A cell-based smoothed radial point interpolation method (CS-RPIM) for static and free vibration of solids

Abstract

A cell-based smoothed radial point interpolation method (CS-RPIM) based on the generalized gradient smoothing operation is proposed for static and free vibration analysis of solids. In present method, the problem domain is first discretized using triangular background cells, and each cell is further divided into several smoothing cells. The displacement field function is approximated using RPIM shape functions which have Kronecker delta function property. Supporting node selection for shape function construction uses the efficient T2L-scheme associated with edges of the background cells. The system equations are derived using the generalized smoothed Galerkin (GS-Galerkin) weak form, and the essential boundary conditions are imposed directly as in the finite element method (FEM). The effects of the number of divisions smoothing cells on the solution properties of the CS-RPIM are investigated in detail, and preferable numbers of smoothing cells is recommended. To verify the accuracy and stability of the present formulation, a number of numerical examples are studied to demonstrate numerically the efficiency of the present CS-RPIM.