Reliability analysis of homogeneous and bimaterial cracked structures by the scaled boundary finite element method and a hybrid random-interval model

• Normalizing procedure introduced to evaluate SIFs for bimaterial interface cracks.
• A SIF shape sensitivity technique is developed for bimaterial interface cracks.
• It is coupled with the random-interval moment method to analyze reliability.

The reliability analysis of cracked homogeneous and bimaterial structures with random and interval uncertainties is addressed. Based on the scaled boundary finite element method, a shape sensitivity technique is proposed to compute the derivatives of the stress intensity factors with respect to the geometry of an interface crack. It is coupled with the random-interval moment method, wherein the reliability is predicted by regarding uncertainties in material properties, loads and fracture toughness as random variables, and uncertainties in the crack geometry as interval variables. The shape sensitivity analysis involves placing the scaling center at the crack tip such that the governing functions are formed in terms of the scaling center coordinates. Only the boundary, excluding the crack surface, is discretized. The sensitivity to the crack geometry is obtained through direct differentiation with respect to the scaling center, without remeshing, mesh perturbation or velocity fields. Numerical examples are presented.