Differential moment equations of FE modelled structures with geometrical non-linearities

In the framework of the finite element (FE) method, by using the “total Lagrangian approach”, the stochastic analysis of geometrically non-linear structures is performed. To this purpose the deterministic equations of motion are written wording the non-linear contribution in an explicit representation as pseudo-forces. Then the equations of moments of the response for external Gaussian white noise processes are obtained by extending the classical Itô's rûle to vectors of random processes. The deterministic equations of motion and the equations of moments, here obtained, show a perfect formal similarity. By using this similarity a very effective computational procedure to evaluate the moments of any order of the response is proposed. It is also shown that the proposed formulation can be considered a very important step towards the actual solution of multidegree-of-freedom systems under Gaussian white processes.