Probability-interval hybrid reliability analysis for cracked structures existing epistemic uncertainty

• A probability-interval hybrid reliability method is proposed for cracked structures.
• Intervals are used to deal with the parameters with epistemic uncertainty.
• The SBFEM is adopted to calculate the stress intensity factors.
• An efficient algorithm is formulated to compute the fracture reliability interval.

The uncertainty modeling and reliability analysis for cracked structures in which there are many inherently uncertain parameters is very important in engineering. This paper presents a probability-interval hybrid uncertainty model and a corresponding efficient reliability analysis method for the structural cracking problem. Through introducing interval uncertainty, the method can effectively address the difficulties in the epistemic uncertainty modeling due to the lack of experimental samples, which expand greatly the applicability of reliability analysis technology in cracked structure research. The parameters are classified, and subsequently the probability and interval methods are separately applied to address the parameters with sufficient and insufficient experimental samples. A probability-interval hybrid reliability analysis model for the cracked structure based on the traditional first-order reliability method is developed. The scaled boundary finite element method is adopted to calculate the stress intensity factors from which the performance function can be obtained. Based on these calculations, an efficient iterative algorithm using the response surface is developed to solve the hybrid reliability model and calculate the interval of the failure probability of the cracked structure. Four numerical examples are presented for verification of the validity of the proposed method.