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.