Probabilistic fracture mechanics by using Monte Carlo simulation and the scaled boundary finite element method

A numerical technique to model the effect of uncertainties in the crack geometry on the reliability of cracked structures is presented. The shape sensitivity analysis of stress intensity factors to the crack size and orientation is performed by using the scaled boundary finite element method (SBFEM). Only a single boundary mesh is required. The varying crack size and orientation are represented by simply moving the scaling center and without the need for remeshing. The reliability assessment is performed by Monte Carlo simulations. Numerical examples are analyzed to verify the accuracy and demonstrate the efficiency and simplicity of the proposed technique.