Life estimation of the beam with normal distribution parameters and subjected to cyclic load

This research aims at estimating the life of the beam with normal distribution parameters and subjected to cyclic load. It is tested by Monte-Carlo simulation that the generalized displacement and velocity are normally distributed when the coefficient of variation (CV) of the random parameter is small (generally CV≤ 0.01). The random perturbation method is employed to estimate the mean and variance of the generalized displacement and velocity. The random dynamic stress and its derivative with respect to the time t of the beam is formulated according to the shape function of beam element and the stress equation in a Euler-Bernoulli beam. Their mean, variance and correlation coefficient are given using the first-order approximation in a Taylor series. Based on Palmgren-Miner rule, the expected cumulative damage equation is given and is used to estimate the life where the random dynamic stress is non-stationary and follows the normal distribution with the nonzero mean at any time t. The presented method could also estimate the life of other structure or component which has several normal random parameters, is subjected to cyclic load and obeys the linear dynamics and elastic theory when the random parameter’s CV is small.