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
, the shape
parameter
, the scale
parameter
, and
the penalty factor
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.
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