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Reliability-based structural optimization
Slowik, Ondřej ; Pukl, Radomír (referee) ; Novák, Drahomír (advisor)
This thesis presents the reader the importance of optimization and probabilistic assessment of structures for civil engineering problems. Chapter 2 further investigates the combination between previously proposed optimization techniques and probabilistic assessment in the form of optimization constraints. Academic software has been developed for the purposes of demonstrating the effectiveness of the suggested methods and their statistical testing. 3th chapter summarizes the results of testing previously described optimization method (called Aimed Multilevel Sampling), including a comparison with other optimization techniques. In the final part of the thesis, described procedures have been demonstrated on the selected optimization and reliability problems. The methods described in text represents engineering approach to optimization problems and aims to introduce a simple and transparent optimization algorithm, which could serve to the practical engineering purposes.
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Calculation of the probability of the endoprosthesis ceramic head with shape deviation
Kučerková, Miroslava ; Fuis, Vladimír (referee) ; Kovář, Jaroslav (advisor)
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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Probabilistic approach for evaluation of the safety of earthing systems
Klíč, Tomáš ; Vyčítal, Václav (referee) ; Topolánek, David (advisor)
This thesis deals with the grounding systems, namely their evaluation in terms of safety. The introduction describes the grounding theory, the principle reason for their use, and the difference between the current evaluation method of grounding systems in terms of security against electric shock and a new approach. Another part is devoted to describing the assessment of grounding systems in terms of safety, respectively. permissible touch and step voltages using currently based ČSN and PNE. Another essential part of the theoretical description of how to assess safety of grounding systems in terms of probabilities, consisting in determining the probability of death of a person, including the probability of failure and the probability of a man close to the rated grounding system during the disturbances, and classify the probability tolerable, moderately tolerable or intolerable and if necessary, assign the risk group appropriate solutions to mitigate the risks. The work, of course, the practical part. Designed for probabilistic approach will be processed illustrative example of evaluation chosen grounding system, which would be the basis for the negotiation of an international group CIRED / CIGRE focused on this issue.
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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 (referee) ; Kovář, Jaroslav (advisor)
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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Reliability-based structural optimization
Slowik, Ondřej ; Červenka,, Jan (referee) ; Lepš, Matěj (referee) ; Novák, Drahomír (advisor)
Presented PhD thesis deals with reliability-based optimization of structures and problems related to automatization of various algorithms of solution for various reliability-based optimization task definitions. The text presents a general definition of the reliability-based optimization problem, followed by a description of state of the art within the broad field of reliability-based optimization as well as the current state of the art of selected methodology utilized or developed by the author during his work in order to meet objectives of his dissertation. The theoretical part of the thesis is supplemented by a description of developed software tools and by examples of described methodology applications during a solution of practical problems of nonlinear numerical models reliability-based optimization and problems of inverse analysis.
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Calculation of the probability of the endoprosthesis ceramic head with shape deviation
Kučerková, Miroslava ; Fuis, Vladimír (referee) ; Kovář, Jaroslav (advisor)
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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Comparing the Results of Probability of Ceramic Head Fracture According to Weibull's Theory with Inclusion of One or Three Principal Stresses
Kovář, J. ; Fuis, Vladimír
This paper focuses on the assessment of probability of ceramic head hip joint endoprothesis fracture.\nThe Weibull's weakest link theory with inclusion of one or all three principal stresses was used for calculations of probability of failure and the results were compared. The test of head of the hip joint endoprothesis according to ISO 7206 was modelled. Three variants were considered. In the first variant, the head of hip joint endoprothesis ended up without any imperfections from ideal geometry. In other two variants, the ceramic head had shape imperfection from nominal conicity. Principal stresses needed for the calculation of probability of failure were calculated by finite element method. The results with the use of linear and quadratic solid elements were compared and better option was chosen for the next calculations. The influence of allowed penetration, density of the mesh on the results of stresses and probability of failure was assessed. The Gaussian quadrature of 13th order was used for integration over the surface of unit hemisphere in space of principal stresses which was needed for computation of probability of failure with inclusion of all principal stresses. The influence of imperfection from nominal conicity on probability of failure of the head hip joint endoprothesis was calculated and the relative difference between the results of Weibull's weakest link theory with the inclusion of one or all three principal stressed was analyzed.
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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 (referee) ; Kovář, Jaroslav (advisor)
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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Probabilistic approach for evaluation of the safety of earthing systems
Klíč, Tomáš ; Vyčítal, Václav (referee) ; Topolánek, David (advisor)
This thesis deals with the grounding systems, namely their evaluation in terms of safety. The introduction describes the grounding theory, the principle reason for their use, and the difference between the current evaluation method of grounding systems in terms of security against electric shock and a new approach. Another part is devoted to describing the assessment of grounding systems in terms of safety, respectively. permissible touch and step voltages using currently based ČSN and PNE. Another essential part of the theoretical description of how to assess safety of grounding systems in terms of probabilities, consisting in determining the probability of death of a person, including the probability of failure and the probability of a man close to the rated grounding system during the disturbances, and classify the probability tolerable, moderately tolerable or intolerable and if necessary, assign the risk group appropriate solutions to mitigate the risks. The work, of course, the practical part. Designed for probabilistic approach will be processed illustrative example of evaluation chosen grounding system, which would be the basis for the negotiation of an international group CIRED / CIGRE focused on this issue.
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Reliability-based structural optimization
Slowik, Ondřej ; Pukl, Radomír (referee) ; Novák, Drahomír (advisor)
This thesis presents the reader the importance of optimization and probabilistic assessment of structures for civil engineering problems. Chapter 2 further investigates the combination between previously proposed optimization techniques and probabilistic assessment in the form of optimization constraints. Academic software has been developed for the purposes of demonstrating the effectiveness of the suggested methods and their statistical testing. 3th chapter summarizes the results of testing previously described optimization method (called Aimed Multilevel Sampling), including a comparison with other optimization techniques. In the final part of the thesis, described procedures have been demonstrated on the selected optimization and reliability problems. The methods described in text represents engineering approach to optimization problems and aims to introduce a simple and transparent optimization algorithm, which could serve to the practical engineering purposes.
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