A novel node-based smoothed radial point interpolation method for 2D and 3D solid mechanics problems

This paper presents a novel node-based radial point interpolation method (NS-RPIM), which has two different versions termed as NS-RPIM−Tr4−Cd (for 2D problems) and NS-RPIM−Tr5−Cd (for 3D problems). These NS-RPIMs are created using edge-based Tr4-scheme and face-based Tr5-scheme, respectively. In the formulation, we use the generalized smoothed Galerkin (GS-Galerkin) weak-form which requires only value of shape functions. Because W² formulation allows the use of discontinuous functions, RPIM can now be used to create proven stable and accurate models. The computational efficiency of the NS-RPIM−Tr4−Cd is rigorously examined against other NS-RPIMs and FEM. It is found that our NS-RPIM produce highly accurate solutions at low computational cost, due to the use of the condensed RPIM shape functions. Numerical results for 2D and 3D problems demonstrate that the NS-RPIMs possess the following important properties: (1) upper bound solution in the strain energy; (2) volumetric locking free; (3) superconvergence in strain energy solution; (4) insensitive to node distribution.