When a failure model with low cycle fatigue is identified

the failure function for reliability analysis reduced as follows:As cumulative damage of varying amplitude cycles is calculated with Miner's law

the total damage is considered to be a random value varying from 0 3 to 3

and follows logarithmic normal distribution.Furthermore

damage of low cycle loads of each amplitude is evaluated according to the formula of flow cycle fatigue life prediction proposed by R.W.Landgraf.Then

the failure function for reliability analysis is derived from the above formulas by transforming strain expression into stress expression.If a stress at certain point of a disk is influenced by a disturbance of some random variables

the stochastic finite element method is employed to find the variance of the stress distribution.When stresses in a disk are in elasto plastic condition

nonlinear SFEM is required to obtain the variance of the stresses.Finally

a numerical example for a disk with equal thickness is presented and is verified by the Monte Carlo simulation.