In this paper a numerical study on the structural behaviour of two-dimensional cracked structures is presented. The stiffness matrix of the cracked element is found as the inverse of the compliance matrix. This matrix is given by the sum of the compliance matrix of the intact element and an additional compliance matrix which contains all the flexibilities given by the presence of the crack. The flexibilities are related to the stress intensity factors. A simple method for obtaining approximate stress intensity factors is applied. It takes into account the elastic crack tip stress singularity while using the elementary beam theory. Moreover, crack depth and location are modelled as random variables in order to take into account the unavoidable uncertainty that always affects damaged structures. A simple and accurate method for the probabilistic characterization of the linear elastic response of cracked structures with uncertain damage is employed. According to this method, 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. Numerical tests evidence excellent accuracy for multicracked structures with large fluctuation of damage.
Nobile, L., & Gentilini, C. (2009). Probabilistic analysis of cracked frame structures taking into account the crack trajectory. In Procedia Engineering (Vol. 1, pp. 83–86). Elsevier Ltd. https://doi.org/10.1016/j.proeng.2009.06.022