Solution of fokker-planck-kolmogorov equation in stochastic modeling of fatigue crack propagation
Journal
Journal of the Chinese Institute of Engineers,Series A/Chung-kuo Kung Ch'eng Hsuch K'an
Journal Volume
13
Journal Issue
1
Pages
25-34
Date Issued
1990
Author(s)
Huang T.-H.
Abstract
Abstract Based on linear fracture mechanics concepts and random process theory, several stochastic models of fatigue crack propagation have been proposed in recent years. One of the models randomizes the fatigue crack propagation equation by employing a random pulse train and applying a stochastic average technique to treat the dynamic fatigue crack propagation as a Markov process. The probabilistic structure of a Markov diffusion process is governed by a Fokker‐Planck‐Kolmogorov equation. Therefore, in the present paper, the probability distribution of crack size at any given time and the probability distribution function of the random time at which a given crack size is reached are treated as solutions of the Fokker‐Planck‐Kolmogorov equation associated with the Markov process. Analytical solutions are found for these quantities and numerical examples are given. The results are compared with some experimentally obtained data.
Type
journal article