Element-free Galerkin method using directed graph and its application to creep problems

Abstract

The element-free Galerkin method (EFGM) is one of the meshless methods proposed by Belytschko et al. Since node-element connectivities used in the finite element method (FEM) are not needed in the EFGM, the EFGM is expected to be applied to many problems of the continuum mechanics and to be utilized for a tool in a CAE system instead of the FEM. However the EFGM requires more CPU time to search nodes of the MLSM than the FEM. In this paper, the method of the directed graph and the Delaunay triangulation are respectively used for searching nodes and the division of the integral domain respectively. These techniques are useful for saving the CPU time and the simplification of the analysis for the EFGM. Furthermore, the EFGM has not been applied to nonlinear problems such as creep problems under elevated temperature. In this paper, the EFGM using the method of the directed graph and the Delaunay triangulation is applied to several creep problems. The CPU times for the analyses are reduced by the proposed EFGM. The results obtained from the EFGM analyses agree well with those of the FEM.