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Lagrange multipliers in linear elastostatics
Ondášová, Annamária ; Květoň, Josef (referee) ; Eliáš, Jan (advisor)
The thesis deals with the use of Lagrange multipliers, explaining the principle of their use and the calculating process. Lagrange multipliers are introduced into joints of a given truss structure. The calculation is conducted using minimalization of the potential energy and the principle of virtual work. Results are verified by direct elimination of the variables.
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Micropolar continuum and its applications in structural mechanics
Fleischerová, Beáta ; Vořechovský, Miroslav (referee) ; Eliáš, Jan (advisor)
Práca sa zaoberá mechanikou kontinua. Konkrétne je zameraná na lineárnu elasticitu homogénnych izotropných pevných telies. Pre dve rôzne kontinuá – klasické kontinuum a mikropolárne je odvodená silná aj slabá formulácia. Cosseratovo (mikropolárne) kontinuum predstavuje rozšírenie ku klasickému, kde je uvažovaný ďalší stupeň voľnosti - nezávislá rotácia. Mikropolárne kontinuum definuje ďalšie dve materiálové konštanty, ktoré súvisia s rotáciou. V súčasnosti je metóda konečných prvkov veľmi populárny spôsob približného riešenia rovníc lineárnej elasticity. Pre účely diplomovej práce bol vyvinutý program pre MKP riešenie 2D rovinných úloh. Pre lepšiu predstavu o vplyvu rôznych parametrov na správanie sa oboch kontinuí analyzujeme jednoduchý príklad konzolového nosníka. Riešenia analyzujeme s využitím 4-uzlového štvorhranného elementu, ktorý je jedným z najpoužívanejších pre MKP. V Cosseratovom kontinue by mali byť rotácie previazené skrz parameter vnútornej dĺžky, čo by sa malo odzrkadliť zvýšenou tuhosťou telesa. Úlohou práce je porovnať výsledky z oboch kontinuí a potvrdiť tento predpoklad.
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Lagrange multipliers in linear elastostatics
Ondášová, Annamária ; Květoň, Josef (referee) ; Eliáš, Jan (advisor)
The thesis deals with the use of Lagrange multipliers, explaining the principle of their use and the calculating process. Lagrange multipliers are introduced into joints of a given truss structure. The calculation is conducted using minimalization of the potential energy and the principle of virtual work. Results are verified by direct elimination of the variables.
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Solved problems in Theoretical Mechanics to Electronic Database of Solved Tasks
Hruška, Viktor ; Dvořák, Leoš (advisor) ; Šabatka, Zdeněk (referee)
Solved Problems in Theoretical Mechanics to Electronic Database of Solved Tasks Abstract: The main goal of this bachelor thesis was to create set of tasks with structural hints and detailed solution in the field of theoretical mechanics. 16 tasks were created and published within The Electronic Collection of Solved Problems in Physics on the web. The tasks are meant to serve the university level students and they are adapted for self study. Keywords: theoretical mechanics, principle of virtual work, Lagrange equations of the second kind, electronic collection of tasks, structured solutions of tasks
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Solved Problems in Theoretical Mechanics
Roskot, Michal ; Koupilová, Zdeňka (advisor) ; Snětinová, Marie (referee)
The object of the bachelor's thesis was the creation of tasks for "Collection of Solved Problems in Physics". I have created 20 structured tasks on the subject of theoretical mechanics. These are mostly on a university level. I have successfully filled the chapters "The Principle of virtual work" and "Hamiltonian mechanics", which are included in the subject of theoretical mechanics. In order to create the bachelor's thesis it was necessary to get familiar with the web interface of the "Collection". At the same time to create pictures I had to learn to work with a graphical editor. In the text of the bachelor's thesis I characterize the technical solution of "Collection of Solved Problems in Physics", describe advantages of the used structure of the solved tasks and I briefly summarize content of the individual tasks.
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Micropolar continuum and its applications in structural mechanics
Fleischerová, Beáta ; Vořechovský, Miroslav (referee) ; Eliáš, Jan (advisor)
Práca sa zaoberá mechanikou kontinua. Konkrétne je zameraná na lineárnu elasticitu homogénnych izotropných pevných telies. Pre dve rôzne kontinuá – klasické kontinuum a mikropolárne je odvodená silná aj slabá formulácia. Cosseratovo (mikropolárne) kontinuum predstavuje rozšírenie ku klasickému, kde je uvažovaný ďalší stupeň voľnosti - nezávislá rotácia. Mikropolárne kontinuum definuje ďalšie dve materiálové konštanty, ktoré súvisia s rotáciou. V súčasnosti je metóda konečných prvkov veľmi populárny spôsob približného riešenia rovníc lineárnej elasticity. Pre účely diplomovej práce bol vyvinutý program pre MKP riešenie 2D rovinných úloh. Pre lepšiu predstavu o vplyvu rôznych parametrov na správanie sa oboch kontinuí analyzujeme jednoduchý príklad konzolového nosníka. Riešenia analyzujeme s využitím 4-uzlového štvorhranného elementu, ktorý je jedným z najpoužívanejších pre MKP. V Cosseratovom kontinue by mali byť rotácie previazené skrz parameter vnútornej dĺžky, čo by sa malo odzrkadliť zvýšenou tuhosťou telesa. Úlohou práce je porovnať výsledky z oboch kontinuí a potvrdiť tento predpoklad.
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Solved Problems in Theoretical Mechanics
Roskot, Michal ; Koupilová, Zdeňka (advisor) ; Snětinová, Marie (referee)
The object of the bachelor's thesis was the creation of tasks for "Collection of Solved Problems in Physics". I have created 20 structured tasks on the subject of theoretical mechanics. These are mostly on a university level. I have successfully filled the chapters "The Principle of virtual work" and "Hamiltonian mechanics", which are included in the subject of theoretical mechanics. In order to create the bachelor's thesis it was necessary to get familiar with the web interface of the "Collection". At the same time to create pictures I had to learn to work with a graphical editor. In the text of the bachelor's thesis I characterize the technical solution of "Collection of Solved Problems in Physics", describe advantages of the used structure of the solved tasks and I briefly summarize content of the individual tasks.
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Solved problems in Theoretical Mechanics to Electronic Database of Solved Tasks
Hruška, Viktor ; Dvořák, Leoš (advisor) ; Šabatka, Zdeněk (referee)
Solved Problems in Theoretical Mechanics to Electronic Database of Solved Tasks Abstract: The main goal of this bachelor thesis was to create set of tasks with structural hints and detailed solution in the field of theoretical mechanics. 16 tasks were created and published within The Electronic Collection of Solved Problems in Physics on the web. The tasks are meant to serve the university level students and they are adapted for self study. Keywords: theoretical mechanics, principle of virtual work, Lagrange equations of the second kind, electronic collection of tasks, structured solutions of tasks
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