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2D finite element formulation of elastic string vibrations with large displacements
Michálek, Jakub ; Horáček, Jaromír (advisor) ; Matyska, Ctirad (referee)
The thesis addresses the numerical solution of the oscillation of the vocal fold at finite strain, whereas the literature has so far been concerned with infinitesimal strain only. The geometry concerned corresponds to the easiest situation of falsetto, since we observe an isolated vocal fold. The vocal fold is treated as non-linear and non-isotropic continuum in 2D space. To demonstrate the function of the model, we simulate the behaviour of the vocal fold with the linear constitutive equation numerically. The vocal fold is modelled by the finite element method with quadratic elements for static and dynamic surface load. We show that a proper simulation of vocal fold tissue deformation requires the equations with finite strain term. Numerical simulation of the vocal fold can be used e.g. for the construction of artificial vocal folds, and for the optimization of their function. Understanding the phonatory mechanism is also essential for discovering the causes of the disorders such as the vocal nodules and for the scientific foundation of phoniatrics and education of singers. The thesis is interdisciplinary and synthesises the facts from mechanics of continuum, anatomy and education of singers.
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Microstructural models of trabecular bone - comparison of CT-based FE models
Jiroušek, Ondřej ; Zlámal, Petr
In the article a detailed comparison of techniques used to developed detailed FE models of trabeculra bone microstructure is presented. The FE models are built using a stack of microtomographic images of trabecular bone. Compression test of a cylindrical sample taken from human proximal femur is virtually performed using FE models developed using different procedures. Effect of improper segmentation, mesh smoothing, mesh density, use of hexahedral/ tetrahedral elements, linear/ quadratic shape function is evaluated in parametric study. Material model is based on nanoindentation and numerical elastic properties of sample are compared to experimental results.
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Modifications of the limited-memory BNS method for better satisfaction of previous quasi-Newton conditions
Vlček, Jan ; Lukšan, Ladislav
Several modifications of the limited-memory variable metric BNS method for large scale un- constrained optimization are proposed, which consist in corrections (derived from the idea of conjugate directions) of the used difference vectors to improve satisfaction of previous quasi-Newton conditions, utilizing information from previous or subsequent iterations. In case of quadratic objective functions, conjugacy of all stored diffrence vectors and satisfaction of quasi-Newton conditions with these vectors is established. There are many possibilities how to realize this approach and although only two methods were implemented and tested, preliminary numerical results are promising.
Fulltext: content.csg -  PDF
Plný tet: v1127-11 - PDF
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Flexible buried structures
Houšť, Vladimír ; Hrdoušek,, Vladislav (referee) ; Barták,, Jiří (referee) ; Klusáček, Ladislav (referee) ; Stráský, Jiří (advisor)
The thesis is devoted to analysing of flexible buried arch structures. Modelling of the flexible concrete arch is carried out via a nonlinear finite element model that accounts for soil constitutive relations, soil-structure interactions, sequential construction stages and soil compaction. Advanced FE-model was verified by measurement obtained by full-scale field testing of two buried arches. Mathematical optimization methods of genetic algorithms and Levenberg-Marquardt method are applied to already calibrated complex computational models in order to reduce bending and associated flexural stresses in the concrete section of buried arch. Centre line of the arch is parameterized by cubic Bezier curve to reach interpolation of thrust line. Optimization technique is applied with extensive parametrical study which shows the optimal shapes for buried arches of various span/rise ratios, backfill depths and foundation soil types. For practical application are given coordinates of Bézier curve control polygons of particular resulting shape. Subsequently is applied optimization method for a theoretical reduction of tensile stresses obtained by shape optimization of previously verified numerical model of buried arch. Comparisons of earth pressure, bending moment axial force and deflection of flexible structure during sequential construction of different span/raise ratios of buried arches are presented. The behaviour of flexible buried arch with effect of local traffic load model LM1 has been analysed via 3D finite elements model with respect to different depth of backfill above crown.
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Influence of lamine thickness on bifurcation appearance in ceramic laminate
Sorokina, Kristina ; Ševeček, Oldřich (referee) ; Hadraba, Hynek (advisor)
Z důvodu rozdílných koeficientů délkové teplotní roztažnosti jednotlivých vrstev vzniká ve vrstvách keramického vrstevnatého kompozitního materiálů reziduální napětí. V průběhu chladnutí vrstevnatého kompozitu ze slinovací teploty jednotlivé vrstvy smršťují různými rychlostmi v závislosti na velikosti koeficientu délkové teplotní roztažnosti. Jestliže jsou tyto vrstvy spolu pevně spojeny vzniká v jednotlivých vrstvách různě velké trvalé zbytkové napětí. Velikost residuálního napětí je dána objemovým podílem obou složek v kompozitu. Tato práce byla zaměřena na přípravu a popis 7-mi a 9-ti vrstevných keramických laminátů složených ze střídajících se vrstev dvou rozdílných materiálů. Keramické lamináty byly připraveny pomocí metody suspenzního lití a elektroforetické depozice. U připravených laminátu byl sledován vznik tzv. hranových trhlin (edge cracks) ve vrstvách obsahujících tlaková zbytková pnutí. Výsledky pozorování přítomnosti hranových trhlin pro různou konfiguraci velikosti zbytkových napětí a tloušťky vrstev byly srovnány s teoretickou předpovědí vytvořenou pomocí parametrického 2D modelu. Vliv vzniklých hranových trhlin na průběh lomu byl studován pomocí 3D rekonstrukce lomového povrchu po ohybové zkoušce připravených vrstevnatých kompozitů.
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Lokální odpory na stěně umístěných překážek
Chára, Zdeněk ; Hoření, Bohumír
The influence of surface mounted obstacles on free level of channel flow is discussed. The obstacles of square cross section are placed sequentially along a hydraulic flume and perpendicularly to the flow direction across the whole channel width. Three various spacing between the obstacles - 5H, 11H and 23H (H is height of the obstacle) were tested for different flow discharges. The surface levels were recorded and the results were compared with numerical simulations. Based on the experimental data and numerical simulations the resistance coefficients of the individual obstacles were determined.
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Parameter Identification for Elastic-plastic Material Models from Experimental Data
Jeník, Ivan ; Šebek, František (referee) ; Kubík, Petr (advisor)
This master's thesis deals with the identification of the material flow curve from record of tensile test of smooth cylindrical specimen. First, necessary theory background is presented. Basic terms of incremental theory of plasticity, tensile test procedure and processing its outputs are described. Furthermore, possibilities of mathematical expression of the elastic-plastic material constitutive law, thus mathematical expression of the material flow curve itself. Mechanism of ductile damage of material is explained briefly as well. Overview of recent methods of the flow curve identification is given, focused on cases, when the stress distribution in a specimen is not uniaxial. That is either kind of analytic correction of basic formulas derived for uniaxial stress state, or application of mathematical optimization techniques combined with numerical simulation of the tensile test. Also unusual method of neural network is mentioned. For 8 given materials, the flow curve identification was performed using different methods. Namely by analytic correction, optimization, sequential identification and neural network. Algorithms of the last two methods were modified. Based on assessment of obtained results, application field and adjusting the parameters of single algorithms was recommended. It showed up, that an effective way to the accurate and credible results is the combination of different methods during flow curve identification procedure.
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