A cell-based smoothed radial point interpolation method (CS-RPIM) for three-dimensional solids

A cell-based smoothed radial point interpolation method (CS-RPIM) is formulated for three-dimensional elasticity problems. In present method, the problem domain is firstly discretized by tetrahedron background cells, and each tetrahedron cell is then 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 the background cells. The smoothed Galerkin weak form is employed to create discretized system equations, and then the gradient smoothing operation is adopted to construct smoothed strain fields in every smoothing cell. Numerical examples are used to examine the present method in terms of accuracy, convergence, and efficiency. Compared with the finite element method using linear interpolation and node-based smoothed finite element method, the CS-RPIM solutions can achieve better efficiency, higher accuracy, and greater stability in static and free vibration analysis in presented examples.