A nodal integration technique for meshfree radial point interpolation method (NI-RPIM)

A novel nodal integration technique for the meshfree radial point interpolation method (NI-RPIM) is presented for solid mechanics problems. In the NI-RPIM, radial basis functions (RBFs) augmented with polynomials are used to construct shape functions that possess the Delta function property. Galerkin weak form is adopted for creating discretized system equations, in which nodal integration is used to compute system matrices. A stable and simple nodal integration scheme is proposed to perform the nodal integration numerically. The NI-RPIM is examined using a number of example problems including stress analysis of an automobile mechanical component. The effect of shape parameters and dimension of local support domain on the results of the NI-RPIM is investigated in detail through these examples. The numerical solutions show that the present method is a robust, reliable, stable meshfree method and possesses better computational properties compared with traditional linear FEM and original RPIM using Gauss integration scheme.