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Micropolar continuum and its applications in structural mechanics
Fleischerová, Beáta ; Vořechovský, Miroslav (oponent) ; Eliáš, Jan (vedoucí práce)
The thesis revolves around continuum mechanics. More specifically, it is focused to linear elasticity of homogenous isotropic solids. The strong and weak formulations are derived for two different continua - classical continuum and micropolar continuum. The Cossserat (micropolar) continuum represents extension to the classical continuum, where another degree of freedom is considered - independent rotation. The micropolar continnuum defines additional two material parameters, which are related to the rotation. Nowadays, Finite Element Method is very popoular way of solving the equations of the linear elasticity in an approximate way. A FEM program for solving 2D structures of plane stress simplification was developer for purpose of the thesis. For detailed examination of the effect of different parameters on both continua behaviour, we analyse simple example of a long cantiliver beam. Solutions are analysed with help of the 4-node quadrilateral elements as one of the most commonly used elements for FEM. The rotations in the Cosserat continuum are related through parameter of internal length. This should result in an increased stiffnes of the stucture. The purpose of the study is to compare solutions from the both continua and comfirm the assumption.
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Micropolar continuum and its applications in structural mechanics
Fleischerová, Beáta ; Vořechovský, Miroslav (oponent) ; Eliáš, Jan (vedoucí práce)
The thesis revolves around continuum mechanics. More specifically, it is focused to linear elasticity of homogenous isotropic solids. The strong and weak formulations are derived for two different continua - classical continuum and micropolar continuum. The Cossserat (micropolar) continuum represents extension to the classical continuum, where another degree of freedom is considered - independent rotation. The micropolar continnuum defines additional two material parameters, which are related to the rotation. Nowadays, Finite Element Method is very popoular way of solving the equations of the linear elasticity in an approximate way. A FEM program for solving 2D structures of plane stress simplification was developer for purpose of the thesis. For detailed examination of the effect of different parameters on both continua behaviour, we analyse simple example of a long cantiliver beam. Solutions are analysed with help of the 4-node quadrilateral elements as one of the most commonly used elements for FEM. The rotations in the Cosserat continuum are related through parameter of internal length. This should result in an increased stiffnes of the stucture. The purpose of the study is to compare solutions from the both continua and comfirm the assumption.
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