A stochastic scaled boundary finite element method

By extending the existing scaled boundary finite element method (SBFEM) into the random field problem, a stochastic scaled boundary finite element method (SSBFEM) is developed in this paper to predict the structural responses with randomly distributed material properties. The analyzed domain is discretized into a number of polygons modeled as sub-domains of the SBFEM so that the non-homogeneous material properties are possible to be considered in establishment of the constitutive equation. The random field represented by the Karhunen-Loève (KL) expansion is then directly incorporated into both the equilibrium equation of the SBFEM and its sensitivity analysis formulation. The perturbation method is employed to calculate the statistical moments of the structural responses and a semi-analytical sensitivity analysis method is used to efficiently calculate the gradients involved. Particularly, the proposed method is successfully applied to the stochastic fracture analysis with spatially varying random material properties. Four numerical examples are investigated to demonstrate the validity of the proposed method.