关键词: 代表点, 可靠性分析, 数论方法

Abstract: An analysis method of structural reliability is presented. It uses representative points of multivariate distribution based on number-theoretic. Uniformly scattered point set is obtained by using uniformly scattered theory based on F-Discrepancy. Using this set, the representative points of multivariate distribution are calculated. The values of failure function are obtained by using representative points as random variables under iterative method. The system reliability analysis is carried out by using approximate distribution function. As a numerical simulation example, this method is used to carry out reliability analysis of the failure function of a beam that has nonlinearity and variable correlations Comparison is made among JC method, Monte Carlo method and this method. The JC method is fast in calculation but not so accurate as Monte Carlo method in calculating nonlinear equations. Monte Carlo method is robust and accurate, but high in computational cost. The number-theoretic method is accurate and efficient without needing a great number of sample points. It can be easily applied to all kinds of problems related to structural reliability.

Key words: Number-theoretic method, Reliability analysis, Representative point