Probabilistic analysis of linear elastic cracked structures with uncertain damage

This paper presents a simple and reliable method for the probabilistic characterization of the linear elastic response of cracked structures with uncertain damage. In particular, truss and frame structures with edge cracks of uncertain depth and location are considered. The method of analysis originates from an approach recently appeared in the literature, which is generalized to treat structures with cracks affected by uncertainty. According to this approach, the uncertainties are transformed into superimposed deformations depending on the distribution of internal forces and an iterative procedure is established to solve the resultant equations. The procedure is optimally tuned based on the convergence analysis. Several numerical tests evidence excellent accuracy and convergence qualities also in the case of multicracked structures with large fluctuation of damage.