Closed-form solutions of redundantly constrained stochastic frames

This paper addresses the determination of the closed-form solutions of redundantly constrained stochastic frames in terms of the probability density function (PDF). The full characterization of any response random variable of the structures, that are characterized by spatially random deformability (or its inverse, the stiffness), has been identified through the application of the force method and the application of the probability transformation method (PTM). The first method one allows for solving the redundancy while the PTM gives the explicit relationship between the PDFs of the response and of bending deformability which is assumed to be a mono-axial Gaussian random field. The formulation becomes particularly simply in the case of beams, for which the exact solutions of some benchmark applications are given, confirming the goodness of the present approach.