Element Free Galerkin Method Using Digraph and Its Application to Creep Nonlinear Problem

The element free Galerkin method (EFGM) is one of the meshless methods proposed by Belytschko, et. al. in 1994. The EFGM is a new numerical method which is expected to be utilized for many problems of the continuum mechanics and for a tool of the seamless system between the CAD and the CAE instead of the finite element method. The EFGM uses the moving least square interpolation (MLSI) for the functional approximation without elements. However the EFGM needs computational time for searching nodes of the MLSI and needs to be provided the integral domain. In this study, the method of the digraph and the Delaunay tessellation are used for the division of the integral domain and the searching nodes. These techniques are useful for the simplification of the analysis and saving the computational time. Furthermore, the EFGM has not been applied to nonlinear problems such as elastic-plastic problems or creep ones under elevated temperature. In this paper, the developed EFGM using the method of the digraph and the Delaunay tesselation is applied to creep nonlinear problems. The results obtained from the EFGM agree well with those of the finite element method