Stochastic response analysis of the scaled boundary finite element method and application to probabilistic fracture mechanics

• We propose an efficient stochastic response analysis method for the SBFEM.
• We give an improved approach to compute the sensitivities of the SBFEM responses.
• Semi-analytical evaluation of the displacement, stress and the SIFs derivatives.
• The stochastic analysis of the orthotropic and cracked structures is performed.
• Reliability analysis is efficiently performed without iteration.

This paper proposes a stochastic response analysis method for the scaled boundary finite element method (SBFEM), through which the statistical characteristics of the structural responses subject to random uncertainty can be efficiently calculated. In the proposed method, an approximate approach is given to solve the first four statistical moments of the random responses of SBFEM. The probability density functions of the structural responses are calculated using the maximum entropy principle constrained by the calculated moments. The semi-analytical gradients of the responses with respect to the random variables are solved by developing an improved sensitivity analysis method of SBFEM. The proposed method is then applied to the structural reliability analysis and the probabilistic fracture mechanics analysis. Four numerical examples are investigated to demonstrate the validity of the proposed method.