The radial basis reproducing kernel particle method for geometrically nonlinear problem of functionally graded materials

Abstract

In this paper, the radial basis function (RBF) is introduced into the reproducing kernel particle method (RKPM), and the radial basis reproducing kernel particle method (RRKPM) is proposed for solving geometrically nonlinear problem of functionally graded materials (FGM). Compared with the RKPM, the advantages of the proposed method are that it can eliminate the negative effect of different kernel functions on the computational accuracy, and has higher computational accuracy and stability. Using the Total Lagrange (T.L.) formulation and the weak form of Galerkin integration, the corresponding formulae for geometrically nonlinear problem of FGM are derived. The penalty factor, shaped parameter of the RBF, the control parameter of influence domain radius, loading step number and node distribution are discussed. Furthermore, the effects of different gradient functions and exponents on displacement and stress are analyzed. Newton-Raphson (N-R) iterative method is utilized for numerical solution. The proposed method is correct and effective for solving geometrically nonlinear problem of FGM, which can be demonstrated by several numerical examples.