極値理論に基く構造安全性について

Errors of the measured data are discussed as the factors which influence upon the accuracy of reliability analysis of the structural member. In the structural reliability analysis, failure probability is calculated by assuming probability density functions for material strength and external force, and following two basic assumptions have been employed as a matter of course; that is, (1)characteristics of the measured data are reliable and are equal to the characteristics of the population from which the measured data have been extracted by chance; (2)probability density functions are estimated directly based on the frequency distributions of the measured data. The error due to the assumption (1)-error of characteristics -is deemed as an error of the most likelihood estimation, and has a strong influence on the estimation of failure probability by reason that size of the measured data is usually very small. The error due to the assumption (2)-error of distributions-also has a strong influence on the estimation of failure probability by reason that theoretical endorsement of the assumed density function is not obtained. First, the error of characteristics is mainly discussed in Chapter 2, and the influence of the error on the estimation of failure probability is evaluated for normal distribution, gamma distribution and long-normal distribution. Then the definition of the usual failure probability is modified with regard to the error. On the contrary, error of distributions is considered unavoidable, and application of the procedure described in Chapter 2 is restricted to the measured data whose frequency distribution is known in advance following to one of three distributions as a result of phenomenology and/or properties of matter. Second, new approach to the reliability analysis without any approximation of distributions for the measured data is proposed in Chapter 3 from the standpoint that error of distributions is hardly solved by extending the usual reliability theory. The content bears no relation to the structural reliability, and describes the statistical treatments of the measured data with the sole object of introducing and demonstrating the new approach. Practical upper bound of population of the measured data is defined based on the variational method under the various restrictive conditions characterizing the measured data. Third, extreme procedure of Chapter 3 is extended and applied to the estimation of structural safety in Chapter 4. Since characteristics introduced in Chapter 3 are unreliable to estimate the extremum, more reliable characteristics are newly introduced. The procedure realizes the structural design where the obtained failure probability never exceed the expected one even at the worst, in other words, where a sort of guarantee for the safety can be obtained based on the variational principle. In Chapter 4, error of characteristics is estimated approximately, and graphical estimation method of extremum is developed.
名古屋大学博士学位論文 学位の種類:工学博士(課程) 学位授与年月日:昭和52年3月25日