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

Stochastic response analysis of 3D vibro‐acoustic systems with geometrical uncertainties based on the extended finite element method

“…Savvas et al 16 analyzed the homogenization of a random multiphase medium with arbitrarily shaped inclusions based on the XFEM and the MCS, where the shape and location of the inclusions were described using level set functions. Similarly, Han et al 17 studied the stochastic void problem based on the XFEM and the gPC with a refinement of the mesh at the boundary. Based on the characteristic that geometrical uncertainty problems have local properties and inspired by the way crack growth is treated in fracture mechanics, we introduce the XFEM, which is enriched using level set functions, to the vibro‐acoustic model to develop the vibro‐acoustic method XFEM/FEM that can capture changes in the boundary geometry.…”

Dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena by the variable-node multiscale XFEM

“…Ding et al [29,30] present a Matlab object-oriented implementation of an efficient V-XFEM for the problems of multiple crack growth simulation and strong and weak discontinuities. Han et al [31] proposed a triangular extended stochastic finite element method (T-XSFEM) for simulation of random void problems with the aid of variable-node elements to couple/link different mesh-scales. More recently, the V-XFEM are extended for detection of multiple complicated flaw clusters in large structures [32].…”