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Calculation of the probability of the endoprosthesis ceramic head with shape deviation
Kučerková, Miroslava ; Fuis, Vladimír (oponent) ; Kovář, Jaroslav (vedoucí práce)
The main content of the diploma thesis is to determine the probability of failure of the hip joint endoprosthesis ceramic head. The assumption is the three-axis state of stress. To calculate the probability of failure three principal stresses, which are determined numerically using finite element method, are needed. Ceramic materials, hip joint endoprosthesis and Weibull weakest link theory, which describes the calculation of the probability of failure of ceramic components, are described in the first part of the thesis, after that, the second part with calculations follows. The first model, for which the stress and probability of failure were calculated, is a cylindrical body. The stress distribution in it was determined numerically as well as analytically. Its primary goal is to verify the developed algorithm of calculating the probability of failure. This algorithm is also used in calculations of probability of failure of ceramic femoral head. The suitability of using averaged principal stress values was also verified here. In the next part of the thesis, a model of an ideal ceramic head was created and its probability of failure was calculated. The impact of friction, penetration and the size of elements used for discretization of the model on the value of probability of failure were all analysed. The evaluated findings were subsequently used in the calculations of the model of ceramic head with an deviation from the ideal ovality. The impact of this change on the resulting probability of failure in comparison with the ideal state was evaluated in the conclusion.
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Calculation of the probability of the ceramic component failure according to the Weibull’s weakest link theory
Kučerková, Miroslava ; Fuis, Vladimír (oponent) ; Kovář, Jaroslav (vedoucí práce)
Weibull weakest link theory is used to determine the probability of failure of ceramic components. This bachelor thesis examines the cylindrical body, beams and rotating circular and intercircular disc. In these bodies it is possible to identify course of the stress in an analytical way. The research part of the work approaches ceramic materials in terms of their structure, composition, method of production or mechanical properties. From a theoretical point of view, Weibull weakest link theory for uniaxial and triaxial stress in the body is described and required relations for further calculations are given here. In the second part, the probability of failure of previously mentioned models is calculated. Beams are stressed by a simple and four - point bending. The impact of the body size on the probability of failure is also analyzed. The cylindrical body is solved for different variants, which are compared afterwards. At last, the effect of operating speed on the probability of failure of the rotating circular and intercircular disc is investigated.
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Calculation of the probability of the endoprosthesis ceramic head with shape deviation
Kučerková, Miroslava ; Fuis, Vladimír (oponent) ; Kovář, Jaroslav (vedoucí práce)
The main content of the diploma thesis is to determine the probability of failure of the hip joint endoprosthesis ceramic head. The assumption is the three-axis state of stress. To calculate the probability of failure three principal stresses, which are determined numerically using finite element method, are needed. Ceramic materials, hip joint endoprosthesis and Weibull weakest link theory, which describes the calculation of the probability of failure of ceramic components, are described in the first part of the thesis, after that, the second part with calculations follows. The first model, for which the stress and probability of failure were calculated, is a cylindrical body. The stress distribution in it was determined numerically as well as analytically. Its primary goal is to verify the developed algorithm of calculating the probability of failure. This algorithm is also used in calculations of probability of failure of ceramic femoral head. The suitability of using averaged principal stress values was also verified here. In the next part of the thesis, a model of an ideal ceramic head was created and its probability of failure was calculated. The impact of friction, penetration and the size of elements used for discretization of the model on the value of probability of failure were all analysed. The evaluated findings were subsequently used in the calculations of the model of ceramic head with an deviation from the ideal ovality. The impact of this change on the resulting probability of failure in comparison with the ideal state was evaluated in the conclusion.
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Calculation of the probability of the ceramic component failure according to the Weibull’s weakest link theory
Kučerková, Miroslava ; Fuis, Vladimír (oponent) ; Kovář, Jaroslav (vedoucí práce)
Weibull weakest link theory is used to determine the probability of failure of ceramic components. This bachelor thesis examines the cylindrical body, beams and rotating circular and intercircular disc. In these bodies it is possible to identify course of the stress in an analytical way. The research part of the work approaches ceramic materials in terms of their structure, composition, method of production or mechanical properties. From a theoretical point of view, Weibull weakest link theory for uniaxial and triaxial stress in the body is described and required relations for further calculations are given here. In the second part, the probability of failure of previously mentioned models is calculated. Beams are stressed by a simple and four - point bending. The impact of the body size on the probability of failure is also analyzed. The cylindrical body is solved for different variants, which are compared afterwards. At last, the effect of operating speed on the probability of failure of the rotating circular and intercircular disc is investigated.
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