Stochastic analysis using the generalized perturbation stable node-based smoothed finite element method

The traditional stochastic finite element method based on the finite element method fails to give the fine solution in precise determination of reliable problems when the computer power consumption is limited. To cure this fatal defect, the generalized nth order stochastic perturbation technique based on a stable node-based smoothed finite element method (GS_SNS-FEM) is presented. The framework intends to essentially improve the accuracy, lower the mesh limitation and occupy much less computational consumption for stochastic problems, especially when its second order realization is ineffective for large variations of input random fields. Besides, the nth orders expansion makes it possible to get the prefect accuracy for expected values and variances. Numerical examples including the static and dynamic problems are completed and compared with the solution of Monte Carlo simulation. It is found that the SNS-FEM applied in the stochastic problem can improve the accuracy of static and dynamic results, largely decrease the time cost, and lower the requirement of mesh.