The presented diploma thesis deals with the modeling of the rotor packet in dynamic calculations and analysis of the influence of the packing pressing force on the critical speed of the electric motor. The thesis can be divided into three main parts. The first part discusses the current level of rotor packet modeling in dynamic calculations and also deals with analytical theories for subsequent experimental tests. The second part describes the implementation of two experiments to determine the equivalent modulus of elasticity. The first experiment is a four-point bending test and the second is an experimental modal analysis. The third part is used for comparing the results obtained from experimental tests and describes the calculation of the critical speed of the rotor package pressed on the shaft by the finite element method.

The diploma thesis deals with influence of the used adhesive to large format tiles properties after installation. Properties on large format tiles were monitored by ultrasonic pulse velocity method. Hydraulic setting adhesives were tested in second part. Strength and modulus of elasticity were tested. The development of shrinkage over time was also monitored. The results were summarized in tabular and graphical form and were examined by simple statistical analysis to determine resulting conclusions.

Die Dynamik von elastischen Membranen, Kapseln und Schalen hat sich zu einem aktiven Forschungsgebiet in der simulationsgestützten Physik und Biologie entwickelt. Die dünne Oberfläche dieser elastischen Materialien ermöglicht es, sie effizient als Hyperfläche zu approximieren. Solche Oberflächen reagieren auf Dehnungen in Oberflächenrichtung und Verformungen in Normalenrichtung mit einer elastischen Kraft. Zusätzlich können Oberflächenspannungskräfte auftreten. In dieser Arbeit präsentieren wir eine neuartige Arbitrary Lagrangian-Eulerian (ALE) Methode um solche in (Navier-Stokes) Fluiden eingebetteten elastischen Schalen zu simulieren. Dadurch, dass das Gitter an die elastische Oberfläche angepasst ist, kombiniert die vorgeschlagene Methode hohe Genauigkeit mit Effizienz in der Berechnung der Lösungen. Folglich kann man die Simulationen mit einer verhältnismäßig geringen Gitterauflösung durchführen. Der Fokus dieser Arbeit liegt bei achsensymmetrischen Formen und Strömungen, wie sie bei vielen biophysikalischen Anwendungen zu finden sind. Neben einer allgemeinen dreidimensionalen Beschreibung formulieren wir achsensymmetrische Kräfte auf der Oberfläche, für welche wir eine Diskretisierung mit der Finite Differenzen Methode vorschlagen, welche an eine Finite-Elemente Methode für die umgebenden Fluide gekoppelt ist. Weiterhin entwickeln wir eine Strategie zur impliziten Kopplung der Kräfte, um Zeitschrittrestriktionen zu reduzieren. In verschiedenen numerischen Tests werden wir zeigen, dass akkurate Ergebnisse schon in einer Größenordnung von Minuten auf einer Single-Core CPU erreicht werden können. Die Methode wurde in drei aktuellen Anwendungen verwendet, wobei mindestens zwei davon nach unserer Kenntnis im Moment mit keiner anderen numerischen Methode simuliert werden können: Zunächst präsentieren wir Simulationen von biologischen Zellen, die im Zuge eines RT-DC (Real-Time Deformability Cytometry) Experiments durch einen schmalen mikrofluidischen Kanal advektiert und dabei verformt werden. Danach zeigen wir die Ergebnisse erster Simulationen der uniaxialen Kompression biologischer Zellen zwischen zwei parallelen Platten im Zuge eines AFM Experiments. Schließlich präsentieren wir Resultate erster Simulationen von neuartigen mikroschwimmenden Schalen, welche lediglich durch äußere Einflüsse (wie z.B. Ultraschall), zum Schwimmen angeregt werden können. / The dynamics of membranes, shells, and capsules in fluid flow has become an active research area in computational physics and computational biology. The small thickness of these elastic materials enables their efficient approximation as a hypersurface, which exhibits an elastic response to in-plane stretching and out-of-plane bending, possibly accompanied by a surface tension force. In this work, we present a novel arbitrary Lagrangian-Eulerian (ALE) method to simulate such elastic surfaces immersed in Navier-Stokes fluids. The method combines high accuracy with computational efficiency, since the grid is matched to the elastic surface and can therefore be resolved with relatively few grid points. The focus of this work is on axisymmetric shapes and flow conditions, which are present in a wide range of biophysical problems. Next to a general three-dimensional description, we formulate axisymmetric elastic surface forces and propose a discretization with surface finite-differences coupled to evolving finite elements. We further develop an implicit coupling strategy to reduce time step restrictions. Several numerical test cases show that accurate results can be achieved at computational times on the order of minutes on a single core CPU. Three state-of-the-art applications are demonstrated, where to our knowledge at least two of them cannot be simulated with any other numerical method so far. First, simulations of biological cells being advected through a microfluidic channel and therefore being deformed during an RT-DC (Real-Time Deformability Cytometry) experiment are presented. Then, the uniaxial compression of the cortex of a biological cell during an AFM experiment is investigated. Finally, we present the results of first simulations of the observed shape oscillations of novel microswimming shells which can be locomoted by exterior influences (e.g. ultrasound waves) only.

The diploma thesis deals with the analyses of demand using standard tools of engineering mathematics. Mathematical models of demand, both single and multi- factor are investigated. Elasticity of demand is applied for decision making in price policy. Problems of optimization of demand reflecting utility and budget constraints are under consideration. Constructions of demand curve and compensated demand curve are presented. The text is accompanied by illustrative examples aiming at methodical aspects of the work

This master’s thesis deals with the determination of dynamic modulus of elasticity non-destructive methods of brick body. The test samples were laboratory-made from two types of brick earth and further were used cotouts from the full brick types clinker. For measuring were used ultrasonic impulse and resonant-impact method.

A study of an influence of strengthening steel beams using reinforcement based on FRP on a moment bearing resistance and bending stiffness. Evaluation of the theoretical calculation methods based on the performed experimental verification. Description of the production of carbon fibres and composite materials on the basis of carbon fibres.

The presented master’s thesis deals with the application of the gradient elasticity in fracture mechanics problems. Specifically, the displacement and stress field around the crack tip is a matter of interest. The influence of a material microstructure is considered. Introductory chapters are devoted to a brief historical overview of gradient models and definition of basic equations of dipolar gradient elasticity derived from Mindlin gradient theory form II. For comparison, relations of classical elasticity are introduced. Then a derivation of asymptotic displacement field using the Williams asymptotic technique follows. In the case of gradient elasticity, also the calculation of the J-integral is included. The mathematical formulation is reduced due to the singular nature of the problem to singular integral equations. The methods for solving integral equations in Cauchy principal value and Hadamard finite part sense are briefly introduced. For the evaluation of regular kernel, a Gauss-Chebyshev quadrature is used. There also mentioned approximate methods for solving systems of integral equations such as the weighted residual method, especially the least square method with collocation points. In the main part of the thesis the system of integral equations is derived using the Fourier transform for straight crack in an infinite body. This system is then solved numerically in the software Mathematica and the results are compared with the finite element model of ceramic foam.

The thesis is focused on the use of R-material into cold asphalt mixtures. It deals with cold recycling and with input materials for this technology. It verifies properties of R-material and residues of bituminous binder. It also verifies properties of designed cold asphalt mixtures by the probative controls (indirect tensile strenght and water resistance). Furthermore is focused on the experimental measurement of selected mixtures to ensure more characteristics. The amount of homogenity of R-material, quantity and quality of residues bituminous binder is essential for positive results.

Le cross-linking du collagène cornéen (CXL) est une cornéoplastie mini-invasive reposant surun concept biomécanique difficile à objectiver physiquement et dont les preuves del’efficacité thérapeutique sont d’interprétation complexe. Les principes, les nuances et lesrésultats du CXL sont colligés dans cette thèse afin de valider l’intérêt du modèleexpérimental choisi pour tester la pertinence de notre travail de recherche sur l’élastographiecornéenne par ondes de cisaillement.Notre cheminement expérimental a abouti au choix du modèle de CXL trans-épithélial (TCXL)assisté par iontophorèse (I-CXL), réalisé in vivo, sur oeil de lapin. Les mesuresélastographiques obtenues après euthanasie ont ainsi pu démontrer une modificationsignificative du profil d’élasticité de la cornée après CXL, testé successivement de manièredynamique et statique.Nos résultats confirment donc l’efficacité biomécanique instantanée du I-CXL et donnent uneidée plus précise de la valeur de la photo-polymérisation du tissu cornéen isolée desphénomènes liés à la cicatrisation. Les enjeux technologiques de l’élastographe cornéen paranalyse des ondes de cisaillement ont pu être définis afin de développer une stratégie de miseen oeuvre d’un système pertinent pour la pratique clinique. / Corneal collagen cross-linking (CXL) is a kind of minimaly invasive corneoplasty mainlybased on a biomechanical concept, which is very difficult to measure physically, and whichthe therapeutic efficacy understanding is complex.Principles, different protocols and resultsare summarized in this thesis in order to illustrate the usefulness of the experimental modelchosen in our experimentations about elastographic corneal shear wave imaging.The pathway of our experimental work have led to the choice of trans-epithelial CXL (TCXL)assisted by iontophoresis (I-CXL), performed in vivo, on rabbits eyes. Elastographicmeasurements we obtained after animals euthanasia have shown a significant change of thecorneal elasticity profile after CXL, successively tested in a dynamic and in a static fashion.Our results do confirm the biomechanical efficacy of the I-CXL procedure and give a moreprecise idea of the sole photo-polymerization effect by avoiding any confounding healingconcern. Technological issues for corneal elastography with shear wave imaging have beenraised in this thesis to develop a realistic strategy for the launch of a clinically useful device.

Dans une première partie, nous proposons une méthodologie innovante pour la comparaison d'images en ingénierie de réservoir. L'objectif est de pouvoir comparer des cubes sismiques obtenus par simulation avec ceux observés sur un champ pétrolier, dans le but de construire un modèle représentatif de la réalité. Nous développons une formulation fondée sur du filtrage, de la classification statistique et de la segmentation d'images. Ses performances sont mises en avant sur des cas réalistes. Dans une seconde partie, nous nous intéressons aux méthodes de recalage d'images utilisées en imagerie médicale pour mettre en correspondance des images. Nous introduisons deux nouveaux modèles de recalage fondés sur l'élasticité non linéaire, où les formes sont appréhendées comme des matériaux de type Saint Venant-Kirchhoff et Ciarlet-Geymonat. Nous justifions théoriquement l'existence de solutions ainsi que la résolution numérique. Le potentiel de ces méthodes est illustré sur des images médicales. / In a first part, we propose an innovative methodology for image matching in the context of reservoir simulation. In order to build a model consistent with data collected on the field, we need to evaluate the error between seismic cubes obtained by simulation and seismic cubes acquired in the oil field. Using image processing tools, we develop a new formulation of the error. The application of this new formulation on synthetic reservoir cases demonstrates its efficiency. In a second part, we address the issue of designing two theoretically well-motivated registration models capable of handling large deformations since they are based on nonlinear elasticity. The shape to be matched are viewed as Ciarlet-Geymonat materials for the first model and as Saint-Venant Kirchhoff materials for the second one. We investigate the efficiency of the proposed matching model for the registration of mouse brain gene expression data to a neuroanatomical mouse atlas.