Probabilistic Transformation Method in Reliability Analysis

A technique is presented in order to evaluate the probability of failure in analytical form instead of approximation methods like FORM/SORM and no series expansion is involved in this expression. This technique is based on the Finite Element Method to obtain the expression of the response of stochastic systems, and the transformation of random variables to obtain the probability density function of the response. The transformation technique evaluates the probability density function (pdf ) of the system output by multiplying the input pdf by the Jacobian of the inverse mechanical function. This approach has the advantage of giving directly the whole density function of the response in closed form, which is very helpful for reliability analysis.