This master thesis deals with the issue of special discounts. Assessments and proposals of successful special offers are based on the analysis of demand price elasticity. The key attribute of this work is the knowledge of product’s price elasticity of demand. The analysis of price elasticity of demand is based on real data. The paper is terminated with suggestions on creating and planning special discounts developed in consideration of the retailers’ specific goals.

The aim of the theoretical part of this Master´s thesis is to make a research of possible ways in repairing PCC pavements without anchoring transverse joints. The pratical part is focused on the design of PCC pavements segmentations in experimental sections and evaluation measurement by testing muted impact.

Thesis describes properties of HPC compared to concretes of normal and high strength. It further describes the input materials and the procedure for designing the composition of the mixture. It gives examples of already completed structures made of HPC. The experimental part describes the optimization of concrete mix and production of specimens. In the end results of testing the properties of the developed mixes from tests of dynamic and static modulus of elasticity, compressive strength and tensile strength by bending are described.

This thesis focuses on the verification of physical and mechanical characteristics of hardened concrete, especially concrete compressive strength, static and dynamic modulus of elasticity. The job description is to perform a series of laboratory analyzes for structural concrete and evaluate the test results meet requirements that are specified in the European standards for designing buildings. The work also includes selected techniques for risk assessment (FMEA, Pareto diagram, Ishikawa diagram) and their application to selected process. Part of the work is also a static comparison of measured characteristics and consideration of the risks associated with variations in the monitored quantities.

Le transport de micro-organismes et de fluides biologiques au moyen de cils et flagelles est un phénomène universel que l’on retrouve chez presque tous les êtres vivants. Le but de cette thèse est la modélisation, l’analyse mathématique et la simulation numérique de problèmes d’interaction fluide-structure qui font intervenir des structures actives, capables de se déformer d’elles-mêmes grâce à des contraintes internes, et un fluide à faible nombre de Reynolds, modélisé par les équations de Stokes. Le Chapitre 2 traite de la modélisation de ces structures actives en considérant la loi de Saint Venant-Kirchhoff dans les équations de l’élasticité et en ajoutant un terme d’activité au second tenseur de contraintes de Piola-Kirchhoff. Les équations fluide et structures sont couplées à l’interface fluide-structure et l’étude mathématique d’un problème linéarisé et discrétisé en temps est ensuite réalisée. Une reformulation sous forme d’un problème point-selle est proposée et utilisée pour la simulation numérique du problème. Le Chapitre 3 s’intéresse à l’analyse du problème d’interaction fluide-structure quasi-statique avec une structure active, pour lequel nous montrons l’existence et l’unicité, pour des données petites, d’une solution forte localement en temps. Le Chapitre 4 présente une nouvelle méthode de type domaine fictif (la méthode de prolongement régulier ) pour la résolution numérique de problèmes de transmission. La méthode est d’abord développée pour un problème de transmission de Laplace, puis étendue aux problèmes de transmission de Stokes et d’interaction fluide-structure. / The transport of microorganisms and biological fluids by means of cilia and flagella is an universal phenomenon found in almost all living beings. The aim of this thesis is to model, analyze and simulate mathematical fluid-structure interaction problems involving active structures, capable of deforming themselves through internal stresses, and a low Reynolds number fluid, modeled by Stokes equations. In Chapter 2, these active structures are modeled as elastic materials satisfying Saint Venant-Kirchhoff law for elasticity whose activity comes from the addition of an activity term to the second Piola-Kirchhoff stress tensor. Elasticity and Stokes equations are coupled on the fluid-structure interface and the mathematical study of the linearized problem discretized in time is realized. Then, the problem is formulated as a saddle-point problem which isused for numerical simulations. Chapter 3 focuses on the analysis of a quasi-static fluid-structure with an active structure, for which we show existence and uniqueness, for small data, of a strong solution locally in time. Chapter 4 presents a new fictitious domain method (the smooth extension method) for the numerical resolution of transmission problems. The method is first developed for a Laplace transmission problem and further extended to Stokes transmission and fluid-structure interaction problems.

Extrapolation methods for the solution of partial differential equations are commonly based on the existence of error expansions for the approximate solution. Implicit extrapolation, in the contrast, is based on applying extrapolation indirectly, by using it on quantities like the residual. In the context of multigrid methods, a special technique of this type is known as \034 -extrapolation. For finite element systems this algorithm can be shown to be equivalent to higher order finite elements. The analysis is local and does not use global expansions, so that the implicit extrapolation technique may be used on unstructured meshes and in cases where the solution fails to be globally smooth. Furthermore, the natural multilevel structure can be used to construct efficient multigrid and multilevel preconditioning techniques. The effectivity of the method is demonstrated for heat conduction problems and problems from elasticity theory.

Ziel dieser Arbeit ist die Simulation der Deformation von Bauteilen, welche aus nahezu inkompressiblem Material bestehen. Dabei soll sich das Material sowohl linear als auch nichtlinear elastisch verhalten können. Zusätzlich soll die Belastung des Bauteils beliebig gewählt werden können, das heißt, es sollen kleine als auch große Deformationen möglich sein.:1. Einleitung 2. Grundlagen 3. Aufgabenstellung für linear elastisches Material unter kleinen Deformationen 4. Gemischte Methode der finiten Elemente 5. Herleitung der Fehlerschätzung 6. Aufgabenstellung für nichtlinear elastisches Material unter großen Deformationen 7. Lösungsstrategie A. Anhang

In this manuscript, distinct problems concerning carbon-bonded materials processing and characterization were analyzed, from bulk to cellular samples. The main motivation was to address central topics that would enhance the comprehension of the material’s behavior, as well as trigger targeted improvements. Some of the topics this thesis covers are: Non-linear Young’s modulus behavior of carbon-bonded alumina at high temperatures; Influence of the processing route on the cold crushing strength of carbon-bonded alumina foam filters; Geometric characterization of ceramic foam filters as a tool to understand processing parameters; Use of advanced techniques such as computer tomography and finite element modelling to correlate processing parameters and mechanical behavior. In most of the analyses, non-standard computational strategies were adopted. In those cases, algorithms were written to facilitate the evaluations, or even enable it in the first place. All the algorithms’ concepts are described in this thesis and their codes are available in the Appendices. The current work was carried out within the framework of the Collaborative Research Center 920 (CRC 920) “Multifunctional filters for metal melt filtration - a contribution to zero defect materials” at the Technische Universität Bergakademie Freiberg funded by the German Research Foundation (DFG).

The analytical solution of a given inhomogeneous boundary value problem of a linear, elliptic, inhomogeneous partial differential equation and a set of inhomogeneous mixed Dirichlet- and Neumann-type boundary conditions is derived in the present paper. In the context of elasticity theory, the problem arises for a non-conservative symmetric ansatz and an extended constitutive law shown earlier. For convenient user application, the scalar function expressed in cylindrical coordinates is primarily obtained for the general case before being expatiated on a special case of linear boundary conditions.

Ti-Nb alloys are characterized by a diverse metallurgy which allows obtaining a wide palette of microstructural configurations and physical properties via careful selection of chemical composition, heat treatment and mechanical processing routes. The present work aims to expand the current state of knowledge about martensite forming Ti-Nb alloys by studying 15 binary Ti-c_{Nb}Nb (9wt.% ≤ c_{Nb} ≤ 44.5wt.%) alloy formulations in terms of their structural and mechanical properties, as well as their thermal stability. The crystal structures of the martensitic phases, α´ and α´´, and the influence of the Nb content on the lattice (Bain) strain and on the volume change related to the β → α´/α´´ martensitic transformations are analyzed on the basis of Rietveld-refinements. The magnitude of the shuffle component of the β → α´/α´´ martensitic transformations is quantified in relation to the chemical composition. The largest transformation lattice strains are operative in Nb-lean alloys. Depending on the composition, both a volume dilatation and contraction are encountered and the volume change may influence whether hexagonal martensite α´ or orthorhombic martensite α´´ forms from β upon quenching. The mechanical properties and the deformation behavior of martensitic Ti-Nb alloys are studied by complementary methods including monotonic and cyclic uniaxial compression, nanoindentation, microhardness and impulse excitation technique. The results show that the Nb content strongly influences the mechanical properties of martensitic Ti-Nb alloys. The elastic moduli, hardness and strength are minimal in the vicinity of the limiting compositions bounding the interval in which orthorhombic martensite α´´ forms by quenching. Uniaxial cyclic compressive testing demonstrates that the elastic properties of strained samples are different than those of unstrained ones. Also, experimental evidence indicates a deformation-induced martensite to austenite (α´´ → β) conversion. The influence of Nb content on the thermal stability and on the occurrence of decomposition reactions in martensitic Ti-Nb alloys is examined by isochronal differential scanning calorimetry, dilatometry and in-situ synchrotron X-ray diffraction complemented by transmission electron microscopy. The thermal decomposition and transformation behavior exhibits various phase transformation sequences during heating into the β-phase field in dependence of composition. Eventually, the transformation temperatures, interval, hysteresis and heat of the β ↔ α´´ martensitic transformation are investigated in relation to the Nb content. The results obtained in this study are useful for the development and optimization of β-stabilized Ti-based alloys for structural, Ni-free shape memory and/or superelastic, as well as for biomedical applications. / Ti-Nb Legierungen zeichnen sich durch eine vielfältige Metallurgie aus, die es nach sorgfältiger Auswahl der chemischen Zusammensetzung sowie der thermischen und mechanischen Prozessierungsroute ermöglicht eine große Bandbreite mikrostruktureller Konfigurationen und physikalischer Eigenschaften zu erhalten. Das Ziel der vorliegenden Arbeit ist es den gegenwärtigen Wissensstand über martensitbildende Ti-Nb Legierungen zu erweitern. Zu diesem Zweck werden 15 binäre Ti-c_{Nb} Nb (9 Gew.% ≤ c_{Nb} ≤ 44.5 Gew.%) Legierungen hinsichtlich ihrer strukturellen und mechanischen Eigenschaften sowie ihrer thermischen Stabilität untersucht. Die Kristallstrukturen der martensitischen Phasen, α´ und α´´, sowie der Einfluss des Nb-Gehalts auf die Gitterverzerrung (Bain-Verzerrung), auf die Verschiebungswellenkomponente (Shuffle-Komponente) und auf die Volumenänderung der martensitischen β → α´/α´´ Transformationen werden anhand von Rietveld-Verfeinerungen analysiert. In Abhängigkeit des Nb-Gehalts tritt entweder eine Volumendilatation oder -kontraktion auf, die bestimmen könnte ob hexagonaler Martensit α´ oder orthorhombischer Martensit α´´ aus β bei Abkühlung gebildet wird. Die mechanischen Eigenschaften und das Verformungsverhalten martensitischer Ti-Nb Legierungen werden mit einer Reihe komplementärer Methoden (monotone und zyklische einachsige Druckversuche, Nanoindentation, Mikrohärte, Impulserregungstechnik) untersucht. Die Ergebnisse zeigen durchgehend, dass die mechanischen Eigenschaften martensitischer Ti-Nb Legierungen stark vom Nb-Gehalt beeinflusst werden. Die mechanischen Kennwerte sind minimal in der Nähe der Zusammensetzungen, innerhalb derer β → α´´ bei Abkühlung auftritt. Aus Druckversuchen geht hervor, dass die elastischen Eigenschaften verformter Proben verschieden zu denen unverformter sind. Die experimentellen Ergebnisse weisen außerdem auf eine verformungsinduzierte Umwandlung von Martensit in Austenit (α´´ → β) hin. Der Einfluss des Nb-Gehalts auf die thermische Stabilität und das Auftreten von Zerfallsreaktionen in martensitischen Ti-Nb Legierungen wird anhand von dynamischer Differenzkalorimetrie, Dilatometrie, und in-situ Synchrotronröntgenbeugung in Kombination mit Transmissionselektronenmikroskopie untersucht. Das thermische Zerfalls- und Umwandlungsverhalten ist durch das Auftreten einer Vielzahl von in Abhängigkeit des Nb-Gehalts unterschiedlichen Phasentransformationssequenzen gekennzeichnet. Abschließend werden die Transformationstemperaturen und -wärmen, das Transformationsinterval und die thermische Hysterese der martensitischen β ↔ α´´ Umwandlung untersucht. Die Ergebnisse dieser Arbeit sind für die Entwicklung und Optimierung β-stabilisierter Ti-Legierungen für strukturelle und biomedizinische Anwendungen sowie Ni-freier Komponenten, die Formgedächtniseffekt und/oder Superelastizität aufweisen, von Nutzen.