NUMERICAL SOLUTION OF BIDIRECTIONAL FUNCTIONALLY GRADED MATERIALS USING A NOVEL MESHLESS GLOBAL RADIAL BASIS REPRODUCING KERNEL PARTICLE METHOD

A novel meshless global radial basis reproducing kernel particle method (GRB-RKPM) is established based on the global radial basis function (GRBF) and the reproducing kernel particle method (RKPM). Subsequently, GRB-RKPM is used to solve the elastic mechanical of bidirectional functionally graded materials (BDFGMs). The influence of the shape parameter q, the shape parameter ac, the scale parameter dmax, and the penalty factor alpha on the GRB-RKPM solving the elastic mechanical of BDFGMs is analyzed, and the optimal value is given. The effectiveness of the GRB-RKPM in solving the elastic mechanical of BDFGMs is verified by comparing solutions calculated by the GRB-RKPM with reference solutions calculated by the finite element method (FEM). Compared with the RKPM, the GRB-RKPM converges faster. The GRB-RKPM solutions are compared with the local radial basis reproducing kernel particle method (LRB-RKPM) solutions and the RKPM solutions. It is proved that the GRB-RKPM has higher computational accuracy. The deformation behavior of the elastic mechanical of BDFGMs under different gradient indexes is studied.