Stochastic fatigue of a mechanical system based on the technique of probabilistic transformation

In this article a new technique proposed to find the probability density function (pdf) of a stress for a stochastic mechanical system. This technique is based on the combination of the Probabilistic Transformation Method (PTM) and the Finite Element Method (FEM) to obtain the pdf of the response. The PTM has the advantage of evaluating the probability density function pdf of a function with random variable, by multiplying the joint density of the arguments by the Jacobien of the opposite function. Thus, the "exact" pdf can be obtained by using the probabilistic transformation method (PTM) coupled with the deterministic finite elements method (FEM). In the method of the probabilistic transformation, the pdf of the response can be obtained analytically when the pdf of the input random variables is known. An industrial application on a plate perforated with random entries was analyzed followed by a validation of our technique using the simulation of Monte Carlo.