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Stochastic finite element method to solve 2d problems
Liščák, Milan ; Boháč, Petr (referee) ; Návrat, Tomáš (advisor)
The thesis focuses on programming of algorithms based on the finite element method (FEM) and the stochastic finite element method (SFEM) used for deformation and stress analysis of truss and plane stress problems. All the codes are developed using a free to use program PyCharm. For both trusses and plane stress problems, the algorithm is illustrated with a simple problem and verified on a more complex one. The results from the FEM calculations are validated using results from ANSYS Workbench. The computed displacements and reaction forces are equal to ANSYS results for all solved cases. There are minor deviations in the stress calculations for plane stress problems. The reason for this is unknown, as ANSYS does not provide an exact methodology for stress computing. In SFEM calculations, the values of Young’s modulus, yield strength and load forces are normally distributed. The codes are run repeatedly and based on the variability of the results the probability of failure is calculated.
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Stress-strain analysis of the process of continuous steel casting
Cabaj, Gabriel ; Petruška, Jindřich (referee) ; Návrat, Tomáš (advisor)
The thesis is focused on the development of a computational model for determination of stress and strain of a round billet in the process of continuous steel casting. The supplied material characteristics, the geometry of the continuous casting machine and the temperature distribution in the billet are applied as input data for stress and strain analysis. The computational model based on the finite element method is developed in the commercial software ANSYS. The thesis can be divided into three parts. The first part includes background information related to the continuous casting of steel and a research analysis of the computational modeling of this process. The second part describes the development of the planar and three-dimensional computational model in detail. Finally, the obtained stress and strain results are analyzed and general conclusions, and recommendations for further development are proposed.
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Application of finite element method to solve plane problems
Langer, David ; Vosynek, Petr (referee) ; Návrat, Tomáš (advisor)
The subject of this thesis is application of finite element method to solve planar problems of mechanical stress of machine components. The goal of the first part of the thesis is to provide the reader with an overview of commonly used FEM software and it's capabilities, both freeware and commercial solutions. Second part of the thesis deals with the usage of freeware for FEM calculations. The last part of the thesis consists of documentation to the FEM software created as a subject of this thesis. The documentation provides a detailed view of the selected type of calculation.
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Analysis of biotribological properties of artificial hip joint
Laštůvka, Jan ; Burša, Jiří (referee) ; Návrat, Tomáš (advisor)
The development of total hip arthroplasty has reached a state when quality prostheses are made, whose longevity is influenced significantly by material properties, design, component fixation and rate of wear of the articulating surfaces. It is the wear rate which is the most important factor influencing successful results for the use of total hip prostheses. The aim of this thesis is to perform a research on the various combinations of hip prostheses and its loading conditions. Also an experimental measurements of Bovine serum lubricating film thickness between the artificial femoral head and a glass disc are performed for different contact kinematic conditions.
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Computer simulations of biaxial tension tests of soft biological tissues
Slažanský, Martin ; Návrat, Tomáš (referee) ; Polzer, Stanislav (advisor)
Within the master thesis a computational model of biaxial tension test of soft biological tissues was developed. The tested specimen can be attached using clamps or hooks. The number and the size of clamps and hooks have a significant impact on the distribution of stress and strain in the centre of the specimen, where deformation is measured. Using the developed computational model, a sensitivity analysis of number and size of clamps and hooks and a sensitivity analysis of placement of clamps was elaborated. The number and size of clamps and hooks were optimized in such a way that the material’s parameters obtained by the tension test correspond to the utmost to the actual parameters of the material. By analyzing the placement of clamps, the influence of selected deviations on the outcome of the tension test was determined. Finally, a plan of the next course of action has been proposed.
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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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Comparative analysis of physiological, degenerative and postoperative lumbar spine using computational modeling
Krejbychová, Adéla ; Návrat, Tomáš (referee) ; Vosynek, Petr (advisor)
This diploma thesis deals with the comparative analysis of the physiological, degenerative and postoperative state of the lumbar spine. The problem was solved by computational modeling using the finite element method. For this solution, it was necessary to create appropriate computational models. The spine physiological state was compared with cases of the lumbar spine with different levels of spondylolisthesis, cases of the lumbar spine with different sacral angles, and cases of lumbar spine with applied fixators. Based on the performed analyses, it was found that spine degenerative state has a great influence on the distribution of stress in the vertebral discs and the vertebra itself. Compared to the physiological state, with increasing level of the spondylolisthesis the stress in the vertebral discs increases, while the stress in the vertebral section decreases. Furthermore, the spondylolisthesis affects the force flow. The higher the level of the spondylolisthesis, the more the force flow is shifted onto the posterior articular ligaments. The best results in terms of the spine physiological state were achieved with the applied fixator model.
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Topology optimization of movable, fixed and based plate of electromechanical injection-moulding machine
Kecík, Samuel ; Halabuk, Dávid (referee) ; Návrat, Tomáš (advisor)
The master thesis deals with the design of geometry of plates of the injection molding unit using the FEM tool Topological Optimization. The reason for this is to reduce the weight of these components, which is beneficial in the transport and assembly of the injection molding machine. However, the final models of geometry of plates must meet certain requirements in terms of the limit state of deformation, the limit state to the critical value of the equivalent stress. This condition involves both limit state of elasticity and limit state of fatigue. Computational modeling and also Topological Optimization are performed in ANSYS Workbench.
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Computational modeling of radial hydrodynamic bearings for water machines
Pokorný, Jan ; Šimek,, Jiří (referee) ; Návrat, Tomáš (advisor)
The aim of this thesis is to calculate the stiffness and damping coefficients for radial hydrodynamic bearings. Cylindrical and lemon hydrodynamic bearings are considered. The solution to this problem mainly depends on the hydrodynamic pressure in the bearing. The numerical solution of the Reynolds equation is used to calculate the pressure. The effect of variable viscosity and density of the lubricant due to temperature changes is considered. The static equilibrium position of the journal centre is also solved. The stiffness and damping coefficients are determined using small amplitude journal motions about the equilibrium position. Three methods for determining these coefficients are presented. The outcome of this thesis is an algorithm for the calculation of stiffness and damping coefficients for cylindrical and lemon bearings. Results for lemon bearings are presented and comparison with the commercial software DynRot BR is made. The benefit of this thesis is the creation of an algorithm for the calculation of journal centre equilibrium position, a new way of incorporating the temperature changes in the viscosity and the density of the lubricant, and the modification of a method for calculating stiffness and damping coefficients based on experimental analogy.
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Strain, stress and strength analysis of the ball bearing considering the contact conditions
Prášil, Jiří ; Návrat, Tomáš (referee) ; Vrbka, Jan (advisor)
Motivation of this master‘s thesis is solution of practical problem of the newly developed slewing ring for tram Škoda, type: 15T. Next impulse for thesis creation was the possibility to extend product range of roller bearing ZKL. There is processed strain – stress analysis of bearing inner design making use the finite element method (FEM). Obtained results are compared with classic approach based on the Hertz theory. Important aim of this work is three main parameters optimal establishment: rolling element diameter, arrangement radius and number of rolling elements. Optimization job is realized by solutions of direct tasks with different parameters. With regard to necessity of detailed stress analysis and conservation of reasonable computational time it was chosen approach of combination global and local FEM model. It was used pre/postprocessor PATRAN and solver MARC for solution of strain and stress analysis. Analytic solution was accomplished in software EXCEL.
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