Random Propagation of a Crack in a Thin-Walled Beam

Probabilistic methodology is used for estimating the growth of an existing crack in a thin-walled beam with a closed cross section. The beam is subjected to stochastic loads. The initial length of the crack is considered to be an uncertain quantity represented by a random variable. The random characteristics of the stress response, needed for crack growth analysis, are obtained by random vibration analysis of the thin-walled beam. The crack growth rate equation is solved for a large number of randomly generated sample values of the random parameters. The simulated crack growth results are then used to calculate the probability of failure. The failure is defined as occurring when the actual crack size exceeds the critical crack size. For demonstration of the methodology, the numerical results for the time-dependent probability of failure are obtained for an example problem of a thin-walled beam.