An exact solution for the static and dynamic analysis of FE discretized uncertain structures

The probabilistic analysis of FE discretized uncertain linear structures in the static and dynamic domain is the goal of this paper. In particular, a procedure able to give the exact relationship between the response and the random variables representing the structural uncertainties is presented, under the assumption that a point-discretization method is used for the representation of the uncertain random field. This procedure is based on the properties of the structural deformation modes and, in particular, on the number of principal deformation modes of the FE type used for the structural discretization. The use of these relationships leads to the exact probabilistic characterization of the response, once that the probabilistic description of the uncertainty is fixed. Moreover, they give the approximate relationship when only some of the random variables, chosen by a sensitivity procedure, are included in the analysis. This allows to obtain an optimum level of accuracy through a reduced computational effort.