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Application of boundary value problems for ordinary differential equations in engineering
Zapoměl, Jakub ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
This bachelor thesis deals with the determination of the shape of the deflection line for boundary value problems in strength of materials. There are several methods for solving boundary value problems. This thesis focuses on the Green's function method. It provides a basic review of the properties of ordinary differential equations, an introduction to the Green's function method and the actual application of the findings to beam bending models. The concrete models are solved using an interactive program developed in Matlab software.
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Boundary problem for beam deflections
Machalová, Monika ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
This bachelor's thesis deals with the deflection of the beam. The second chapter is devoted to the linear differential equations and their solution, followed by a description of the different types of prescribed boundary conditions. In the third chapter the linear differential equation of second and fourth order for the deflection of the beam is derived. The last chapter is focused on comparing linear and nonlinear models. The theory is complemented by some solved examples, in which analytical solutions are plotted by using mathematical software Matlab.
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Application of boundary value problems for ordinary differential equations in engineering
Zapoměl, Jakub ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
This bachelor thesis deals with the determination of the shape of the deflection line for boundary value problems in strength of materials. There are several methods for solving boundary value problems. This thesis focuses on the Green's function method. It provides a basic review of the properties of ordinary differential equations, an introduction to the Green's function method and the actual application of the findings to beam bending models. The concrete models are solved using an interactive program developed in Matlab software.
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Method of Green function for boundary value problems for ODR
Héda, Ivan ; Rokyta, Mirko (advisor) ; Pražák, Dalibor (referee)
The main aim of this work is to summarize the basic knowledge of method which is using Green's functions for solving boundary value problems for linear diffe- rential equations. These functions will be defined and, with some not very strong presumptions, uniquely constructed. This method is primarily derived for solving problems with homogenous boundary conditions. However it will be shown that there is no more presumtions needed to use this method to solve problems with non-homogenous linear boundary conditions. As a main consequence of preceding existence and uniqueness of solution for relatively wide class of linear boundary problems will be provided. 1
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Boundary problem for beam deflections
Machalová, Monika ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
This bachelor's thesis deals with the deflection of the beam. The second chapter is devoted to the linear differential equations and their solution, followed by a description of the different types of prescribed boundary conditions. In the third chapter the linear differential equation of second and fourth order for the deflection of the beam is derived. The last chapter is focused on comparing linear and nonlinear models. The theory is complemented by some solved examples, in which analytical solutions are plotted by using mathematical software Matlab.
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Spline-base functions for the soulution of boundary-value problems
Horčička, Martin ; Dolejší, Vít (advisor) ; Feistauer, Miloslav (referee)
Solving the Poisson equation using finite element method with a basis com- posed of natural cubic splines. In this thesis we introduce the notion of weak derivatives, Sobolev spaces and formulate the weak form of the Poisson equation in order to build up to the finite element method. Furthermore, the thesis contains a construction of a natural cubic spline and a description of the used basis. The computed solution approximates well the exact solution, especially if the right side satisfies certain conditions. 1
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Method of Green function for boundary value problems for ODR
Héda, Ivan ; Rokyta, Mirko (advisor) ; Pražák, Dalibor (referee)
The main aim of this work is to summarize the basic knowledge of method which is using Green's functions for solving boundary value problems for linear diffe- rential equations. These functions will be defined and, with some not very strong presumptions, uniquely constructed. This method is primarily derived for solving problems with homogenous boundary conditions. However it will be shown that there is no more presumtions needed to use this method to solve problems with non-homogenous linear boundary conditions. As a main consequence of preceding existence and uniqueness of solution for relatively wide class of linear boundary problems will be provided. 1
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High performance computing in micromechanics
Blaheta, Radim ; Hrtus, Rostislav ; Jakl, Ondřej ; Starý, Jiří
By micromechanics we understand analysis of the macroscale response of materials through investigation of processes in their microstructure. Here by the macroscale, we mean the scale of applications, where we solve engineering problems involving materials like different metals and composites in aircraft design or rocks and concrete in a dam construction. Different applications are characterized by different characteristic size. At macroscale the materials mostly look as homogeneous or they are idealized as homogeneous or piecewise homogeneous. A substantial heterogeneity is hidden and appears only after more detailed zooming view into the material.
Fulltext: content.csg -  PDF
Plný tet: UGN_0426823 - PDF
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Fast direct methods
Práger, Milan
A short survey of standard fast methods for the solution of algebraic systems arising when solving elliptic boundary value problems. It is shown how these methods can be used for the solution of more general problems. AAll polygons and tetrahedra are found where boundary problems can be transformedby reflection and solved with fast methods.
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