Extended stochastic finite element method enhanced by local mesh refinement for random voids analysis

Abstract We present in this paper a novel and efficient computational approach in terms of triangular extended stochastic finite element method (T-XSFEM) for simulation of random void problems. The present T-XSFEM is further enhanced by local mesh refinement with the aid of variable-node elements to couple/link different mesh-scales, increasing the efficiency of the developed approach and saving the computational cost. The degrees of freedom are approximated with a truncated generalized polynomial chaos (GPC). The present work depends on the extension of extended finite element method (XFEM) to the stochastic context, containing implicit expression of voids through the random level set functions. A new partition technique is defined to divide the random domain for integration by using a priori knowledge of the void shape function, which can further reduce the computational time. To show the effectiveness and accuracy of the developed approach, numerical experiments are studied and computed results are compared with existing reference solutions.