Recursive distribution method for probabilistic structural integrity analysis

The Recursive Distribution (RD) method represents a time-evolution law of a joint distribution function of a random vector which follows a determinist ic time-evolution law under the prescription of an initial random vector. T he recursive formula for the distribution function can be decomposed into t he absolutely continuous part and the singular part, which is the Lebesgue decomposition of the distribution function. In this paper, a theory of the Lebesgue decomposition of the recursive formula is discussed, and a numeric al algorithm of the RD method is given. The present method is applied to a probabilistic fracture mechanics analysis for piping integrity problem. In order to calculate the probability of the unstable fracture of the pipe, it is needed to evaluate the singular part of the Lebesgue decomposition. A n umerical example and its comparison with the MC method are presented. (C) 1 999 Elsevier Science S.A.