The elastoplastic analysis of functionally graded materials using a meshfree RRKPM

A meshfree approach, the radial basis reproducing kernel particle method (RRKPM), is proposed in this study, which is based on the radial basis functions (RBFs) and the reproducing kernel particle method (RKPM). The presented approach eliminates the negative effects of different kernel functions on numerical accuracy, which has the advantages of greater accuracy and convergence. Furthermore, the presented approach is adopted to solve the elastoplastic problem of functionally graded materials (FGMs). Using Galerkin weak form of elastoplastic problem, the meshfree RRKPM for elastoplastic problem of FGMs is established, and the penalty method is employed to impose the essential boundary conditions, then the corresponding formulas are obtained. The effects of the scaling factor, loading steps, number of nodes and node distributions on computational results of numerical accuracy are discussed in detail, and the influences of different functional gradient indexes on displacements are studied. To validate the applicability and reliability of the presented meshfree RRKPM, several elastoplastic examples of FGMs are performed and compared to the RKPM and the finite element method (FEM) solutions. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

A new meshfree method, RRKPM, based on RBFs and RKPM is proposed for solving elastoplastic problems of FGMs, which offers greater accuracy and convergence advantages. The applicability and reliability of RRKPM are validated through examples and comparison with RKPM and FEM solutions.