An interpolating reproducing kernel particle method for two-dimensional scatter points

Abstract

An interpolating reproducing kernel particle method for two-dimensional (2D) scatter points is introduced. It eliminates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating reproducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.

The high-order smooth interpolated reproducing kernel particle method for elastodynamics problems

“…Without the dependence of the grids, the output displacement, strain, and stress are continuous in the whole analysis domain, and the error of the quadratic approximation is avoided [29,30]. Two mainstream meshless methods are the element-free Galerkin methods [31][32][33][34][35] and the reproducing kernel particle methods [36][37][38][39]. However, the meshless method based on the Galerkin discretization scheme is not easy to apply the boundary conditions.…”

The dimension splitting reproducing kernel particle method for three‐dimensional potential problems

“…Chen et al have done much work on large deformation problems with this method . The interpolation properties of the RKPM nodes were discussed by Chen et al Qin et al used an interpolating RKPM for crane hook stress analysis and 2D scatter points . Dehghan and Abbaszadeh solved some 2D and multidimensional problems with RKPM .…”

“…13,14 The interpolation properties of the RKPM nodes were discussed by Chen et al 15 Qin et al used an interpolating RKPM for crane hook stress analysis 16 and 2D scatter points. 17 Dehghan and Abbaszadeh solved some 2D and multidimensional problems with RKPM. [18][19][20] Cheng et al applied the RKPM for three-dimensional (3D) transient conduction problems 21 and steady-state heat conduction problems.…”