
A torsion of the beam with noncircular crosssection
Kalivoda, Ondřej ; Hrstka, Miroslav (referee) ; Profant, Tomáš (advisor)
Bachelor thesis deals with the analytical and numerical methods solving the problems of the torsion of bars with various geometries of crosssections. The theoretical background of the problem is introduced in the beginning of the thesis. The possibilities of the analytical solution of the partial differential equations in the case of the simplified shapes of the crosssections are discussed in the following part. These results are compared with the numerical ones received from the finite element analysis via the ANSYS software. The numerical results are extended to the cases of the generalized shapes of the beam crosssections.

 

Explanation of the sloshing motion in a tank, for a moving tank, for a fixed tank
Mrázek, Michal ; Habán, Vladimír (referee) ; Fialová, Simona (advisor)
This bachelor's thesis deals with mathematical model of sloshing in a tank. Laplace's equation is developed. Boundary conditions for a still rectangular container and for a container under sinusoidal translation are established. Expressions for the free surface elevation and natural frequencies in oscillating tank are determined. Baffles are suggested as a method to minimize the free surface elevation. In the final part, analytical model is compared with numerical solution with overall good agreement.

 

Laplace equation in fractional Sobolev spaces
Bartoš, Ondřej ; Bárta, Tomáš (advisor) ; Vybíral, Jan (referee)
The goal of this thesis is to study Laplace's equation on a unit disc. The given function values on a unit circle can be interpreted as a 2πperiodic function and the solution can be derived using Fourier method. We introduce general integer Sobolev spaces and their alternatives useful for describing functions on a unit disc and a unit circle. Using elementary methods, we show how they are related to each other. The same results are shown for fractional Sobolev spaces. The main result is that functions from some Sobolev space on a unit disc that solve Laplace's equation correspond to functions from a one half lower Sobolev space on a unit circle. These results can be used to show for a function from some Sobolev space on a unit circle in how strong norm the solution of Laplace's equation converges to the given function. 1


Laplace equation in fractional Sobolev spaces
Bartoš, Ondřej ; Bárta, Tomáš (advisor) ; Vybíral, Jan (referee)
The goal of this thesis is to study Laplace's equation on a unit disc. The given function values on a unit circle can be interpreted as a 2πperiodic function and the solution can be derived using Fourier method. We introduce general integer Sobolev spaces and their alternatives useful for describing functions on a unit disc and a unit circle. Using elementary methods, we show how they are related to each other. The same results are shown for fractional Sobolev spaces. The main result is that functions from some Sobolev space on a unit disc that solve Laplace's equation correspond to functions from a one half lower Sobolev space on a unit circle. These results can be used to show for a function from some Sobolev space on a unit circle in how strong norm the solution of Laplace's equation converges to the given function. 1


Explanation of the sloshing motion in a tank, for a moving tank, for a fixed tank
Mrázek, Michal ; Habán, Vladimír (referee) ; Fialová, Simona (advisor)
This bachelor's thesis deals with mathematical model of sloshing in a tank. Laplace's equation is developed. Boundary conditions for a still rectangular container and for a container under sinusoidal translation are established. Expressions for the free surface elevation and natural frequencies in oscillating tank are determined. Baffles are suggested as a method to minimize the free surface elevation. In the final part, analytical model is compared with numerical solution with overall good agreement.

 

A torsion of the beam with noncircular crosssection
Kalivoda, Ondřej ; Hrstka, Miroslav (referee) ; Profant, Tomáš (advisor)
Bachelor thesis deals with the analytical and numerical methods solving the problems of the torsion of bars with various geometries of crosssections. The theoretical background of the problem is introduced in the beginning of the thesis. The possibilities of the analytical solution of the partial differential equations in the case of the simplified shapes of the crosssections are discussed in the following part. These results are compared with the numerical ones received from the finite element analysis via the ANSYS software. The numerical results are extended to the cases of the generalized shapes of the beam crosssections.

 