A new adaptive scheme for crack analysis with element-free Galerkin method

In this study, a new adaptive scheme for crack propagation based on the element-free Galerkin(EFG) method is proposed. The adaptive analysis in crack propagation is achieved by adding and/or removing the nodes in accordance with the estimated error distribution. In this scheme, to keep the pre-specified accuracy level of the analysis through the whole propagation process, the optimal configuration of nodes is continuously reconstructed based on the error redistribution in the analysis domain. Triangular background cells are used for numerical integration and nodes are located at vertexes of each cell. The optimal configuration of background cells that reflects the distribution of estimated local error is constructed adaptively at each iteration step by Delaunay triangle technique. By the use of this approach, the resolution of numerical integration can be maintained automatically and abrupt change of nodal density between higher and lower error regions which induces additional error can be avoided. To evaluate the performance of proposed adaptive procedure, the crack propagation behavior is investigated for several examples. The results of these examples show the good efficiency and accuracy of proposed scheme in crack propagation analysis.