Meshless Radial Point Interpolation Method with Polynomial Basis

The interpolation functions with the combination of radial and polynomial basis overcomes possible singularity associated with the PIM based on only the polynomial basis. As its shape functions possess the Kronecker delta function property,essential boundary conditions can be imposed easily. In this paper,the basic theory was introduced,based on the variational principle,the basic equations and numerical integration method were proposed. Numerical examples of orifice plate were given to verify the validity and availability. The simulation result shows that the meshless method has high efficiency,high stability,the obtained results agree well with the elasticity analytical solution and with the results obtained with the finite element method.