On the generalization of probabilistic transformation method

The probabilistic transformation method with the finite element analysis is a new technique to solve random differential equation. The advantage of this technique is finding the “exact” expression of the probability density function of the solution when the probability density function of the input is known. However the disadvantage is due to the characteristics (geometrics and materials) of the analyzed structure included in the random differential equation.In this paper, a developed formula is used to generalize this technique by obtaining the “exact” joint probability density function of the solution in any situations, as well as the proposed technique for the non-linear case.