights, the length of the section and the number of intersections. For every type of section, a linear mixed regression model describes the average running time and its variance as functions of the length of the section and the number of intersections. The regression coefficients are estimated by the iterative re-weighted least square method. Alighting and boarding time mainly depends on type of vehicle, number of passengers alighting and boarding and occupancy of vehicle. For the distribution of the time waiting for possibility of departure suitable distributions like Gamma distribution and Lognormal distribution are fitted.

SIMULATION AND MATHEMATICAL OPTIMIZATION OF THE HYDRATION OF CONCRETE FOR AVOIDING THERMAL CRACKS
(2010)

After mixing of concrete, the hardening starts by an exothermic chemical reaction known as hydration. As the reaction rate depends on the temperature the time in the description of the hydration is replaced by the maturity which is defined as an integral over a certain function depending on the temperature. The temperature distribution is governed by the heat equation with a right hand side depending on the maturity and the temperature itself. We compare of the performance of different time integration schemes of higher order with an automatic time step control. The simulation of the heat distribution is of importance as the development of mechanical properties is driven by the hydration. During this process it is possible that the tensile stresses exceed the tensile strength and cracks occur. The goal is to produce cheap concrete without cracks. Simple crack-criterions use only temperature differences, more involved ones are based on thermal stresses. If the criterion predicts cracks some changes in the input data are needed. This can be interpreted as optimization. The final goal will be to adopt model based optimization (in contrast to simulation based optimization) to the problem of the hydration of young concrete and the avoidance of cracks. The first step is the simulation of the hydration, which we focus in this paper.

In this paper three different formulations of a Bernoulli type free boundary problem are discussed. By analyzing the shape Hessian in case of matching data it is distinguished between well-posed and ill-posed formulations. A nonlinear Ritz-Galerkin method is applied for discretizing the shape optimization problem. In case of well-posedness existence and convergence of the approximate shapes is proven. In combination with a fast boundary element method efficient first and second order shape optimization algorithms are obtained.

In spite of the extensive research in dynamic soil-structure interaction (SSI), there still exist miscon-ceptions concerning the role of SSI in the seismic performance of structures, especially the ones founded on soft soil. This is due to the fact that current analytical SSI models that are used to evaluate the influence of soil on the overall structural behavior are approximate models and may involve creeds and practices that are not always precise. This is especially true in the codified approaches which in-clude substantial approximations to provide simple frameworks for the design. As the direct numerical analysis requires a high computational effort, performing an analysis considering SSI is computationally uneconomical for regular design applications. This paper outlines the set up some milestones for evaluating SSI models. This will be achieved by investigating the different assumptions and involved factors, as well as varying the configurations of R/C moment-resisting frame structures supported by single footings which are subject to seismic excita-tions. It is noted that the scope of this paper is to highlight, rather than fully resolve, the above subject. A rough draft of the proposed approach is presented in this paper, whereas a thorough illustration will be carried out throughout the presentation in the course of the conference.

We investigate aspects of tram-network section reliability, which operates as a part of the model of whole city tram-network reliability. Here, one of the main points of interest is the character of the chronological development of the disturbances (namely the differences between time of departure provided in schedule and real time of departure) on subsequent sections during tram line operation. These developments were observed in comprehensive measurements done in Krakow, during one of the main transportation nodes (Rondo Mogilskie) rebuilding. All taken building activities cause big disturbances in tram lines operation with effects extended to neighboring sections. In a second part, the stochastic character of section running time will be analyzed more detailed. There will be taken into consideration sections with only one beginning stop and also with two or three beginning stops located at different streets at an intersection. Possibility of adding results from sections with two beginning stops to one set will be checked with suitable statistical tests which are used to compare the means of the two samples. Section running time may depend on the value of gap between two following trams and from the value of deviation from schedule. This dependence will be described by a multi regression formula. The main measurements were done in the city center of Krakow in two stages: before and after big changes in tramway infrastructure.

Due to increasing numbers of wind energy converters, the accurate assessment of the lifespan of their structural parts and the entire converter system is becoming more and more paramount. Lifespan-oriented design, inspections and remedial maintenance are challenging because of their complex dynamic behavior. Wind energy converters are subjected to stochastic turbulent wind loading causing corresponding stochastic structural response and vibrations associated with an extreme number of stress cycles (up to 109 according to the rotation of the blades). Currently, wind energy converters are constructed for a service life of about 20 years. However, this estimation is more or less made by rule of thumb and not backed by profound scientific analyses or accurate simulations. By contrast, modern structural health monitoring systems allow an improved identification of deteriorations and, thereupon, to drastically advance the lifespan assessment of wind energy converters. In particular, monitoring systems based on artificial intelligence techniques represent a promising approach towards cost-efficient and reliable real-time monitoring. Therefore, an innovative real-time structural health monitoring concept based on software agents is introduced in this contribution. For a short time, this concept is also turned into a real-world monitoring system developed in a DFG joint research project in the authors’ institute at the Ruhr-University Bochum. In this paper, primarily the agent-based development, implementation and application of the monitoring system is addressed, focusing on the real-time monitoring tasks in the deserved detail.

Quality is one of the most important properties of a product. Providing the optimal quality can reduce costs for rework, scrap, recall or even legal actions while satisfying customers demand for reliability. The aim is to achieve ``built-in'' quality within product development process (PDP). The common approach therefore is the robust design optimization (RDO). It uses stochastic values as constraint and/or objective to obtain a robust and reliable optimal design. In classical approaches the effort required for stochastic analysis multiplies with the complexity of the optimization algorithm. The suggested approach shows that it is possible to reduce this effort enormously by using previously obtained data. Therefore the support point set of an underlying metamodel is filled iteratively during ongoing optimization in regions of interest if this is necessary. In a simple example, it will be shown that this is possible without significant loss of accuracy.

Public Private Partnership (PPP) setzt sich zunehmend als alternative Beschaffungsvariante für die öffentliche Hand durch. Im Krankenhausbereich bestehen erste Erfahrungen mit PPP, allerdings kann hier im Gegensatz zu anderen öffentlichen Bereichen noch nicht von einer Etablierung gesprochen werden. In vielen Krankenhäusern besteht Unklarheit über dieses neue Organisationskonzept. Was steckt hinter diesem Begriff, der teilweise synonym zur „Privatisierung“ verwendet wird? Ausgehend von dieser Fragestellung wird in der vorliegenden Arbeit gezeigt, dass PPP bei richtiger Anwendung eine Alternative zum Verkauf eines öffentlichen Krankenhauses darstellt. PPP ist ein Instrument, mit dem privates Know-how und Kapital für den öffentlichen Krankenhausträger nutzbar gemacht wird. Die öffentliche Trägerschaft des Krankenhauses bleibt dabei, im Gegensatz zu einer materiellen Privatisierung, erhalten. Die Rahmenbedingungen des Gesundheitswesens stellen insbesondere die öffentlichen Krankenhäuser vor große Herausforderungen. Die Lage ist zunehmend geprägt von Mittelknappheit, Sanierungsstau und stetig steigendem Wettbewerbsdruck um die Patienten. Die Reformbemühungen der Bundesregierung zur Senkung der Gesundheitsausgaben haben in den letzten Jahrzehnten zu immer neuen Gesetzesregelungen in immer kürzeren Zeitabständen geführt. Den bisher letzten großen Schritt in dieser Entwicklung stellt die Umstellung der Krankenhausvergütung auf DRG-Fallpauschalen dar. Die Auswirkungen sind insbesondere in den öffentlichen Krankenhäusern zu spüren. Defizitäre Einrichtungen, die bisher durch Subventionen gestützt wurden, werden nun nicht mehr „künstlich am Leben“ erhalten. Alle Krankenhäuser erhalten eine leistungsorientierte Vergütung, weitgehend unabhängig von den krankenhausspezifisch anfallenden Kosten. Durch diese Entwicklungen wurde das Bestreben in den Krankenhäuser, die internen Leistungsprozesse zu optimieren, weiter forciert. Dabei kommt den mit der Gebäudesubstanz verbundenen Leistungen eine besondere Bedeutung zu. Aufgrund hoher Investitionskosten und bedeutender Aufwendungen in der Nutzungsphase erreichen die nicht-medizinischen Leistungen in einem Krankenhaus einen beachtlichen Anteil an den Gesamtkosten. Fast ein Drittel der Krankenhaus-Kosten steht nicht in direkter Beziehung zum Heilungsprozess. In Deutschland macht dieser Anteil der nicht-medizinischen Abläufe jährlich rd. 18 Mrd. Euro aus. Das Optimierungspotenzial des nicht-medizinischen Leistungsbereichs, der auch die bau- und immobilienwirtschaftlichen Leistungen umfasst, wird bisher oft noch unterschätzt und ist in den meisten Fällen noch nicht ausgeschöpft. Allein schon aufgrund dessen finanzieller Bedeutung bedarf es einer verstärkten wissenschaftlichen Auseinandersetzung. Dieser Notwendigkeit ist bisher noch unzureichend Rechnung getragen wurden. Die vorliegende Arbeit will mit der Erforschung der Anwendbarkeit von PPP für Krankenaus-Immobilien einen Beitrag dazu leisten, diese Lücke zu schließen. Mit dieser für den deutschen Krankenhausbereich neuartigen Beschaffungsvariante wird ein Weg aufgezeigt, wie bei den nicht-medizinischen Leistungen nachhaltig Effizienzpotenziale erschlossen werden können und auf diese Weise ein Beitrag zum wirtschaftlichen Erfolg des gesamten Krankenhauses erzielt werden kann.

PARAMETER IDENTIFICATION OF MESOSCALE MODELS FROM MACROSCOPIC TESTS USING BAYESIAN NEURAL NETWORKS
(2010)

In this paper, a parameter identification procedure using Bayesian neural networks is proposed. Based on a training set of numerical simulations, where the material parameters are simulated in a predefined range using Latin Hypercube sampling, a Bayesian neural network, which has been extended to describe the noise of multiple outputs using a full covariance matrix, is trained to approximate the inverse relation from the experiment (displacements, forces etc.) to the material parameters. The method offers not only the possibility to determine the parameters itself, but also the accuracy of the estimate and the correlation between these parameters. As a result, a set of experiments can be designed to calibrate a numerical model.

Steel structural design is an integral part of the building construction process. So far, various methods of design have been applied in practice to satisfy the design requirements. This paper attempts to acquire the Differential Evolution Algorithms in automatization of specific synthesis and rationalization of design process. The capacity of the Differential Evolution Algorithms to deal with continuous and/or discrete optimization of steel structures is also demonstrated. The goal of this study is to propose an optimal design of steel frame structures using built-up I-sections and/or a combination of standard hot-rolled profiles. All optimized steel frame structures in this paper generated optimization solutions better than the original solution designed by the manufacturer. Taking the criteria regarding the quality and efficiency of the practical design into consideration, the produced optimal design with the Differential Evolution Algorithms can completely replace conventional design because of its excellent performance.

Using a quaternionic reformulation of the electrical impedance equation, we consider a two-dimensional separable-variables conductivity function and, posing two different techniques, we obtain a special class of Vekua equation, whose general solution can be approach by virtue of Taylor series in formal powers, for which is possible to introduce an explicit Bers generating sequence.

On the mechanisms of shrinkage reducing admixtures in self con-solidating mortars and concretes
(2010)

Self Consolidating Concrete – a dream has come true!(?) Self Consolidating Concrete (SCC) is mainly characterised by its special rheological properties. With-out any vibration this concrete can be placed and compacted under its own weight, without segrega-tion or bleeding. The use of such concrete can increase the productivity on construction sites and en-able the use of a higher degree of well distributed reinforcement for thin walled structural members. This new technology also reduces health risks since in contrast to the traditional handling of concrete, the emission of noise and vibration are substantially decreased. The specific mix design for self consolidating concretes was introduced around the 1980s in Japan. In comparison to normal vibrated concrete an increased paste volume enables a good distribution of aggregates within the paste matrix, minimising the influence of aggregates friction on the concrete flow property. The introduction of inert and/or pozzolanic additives as part of the paste provides the required excess paste volume without using disproportionally high amounts of plain cement. Due to further developments of concrete admixtures such as superplasticizers, the cement paste can gain self levelling properties without causing segregation of aggregates. Whereas SCC differs from normal vibrated concrete in its fresh attributes, it should reach similar properties in the hardened state. Due to the increased paste volume it usually shows higher shrinkage. Furthermore, owing to strength requirements, SCC is often produced at low water to cement ratios and hence may additionally suffer from autogenous shrinkage. This means that cracking caused by drying or autogenous shrinkage is a real risk for SCC and can compromise its durability as cracks may serve as ingression paths for gases and salts or might permit leaching. For the time being SCC still exhibits increased shrinkage and cracking probability and hence may be discarded in many practical applications. This can be overcome by a better understanding of those mechanisms and the ways to mitigate them. It is a target of this thesis to contribute to this. How to cope with increased shrinkage of SCC? In general, engineers are facing severe problems related to shrinkage and cracking. Even for normal and high performance concrete, containing moderate amounts of binder, a lot of effort was put on counteracting shrinkage and avoiding cracking. For the time being these efforts resulted in the knowledge of how to distribute cracks rather to avoid them. The most efficient way to decrease shrinkage turned out to be to decrease the cement content of concrete down to a minimum but still sufficient amount. For SCC this obviously seems to be contradictory with the requirement of a high paste volume. Indeed, the potential for shrinkage reduction is limited to some small range modifications in the mix design following two major concepts. The first one is the reduction of the required paste volume by optimising the aggregate grading curve. The second one involves high volume substitution of cement, preferentially using inert mineral additives. The optimization of grading curves is limited by several severe practical issues. Problems start with the availability of sufficiently fractionated aggregates. Usually attempts fail because of the enormous effort in composing application-optimized grading curves or mix designs. Due to durability reasons, the substitution rate for cement is limited depending on the application purpose and on environmental exposure of the hardened concrete. In the early 1980s Shrinkage Reducing Admixtures (SRA) were introduced to counteract drying shrinkage of concrete. The first publications explicitly dealing with SRA go back to Goto and Sato (Japan). They were published in 1983, which is also the time when the SCC concept was introduced. SRA modified concretes showed a substantial reduction of free drying shrinkage contributing to crack prevention or at least a significant decrease of crack width in situations of restrained drying shrinkage. Will shrinkage reducing admixtures contribute to a broader application of SCC? Within the last three decades performance tests on several types of concrete proved the efficiency of shrinkage reducing admixtures. So, at least in terms of shrinkage and cracking, concretes in general and SCC in particular can benefit from SRA application. But "One man's meat is another man's poison" and with respect to long term performance of SRA modified concretes there are still several issues to be clarified. One of these concerns the impact of SRAs on cement hydration. It is therefore an issue to know if changes in the hydrated phase composition, induced by SRA, result in undesired properties or decreased durability. Another issue is that the long term shrinkage reduction has to be evaluated. For example, one can wonder if SRA leaching may diminish or even eliminate long term shrinkage reduction and if the release of admixtures could be a severe environmental issue. It should also be noted that the basic mechanism or physical impact of SRA as well as its implementation in recent models for shrinkage of concrete is still being discussed. The present thesis tries to shed light on the role of SRA in self consolidating concrete focusing on the three questions outlined above: basic mechanisms of cement hydration, physical impact on shrinkage and the sustainability of SRA-application. Which contributions result from this study? Based on an extensive patent search, commercial SRAs could be identified to be synergistic mixtures of non-ionic surfactants and glycols. This turns out to be most important information for more than one reason and is the subject of chapter 4. An abundant literature focuses on properties of these non-ionic surfactants. Moreover, from this rich pool of information, the behaviour of SRAs and their interactions in cementitious systems were better understood through this thesis. For example, it could be anticipated how SRAs behave in strong electrolytes and how surface activity, i.e. surface tension, and interparticle forces might be affected. The synergy effect regarding enhanced performance induced by the presence of additional glycol in SRAs could be derived from the literature on the co-surfactant nature of glycols. Generally it now can be said that glycols ensure that the non-ionic surfactant is properly distributed onto the paste interfaces to efficiently reduce surface tension. In literature, the impact of organic matter on cement hydration was extensively studied for other admixtures like superplasticizer. From there, main impact factors related to the nature of these molecules could be identified. In addition, here again, the literature on non-ionic surfactants provides sufficient information to anticipate possible interactions of SRA with cement hydration based on the nature of non-ionic surfactants. All in all, the extensive study on the nature of non-ionic surfactants, presented in chapter 4, provides fundamental understanding of the behaviour of SRAs in cement paste. Taking a step further to relate this to the impact on drying and shrinkage required to review recent models for drying and shrinkage of cement paste as presented in chapter 3. There, it is shown that macroscopic thermodynamics of the open pore systems can be successfully applied to predict drying induced deformation, but that surface activity of SRA still has to be implemented to explain the shrinkage reduction it causes. Because of severe issues concerning the importance of capillary pressure on shrinkage, a new macroscopic thermodynamic model was derived in a way that meets requirements to properly incorporate surface activity of SRA. This is the subject of chapter 5. Based on theoretical considerations, in chapter 5 the broader impact of SRA on drying cementitious matter could be outlined. In a next step, cement paste was treated as a deformable, open drying pore system. Thereby, the drying phenomena of SRA modified mortars and concrete observed by other authors could be retrieved. This phenomenological consistency of the model constitutes an important contribution towards the understanding of SRA mechanisms. Another main contribution of this work came from introducing an artificial pore system, denominated the normcube. Using this model system, it could be shown how the evolution of interfacial area and its properties interact in presence of SRAs and how this impacts drying characteristics. In chapter 7, the surface activity of commercial SRAs in aqueous solution and synthetic pore solution was investigated. This shows how the electrolyte concentration of synthetic pore solution impacts the phase behaviour of SRA and conversely, how the presence of SRA impacts the aqueous electrolyte solution. Whilst electrolytes enhance self-aggregation of SRAs into micelles and liquid crystals, the presence of SRAs leads to precipitation of minerals as syngenite and mirabilite. Moreover, electrolyte solutions containing SRAs comprise limited miscibility or rather show miscibility gaps, where the liquid separates into isotropic micellar solutions and surfactant rich reverse micellar solutions. The investigation of surface activity and phase behaviour of SRA unravelled another important contribution. From macroscopic surface tension measurements, a relationship between excess surface concentration of SRA, bulk concentration of SRA and exposed interfacial area could be derived. Based on this, it is now possible to predict the actual surface tension of the pore fluid in the course of drying once the evolution of internal interfacial area is known. This is used later in this thesis to describe the specific drying and shrinkage behaviour of SRA modified pastes and mortars. Calorimetric studies on normal Portland cement and composite binders revealed that SRA alone show only minor impact on hydration kinetics. In presence of superplasticizer however the cement hydration can be significantly decelerated. The delaying impact of SRA could be related to a selective deceleration of silicate phase hydration. Moreover, it could be shown that portlandite precipitation in presence of SRA is changed, turning the compact habitus into more or less layered structures. Thereby, the specific surface increases, causing the amount of physically bound water to increase, which in turn reduces the maximum degree of hydration achievable for sealed systems. Extensive phase analysis shows that the hydrated phase composition of SRA modified binders re-mains almost unaffected. The appearance of a temporary mineral phase could be detected by environmental scanning electron microscopy. As could be shown for synthetic pore solutions, syngenite precipitates during early hydration stages and is later consumed in the course of aluminate hydration, i.e. when sulphates are depleted. Moreover, for some SRAs, the salting out phenomena supposed to be enhanced in strong electrolytes could also be shown to take place. The resulting organic precipitates could be identified by SEM-EDX in cement paste and by X-ray diffraction on solid residues of synthetic pore solution. The presence of SRAs could also be identified to impact microstructure of well cured cement paste. Based on nitrogen adsorption measurements and mercury intrusion porosimetry the amount of small pores is seen to increase with SRA dosage, whilst the overall porosity remains unchanged. The question regarding sustainability of SRA application is the subject of chapter 10. By means of leaching studies it could be shown that SRA can be leached significantly. The mechanism could be identified as a diffusion process and a range of effective diffusion coefficients could be estimated. Thereby, the leaching of SRA can now be estimated for real structural members. However, while the admixture can be leached to high extents in tank tests, the leaching rates in practical applications can be assumed to be low because of much reduced contact with water. This could be proven by quantifying admixture loss during long term drying and rewetting cycles. Despite a loss of admixture shrinkage reduction is hardly impacted. Moreover, the cyclic tests revealed that the total deformations in presence of SRA remain low due to a lower extent of irreversibly shrinkage deformations. Another important contribution towards the better understanding of the working mechanism of SRA for drying and shrinkage came from the same leaching tests. A significant fraction of SRA is found to be immobile and does not diffuse in leaching. This fraction of SRA is probably strongly associated to cement phases as the calcium-silicate-hydrates or portlandite. Based on these findings, it is now also possible to quantify the amount of admixture active at the interfaces. This means that, the evolution of surface tension in the course of drying can be approximated, which is a fundamental requirement for modeling shrinkage in presence of SRA. The last experimental chapter of this study focuses on the working mechanism and impact of SRA on drying and shrinkage. Based on the thermodynamics of the open deformable pore system introduced in chapter 5, energy balances are set up using desorption and shrinkage isotherms of actual samples. Information on distribution of SRA in the hydrated paste is used to estimate the actual surface tensions of the pore solution. In other words, this is the first time that the surface activity of the SRA in the course of the drying is fully accounted for. From the energy balances the evolution and properties of the internal interface are then obtained. This made it possible to explain why SRAs impact drying and shrinkage and in what specific range of relative humidity they are active. Summarising the findings of this thesis it can be said that the understanding of the impact of SRAs on hydration, drying and shrinkage was brought forward. Many of the new insights came from the careful investigation of the theory of non-ionic surfactants, something that the cement community had generally overlooked up to now.

In this paper we consider the time independent Klein-Gordon equation on some conformally flat 3-tori with given boundary data. We set up an explicit formula for the fundamental solution. We show that we can represent any solution to the homogeneous Klein-Gordon equation on the torus as finite sum over generalized 3-fold periodic elliptic functions that are in the kernel of the Klein-Gordon operator. Furthermore we prove Cauchy and Green type integral formulas and set up a Teodorescu and Cauchy transform for the toroidal Klein-Gordon operator. These in turn are used to set up explicit formulas for the solution to the inhomogeneous version of the Klein-Gordon equation on the 3-torus.

As numerical techniques for solving PDE or integral equations become more sophisticated, treatments of the generation of the geometric inputs should also follow that numerical advancement. This document describes the preparation of CAD data so that they can later be applied to hierarchical BEM or FEM solvers. For the BEM case, the geometric data are described by surfaces which we want to decompose into several curved foursided patches. We show the treatment of untrimmed and trimmed surfaces. In particular, we provide prevention of smooth corners which are bad for diffeomorphism. Additionally, we consider the problem of characterizing whether a Coons map is a diffeomorphism from the unit square onto a planar domain delineated by four given curves. We aim primarily at having not only theoretically correct conditions but also practically efficient methods. As for FEM geometric preparation, we need to decompose a 3D solid into a set of curved tetrahedra. First, we describe some method of decomposition without adding too many Steiner points (additional points not belonging to the initial boundary nodes of the boundary surface). Then, we provide a methodology for efficiently checking whether a tetrahedral transfinite interpolation is regular. That is done by a combination of degree reduction technique and subdivision. Along with the method description, we report also on some interesting practical results from real CAD data.

The paper is devoted to a study of properties of homogeneous solutions of massless field equation in higher dimensions. We first treat the case of dimension 4. Here we use the two-component spinor language (developed for purposes of general relativity). We describe how are massless field operators related to a higher spin analogues of the de Rham sequence - the so called Bernstein-Gel'fand-Gel'fand (BGG) complexes - and how are they related to the twisted Dirac operators. Then we study similar question in higher (even) dimensions. Here we have to use more tools from representation theory of the orthogonal group. We recall the definition of massless field equations in higher dimensions and relations to higher dimensional conformal BGG complexes. Then we discuss properties of homogeneous solutions of massless field equation. Using some recent techniques for decomposition of tensor products of irreducible $Spin(m)$-modules, we are able to add some new results on a structure of the spaces of homogenous solutions of massless field equations. In particular, we show that the kernel of the massless field equation in a given homogeneity contains at least on specific irreducible submodule.

Since the 90-ties the Pascal matrix, its generalizations and applications have been in the focus of a great amount of publications. As it is well known, the Pascal matrix, the symmetric Pascal matrix and other special matrices of Pascal type play an important role in many scientific areas, among them Numerical Analysis, Combinatorics, Number Theory, Probability, Image processing, Sinal processing, Electrical engineering, etc. We present a unified approach to matrix representations of special polynomials in several hypercomplex variables (new Bernoulli, Euler etc. polynomials), extending results of H. Malonek, G.Tomaz: Bernoulli polynomials and Pascal matrices in the context of Clifford Analysis, Discrete Appl. Math. 157(4)(2009) 838-847. The hypercomplex version of a new Pascal matrix with block structure, which resembles the ordinary one for polynomials of one variable will be discussed in detail.

Building information modeling offers a huge potential for increasing the productivity and quality of construction planning processes. Despite its promising concept, this approach has not found widespread use. One of the reasons is the insufficient coupling of the structural models with the general building model. Instead, structural engineers usually set up a structural model that is independent from the building model and consists of mechanical models of reduced dimension. An automatic model generation, which would be valuable in case of model revisions is therefore not possible. This can be overcome by a volumetric formulation of the problem. A recent approach employed the p-version of the finite element method to this problem. This method, in conjunction with a volumetric formulation is suited to simulate the structural behaviour of both „thick“ solid bodies and thin-walled structures. However, there remains a notable discretization error in the numerical models. This paper therefore proposes a new approach for overcoming this situation. It sugggests the combination of the Isogeometric analysis together with the volumetric models in order to integrate the structural design into the digital, building model-centered planning process and reduce the discretization error. The concept of the isogeometric analysis consists, roughly, in the application of NURBS functions to represent the geometry and the shape functions of the elements. These functions possess some beneficial properties regarding numerical simulation. Their use, however, leads to some intricacies related to the setup of the stiffness matrix. This paper describes some of these properties.

NUMERICAL SIMULATION OF THERMO-HYGRAL ALKALI-SILICA REACTION MODEL IN CONCRETE AT THE MESOSCALE
(2010)

This research aims to model Alkali-Silica Reaction gel expansion in concrete under the influence of hygral and thermal loading, based on experimental results. ASR provokes a heterogeneous expansion in concrete leading to dimensional changes and eventually the premature failure of the concrete structure. This can result in map cracking on the concrete surface which will decrease the concrete stiffness. Factors that influence ASR are parameters such as the cement alkalinity, the number of deleterious silica from the aggregate used, concrete porosity, and external factors like temperature, humidity and external source of alkali from ingression of deicing salts. Uncertainties of the influential factors make ASR a difficult phenomenon to solve; hence my approach to this matter is to solve the problem using stochastic modelling, where a numerical simulation of concrete cross-section with integration of experimental results from Finger-Institute for Building Materials Science at the Bauhaus-Universität Weimar. The problem is formulated as a multi-field problem, combining heat transfer, fluid transfer and the reaction rate model with the mechanical stress field. Simulation is performed as a mesoscale model considering aggregates and mortar matrix. The reaction rate model will be conducted using experimental results from concrete expansions due to ASR gained from concrete prism tests. Expansive strains values for transient environmental conditions due to the reaction rate will be determined from calculation based on the reaction rate model. Results from these models will be able to predict the rate of ASR expansion and the cracking propagation that may arise.

Sand-bentonite mixtures are well recognized as buffer and sealing material in nuclear waste repository constructions. The behaviour of compacted sand-bentonite mixture needs to be well understood in order to guarantee the safety and the efficiency of the barrier construction. This paper presents numerical simulations of swelling test and coupled thermo-hydro-mechanical (THM) test on compacted sand-bentonite mixture in order to reveal the influence of the temperature and hydraulic gradients on the distribution of temperature, mechanical stress and water content in such materials. Sensitivity analysis is carried out to identify the parameters which influence the most the response of the numerical model. Results of back analysis of the model parameters are reported and critically assessed.

We present the way of calculation of displacement in the bent reinforced concrete bar elements where rearrangement of internal forces and plastic hinge occurred. The described solution is based on prof. Borcz’s mathematical model. It directly takes into consideration the effects connected with the occurrence of plastic hinge, such as for example a crack, by means of a differential equation of axis of the bent reinforced concrete beam. The EN Eurocode 2 makes it possible to consider the influence of plastic hinge on the values of the reinforced concrete structures. This influence can also be assumed using other analytical methods. However, the results obtained by the application of Eurocode 2 are higher from those received in testing. Just comparably big error level occurs when calculations are made by means of Borcz’s method, but in the latter case, the results depend on the assumptions made beforehand. This method makes it possible to apply the experimental results using parameters r1 i r0. When the experimental results are taken into account, one could observe the compatibility between the calculations and actual deflections of the structure.

The article presents analysis of stress distribution in the reinforced concrete support beam bracket which is a component of prefabricated reinforced concrete building. The building structure is spatial frame where dilatations were applied. The proper stiffness of its structure is provided by frames with stiff joints, monolithic lift shifts and staircases. The prefabricated slab floors are supported by beam shelves which are shaped as inverted letter ‘T’. Beams are supported by the column brackets. In order to lower the storey height and fulfill the architectural demands at the same time, the designer lowered the height of beam at the support zone. The analyzed case refers to the bracket zone where the slant crack. on the support beam bracket was observed. It could appear as a result of overcrossing of allowable tension stresses in reinforced concrete, in the bracket zone. It should be noted that the construction solution applied, i.e. concurrent support of the “undercut” beam on the column bracket causes local concentration of stresses in the undercut zone where the strongest transverse forces and tangent stresses occur concurrently. Some additional rectangular stresses being a result of placing the slab floors on the lower part of beam shelves sum up with those described above.

NONZONAL WAVELETS ON S^N
(2010)

In the present article we will construct wavelets on an arbitrary dimensional sphere S^n due the approach of approximate Identities. There are two equivalently approaches to wavelets. The group theoretical approach formulates a square integrability condition for a group acting via unitary, irreducible representation on the sphere. The connection to the group theoretical approach will be sketched. The concept of approximate identities uses the same constructions in the background, here we select an appropriate section of dilations and translations in the group acting on the sphere in two steps. At First we will formulate dilations in terms of approximate identities and than we call in translations on the sphere as rotations. This leads to the construction of an orthogonal polynomial system in L²(SO(n+1)). That approach is convenient to construct concrete wavelets, since the appropriate kernels can be constructed form the heat kernel leading to the approximate Identity of Gauss-Weierstra\ss. We will work out conditions to functions forming a family of wavelets, subsequently we formulate how we can construct zonal wavelets from a approximate Identity and the relation to admissibility of nonzonal wavelets. Eventually we will give an example of a nonzonal Wavelet on $S^n$, which we obtain from the approximate identity of Gauss-Weierstraß.

An energy method based on the LAGRANGE Principle of the minimum of total potential en-ergy is presented to calculate the stresses and strains of composite cross-sections. The stress-strain relation of each partition of the cross-section can be an arbitrary piecewise continuous function. The strain energy is transformed into a line integral by GAUSS’s integral theorem. The total strain of each partition of the cross-section is split into load-dependent strain and pre-strain. Pre-strains have to be taken into account when the cross-section is pre-stressed, retrofit-ted or influenced by shrinkage, temperature etc. The unconstrained minimum problem can be solved for each load combination using standard software. The application of the method presented in the paper is demonstrated by means of examples.

In the paper presented, reinforced concrete shells of revolution are analyzed in both meridional and circumferential directions. Taking into account the physical non-linearity of the material, the internal forces and the deflections of the shell as well as the strain distribution at the cross-sections are calculated. The behavior of concrete under compression is described by linear and non-linear stress-strain relations. The description of the behavior of concrete under tension must account for tension stiffening effects. A tri-linear function is used to formulate the material law of reinforcement. The problem cannot be solved analytically due to the physical non-linearity. Thus a numerical solution is formulated by means of the LAGRANGE Principle of the minimum of the total potential energy. The kinematically admissible field of deformation is defined by the displacements u in the meridional and w in the radial direction. These displacements must satisfy the equations of compatibility and the kinematical boundary conditions of the shell. The strains are linearly distributed across the wall thickness. The strain energy depends on the specific of the material behavior. Using integral formulations of the material law [1], the strain energy of each part of the cross-section is defined as a function of the strains at the boundaries of the cross-sections. The shell is discretised in the meridional direction. Various methods of numerical differentiation and numerical integration are applied in order to determine the deformations and the strain energy. The unknown displacements u and w are calculated by a non-restricted extremum problem based on the minimum of the total potential energy. From mathematical point of view, the objective function is a convex function, thus the minimum can be determined without difficulty. The advantage of this formulation is that unlike non-linear methods with path-following algorithms the calculation does not have to account for changing stiffness and load increments. All iterations necessary to find the solution are integrated into the “Solver”. The model presented provides many ways of investigating the influence of various material parameters on the stresses and deformations of the entire shell structure.