Numerical solution of functionally graded materials based on radial basis reproducing kernel particle method

In this paper, the radial basis function (RBF) is used to construct the approximating function of the reproducing kernel particle method (RKPM), which can eliminate the negative effect of different kernel functions on the calculating accuracy. The radial basis reproducing kernel particle method (RRKPM) is proposed. Furthermore, the RRKPM is applied to solve the elastic mechanical problems of the functionally graded materials (FGM), and the RRKPM for FGM is established. The corresponding formulae of the RRKPM for FGM are derived. Compared with the traditional RKPM, the RRKPM has higher calculating accuracy and stability. Finally, the numerical examples illustrate that the RRKPM is correct and effective to solve the elastic mechanical problems of the FGM.