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Since meshless reproducing kernel particle method (RKPM) is easily affected by different kernel functions in numerical accuracy and stability, the Hermit-type function is introduced to the construction of trial function on boundary nodes. Meanwhile, the radial basis function is applied to establish the trial function in internal nodes, then a meshless Hermit-type radial basis function RKPM (Hermit-type RRKPM) is constructed. The advantage of this proposed method is that the numerical solution is more stable and the accuracy is higher. Furthermore, the meshless Hermit-type RRKPM is used to analyze viscoelastic problems. Finally, to illustrate the accuracy and stability, we compare the results of the proposed method and RRKPM with finite element method (FEM) solutions in solving viscoelastic problems.

The computational accuracy of the traditional reproducing kernel particle method (RKPM) is susceptible to different kernel functions. To eliminate the adverse effects of the different kernel functions on the computational accuracy of the RKPM, the radial basis function (RBF) is introduced and the radial basis reproducing kernel particle method (RRKPM) is proposed. Compared with the RKPM, the proposed method has the advantages of greater computational accuracy and faster convergence speed. Furthermore, the proposed method is applied to analyze the elastic deformation process of materials with various defects. Utilizing the Galerkin weak form of elastic mechanical problem, the RRKPM of elastic mechanics is established and the corresponding formulae are derived. Combined with the numerical examples, the shaped parameter of the RBF, the scaling parameter and the penalty factor are discussed. Finally, several different examples are adopted to demonstrate the applicability and correctness of the RRKPM.

In this paper, the method of radial basis function (RBF) is employed to construct the approximating function of the reproducing kernel particle method (RKPM), which can reduce the adverse effect of different kernel functions on computational accuracy and improve stability in the problem domain, and the radial basis reproducing kernel particle method (RRKPM) is presented. Compared with the RKPM, the RRKPM has higher computational accuracy and better stability. Then RRKPM is applied to wave propagation, and the discretized system equation can be obtained using the integral weak form. The penalty method is applied to imposing the essential boundary condition, and the two-point difference method is selected to discretize the time. The accuracy and stability of the RRKPM for wave propagation problem are illustrated by the numerical examples.