The meshfree analysis of elasticity problem utilizing radial basis reproducing kernel particle method

Abstract

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.

Keywords

• Meshfree method
• Radial basis function
• Reproducing kernel particle method
• Elasticity problem
• Numerical analysis