Weighted integral method in stochastic finite element analysis

This paper, introducing a weighted integral method, formulates the new stochastic finite element method for estimating the response variability of stochastic systems consisting of line elements. The essential feature of the proposed method is that the continuous stochastic field is rigorously taken care of by-means of weighted integrations to construct not only the element stiffness matrix but also the equivalent nodal forces. As a result, the issue involving the stochastic field is transformed into a problem involving only a few random variables, and then the perturbation or Monte Carlo simulation methods is utilized. This has lead to substantial improvement in computational efficiency whether the perturbation or Monte Carlo simulation method is used. Furthermore, the accuracy of the solution from the proposed method is independent of the way in which discretization is performed, while this certainly is not the case for the conventional methods.