| Summary: | 碩士 === 國立臺灣科技大學 === 營建工程系 === 98 === Assessment of structural reliability is an important field of research in the last decades. Numerous methods have been developed in order to calculate the failure probabilities and/or the reliability indices of structures. Some of the developed methods are only applicable for particular cases; some methods are not accurate and efficient enough for practical applications; e,g., they may require evaluation of multi-fold numerical integrations, large-size sampling and/or search of design points. In this thesis, a modified moments-based reliability method is proposed. The Probability Density Function (PDF) of each random variable is approximated by an “equivalent” Probability Mass Function (PMF) containing several “weighted” delta functions. The “weighted” delta functions of the equivalent PMF have specific locations and weights such that the first few moments of this PMF match those of the original PDF. Afterwards, the first four moments of the performance function can be obtained by taking the “weighted” averages of all equivalent PMFs. Based on moments of performance function, the reliability index and the failure probability can be therefore calculated by the Hermite moment formulas. The calculation procedure is simple and convenient because it requires neither iteration nor the evaluation of derivatives and integration. Various types of problems are considered to examine the effect of type and number of random variables, nonlinearity of performance function and the target failure probability on the accuracy and efficiency of the proposed method. The proposed method gives the best result when performing those problems. It is found that the applicability and efficiency of the proposed method are quite satisfactory. It is suggested that the number of “weighted” delta functions of the equivalent PMF must be selected based on the required accuracy and efficiency. The proposed method derives the first four moments of performance function based on the exact performance function and applies the closed form formulas for reliability index and failure probability.
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