A Meshless Solution of Nonlinear Elastoplastic Problems Based on the RRKPM

Abstract

In this paper, a numerical approach based on the reproducing kernel particle method (RKPM) and the radial basis function (RBF), which is defined as meshless radial basis reproducing kernel particle method (RRKPM), is developed and presented for solving nonlinear elastoplastic problems. Different from the mesh-based numerical methods, the RRKPM is a meshless technique, which does not require the discretization of elements and meshes as is usually done in the finite element method (FEM). The meshless RRKPM possesses the advantage of greater accuracy in comparison with the traditional RKPM. For nonlinear elastoplastic problems, Galerkin weak form is adopted to establish equation system. Utilizing the penalty method, the essential boundary conditions are imposed, and then the corresponding formulas of the meshless RRKPM for nonlinear elastoplastic problems are derived. Furthermore, the effects of the scaling parameter and node number on computational accuracy of obtained results are discussed in detail. Finally, a few elastoplastic examples are used to show the correctness and effectiveness of the presented method for solving nonlinear elastoplastic problems.