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Computational study of the impact of disorders in excitation propagation on left ventricular contraction
Vaverka, Jiří ; Rohan,, Eduard (referee) ; Horný, Lukáš (referee) ; Burša, Jiří (advisor)
Tato disertační práce se zabývá výpočtovým modelováním kontrakce levé srdeční komory pomocí metody konečných prvků. Primárním cílem práce je vyhodnotit vliv blokády levého Tawarova raménka na ejekční frakci komory. Dále je vyšetřován dopad blokády na pohyby komory během srdečního cyklu, na lokální hodnoty přetvoření a na rozložení napětí ve stěně. Průběh elektrické aktivace jak zdravé komory, tak i komory s blokádou je modelován pomocí monodoménové rovnice svázané s pseudo-modelem buněčné membrány, který byl navržen za účelem snížení výpočetní náročnosti monodoménové rovnice. Rychlost šíření vzruchu v myokardu je uvažována ortotropní. Vypočítané časové průběhy elektrické aktivace ukazují, že blokáda levého Tawarova raménka prodlužuje dobu depolarizace komory o 50 %, což je v souladu s udávanými délkami trvání QRS komplexu na EKG u zdravých jedinců a u pacientů s blokádou. Průběhy elektrické aktivace jsou následně využity v simulacích kontrakce komory pro předepsání počátku kontrakce jednotlivých prvků sítě. Pasivní mechanická odezva myokardu je v těchto simulacích popsána pomocí ortotropního hyperelastického modelu. Aktivní napětí vyvolané svalovou kontrakcí je do modelu zahrnuto prostřednictvím časově závislého tenzoru aktivního přetvoření. Do počáteční konfigurace modelu, reprezentující stav komory na konci diastoly, je před zahájením kontrakce zahrnuto předpětí odpovídající end-diastolickému tlaku v komoře. Časový průběh komorového tlaku během ejekční fáze je modelován pomocí dvouparametrického modelu Windkessel. Výsledky simulací ukazují, že blokáda levého Tawarova raménka nesnižuje významně čerpací schopnost komory. Predikovaný pokles ejekční frakce v důsledku blokády činí pouze 2,3 %, což je v souladu s některými publikovanými klinickými výsledky. Vypočítané časové průběhy posuvů a přetvoření ve vybraných místech modelu taktéž vykazují některé charakteristiky popisované klinickými nebo experimentálními studiemi. V oblasti mezikomorového septa byly pozorovány výrazně vyšší hodnoty napětí než v ostatních částech komory; tyto výsledky však bude nutné ověřit dalšími výpočty, neboť v současném modelu není septum zatíženo silovými účinky vyvolanými kontrakcí pravé komory.
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Inverse modelling of stresses in deformed configuration of left ventricle
Zajac, Radim ; Hájek, Petr (referee) ; Vaverka, Jiří (advisor)
The bachelor thesis deals with the development of a FEM model of the left ventricle from a freely available stl model obtained from magnetic resonance images and the modification of this model to make it usable for calculation in Ansys MAPDL. The model was defined with isotropic hyperelastic mechanical properties obtained from the actual myocardial properties obtained from tensile tests described in the accompanying literature. A FEM model corresponding to the stress-free state of the left ventricle was obtained and the stress field of the loaded geometry was reconstructed after loading this null geometry. The reconstructed stress field cannot be considered as real due to the idealization of the material and the neglect of the application of pressures on the epicardium of the left ventricle.
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Stress-strain analysis of the mast in Lelekovice
Vitouch, Matěj ; Vaverka, Jiří (referee) ; Fuis, Vladimír (advisor)
This bachelor thesis is focused on stress and deformation analysis of 3D strut frame. The main goal of this thesis is to create model of strut frame, which is based on TV transmitter in Lelekovice, and his resulting analysis at various degree of static indeterminateness and loads. There is also verification of analytic results by numeric method in Ansys Workbench.
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Finite element solution of axially loaded bars using quadratic element
Janáčik, Lukáš ; Halabuk, Dávid (referee) ; Vaverka, Jiří (advisor)
This bachelor thesis describes an algorithm for programming finite-element model with quadratic elements for axial loaded bar. In the introduction, we define the basic concepts of mechanics of materials, which are used in this thesis and are necessary to understand problems, for which finite element method was formulated. The thesis clarifies a transition from basic differential equation to weak formulation, which is the base of finite element method. We define element matrices and describe transition to global matrices, relating to the whole body. Then describe implementation of boundary conditions and postprocessing of the results, necessary for calculation and displaying of other unknowns. In the practical part, 3 illustrative problems are presented and calculated numerically in FEM solver using Matlab, analytically and in software ANSYS Workbench. Results are then compared and evaluated. Problems have different boundary conditions (linear axial load, tempered cross section, statically indeterminate fixation). Results of displacement and normal stress for programmed solver are identical to those from Ansys (using the same settings) and analytical solution (after more elements are added, if necessary). Problem with tempered cross section was simulated in Ansys using plain stress, because the program can’t define bar with tempered cross section. This revealed sheer stress contained in parts of cross section further from centreline, which are not calculated in our FEM solver and in some cases might be significant.
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Finite element solution of axially loaded bars using linear element
Plucnar, Tomáš ; Návrat, Tomáš (referee) ; Vaverka, Jiří (advisor)
This bachelor thesis deals with the finite element method for axially loaded bars using linear basis functions. The theoretical part briefly describes the theory of axially loaded bars and states the individual steps that lead from the initial differential equation to a system of linear algebraic equations. A Weak formulation of the differential equation is used to derive the system. Using the theory described in the first part, an algorithm is created in Matlab, which is used to solve four problems. The results are then compared with the analytical solution and with the model in Ansys.
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Analysis of stresses in left ventricular wall during isovolumic contraction
Janoušek, Petr ; Burša, Jiří (referee) ; Vaverka, Jiří (advisor)
The objective of this work is the analysis of stresses in the left heart ventricle during the isovolumic-contraction phase, in which blood is compressed without changing its volume in the ventricle. In this work, the left ventricle is modeled using a simplified axisymmetric sphere in order to be able to (1) perform an analytical solution from the relations given in the literature corresponding to the theory of linear elasticity, and (2) compare this solution with the model calculated by the finite element method. The model itself is a thick-wall sphere, which is affected by an internal overpressure arised as a reaction from the compressed blood. In order to achieve a constant internal volume, an active strain which acts against the internal pressure is also considered.
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Feasibility study of welding for stainless part „ guide rail"
Vaverka, Jiří ; Mrňa, Libor (referee) ; Sigmund, Marian (advisor)
Robotization of industry is very important in these days. It is possible to replace human workers with robots and because of that make manufacturing faster. This master’s thesis includes feasibility study of robotic welding for stainless steel part guide rail. Quality of robotic welding was evaluated on testing pieces. Robotic welding was 88,5 % faster than current welding method. Costs of manufacture of one piece were 40 % cut.
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Determination of stress resultants in closed frames
Horák, Richard ; Horníková, Jana (referee) ; Vaverka, Jiří (advisor)
The bachelor's thesis deals with the determination of the internal stress resultants (ISR) of planar beams with a closed centerline. The first part of the thesis presents a theoretical basis, which is then applied in the second part to solve three tasks. In the first task, the theory of symmetrical and antimetrical course of ISR is applied to reduce the degree of static indeterminacy of a symmetrical planar beam loaded by a symmetrical and antimetrical force system. In the second task the method of superposition is used to replace the general external load of the beam by symmetrical and antimetrical external loads. The task is further solved in the same way as in the case of the first task. The third task is solved by a general procedure with several options of released structures. Furthermore, the assumption enabling the solution of the stress energy due to the bending moment only is verified. At the end of the third task, the analytically determined values are compared with the values determined by the numerical method using the software ANSYS.
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Stress-strain analysis of crane truss loaded by a force with varying position
Cabaj, Gabriel ; Fuis, Vladimír (referee) ; Vaverka, Jiří (advisor)
The bachelor thesis deals with the stress-strain analysis of the truss of a gantry crane. The theoretical part clarifies the basic concepts of statics, elasticity and strength. The concept of influence lines and its use for solving stress-strain analyses of structures with variable position of the loading force is further presented. The practical part deals with a model 2D example, specifically, the design of a cross section for a simplified model of a gantry crane, which is represented by the truss structure. The results for trusses with different degrees of static indeterminacy are compared. Subsequently, the analytical results are verified by the numerical solution in ANSYS software. In the last analysis, a 3D model of a gantry crane with realistic parameters from available sources is created. Finally, the stress-strain analysis of the gantry crane is performed considering the variable position of the loading force.
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