3D Element-free Galerkin method and its application

The study and application of Element-free Galerkin Method (EFGM) to three-dimensional problems is presented. Based on moving least squares method (MLSM), EFGM formulates the discrete model by using only a set of nodes, so the pre-processing of the method is simplified and the approximating function is continuous with higher-order differentials over the entire domain. The relevant theories of EFGM are introduced and the derivation of discrete equations using variational principle is presented. The visibility criterion is used to deal with the effect of discontinuities on the influence domain of a gauss point. Contribution to the system of equilibrium equations of the reciprocity between two surfaces of discontinuities is considered. To investigate the accuracy of the proposed method, a cantilever beam and Laxiwa arch dam-foundation system are analyzed in detail. The results show that the method is effective and accurate in 3D problems.