Generalized stochastic cell-based smoothed finite element method (GS_CS-FEM) for solid mechanics

The smoothed finite element method (S-FEM) was recently proposed to inject softening effects into and improve the accuracy of the standard FEM. In the S-FEM, the system stiffness matrix is obtained using strain smoothing technique over the smoothing domains associated with cells, nodes, edges or faces to establish models of desired properties. Stochastic FEM is regarded as an extension of the classical deterministic FEM to deal with the randomness of properties of input parameters in solid mechanics problems. In this paper, the cell-based S-FEM (or CS-FEM) is extended for stochastic analysis based on the generalized stochastic perturbation technique. Numerical examples are presented and obtained results are compared with the solution of Monte Carlo simulation. It is found that the present GS_CS-FEM method can improve the solution accuracy significantly for stochastic problems, in terms of the estimated means, variances and other probabilistic characteristics.

► A generalized stochastic cell-based smoothed finite element method is proposed.
► CS-FEM improves the solution accuracy for deterministic analysis.
► Generalized stochastic perturbation allows large variations of random variables.
► Numerical solutions are compared with the results of Monte Carlo simulation.