Three Dimensional Frame Structures with Edge-Cracks of Uncertain Depth and Location

In this paper, a numerical study on the structural behaviour of three-dimensional cracked structures have been presented. The \nstiffness matrix of the cracked element is found as the inverse of the compliance matrix. This matrix is given by the sum of the \ncompliance matrix of the intact element and an additional compliance matrix which contains all the flexibilities given by the presence of \nthe crack. The flexibilities are related to the stress intensity factors. A simple method for obtaining approximate stress intensity factors is \napplied. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. \nMoreover, crack depth and location are modelled as random variables in order to take into account the unavoidable uncertainty that \nalways affects damaged structures. A simple and accurate method for the probabilistic characterization of the linear elastic response of \ncracked structures with uncertain damage is employed. According to this method, the uncertainties are transformed into superimposed \ndeformations depending on the distribution of internal forces and an iterative procedure is established to solve the resultant equations. \nNumerical tests evidence excellent accuracy for multicracked structures with large fluctuation of damage. Present manuscript also \ndiscusses relevant patents.