An error-driven grid refinement for 2-D reliable crack analysis by enriched natural element method

Abstract

An error-driven grid refinement technique is introduced for 2-D reliable crack analysis by an enriched natural element method (more exactly, Petrov-Galerkin natural element method). A quasi-exact solution for a posteriori error estimation was obtained by enhancing the bare approximation solution of NEM (natural element method) using the enrichment method and the global patch recovery. The proposed method is illustrated through the error-driven grid refinement for a rectangular plate with a slant edge crack. The quantitative error amount is measured in terms of the energy norm, and the accuracy (i.e., the effective index) of the proposed method was evaluated from the comparison with the errors which were obtained by FEM using a very fine mesh. The proposed method provides the effective index which is much improved from that of non-enriched PG-NEM. The NEM grid was non-uniformly refined based on the local error information, and the resulting error distributions were investigated. It has been observed that the difference between the maximum and minimum values in the local error distribution of enriched PG-NEM is larger than that of non-enriched PG-NEM. The reduction of global errors according to the non-uniform grid refinement was also investigated to the grid density, from which it is found that the enriched PF-NEM provides smaller errors than the non-enriched PG-NEM. In addition, the proposed grid refinement provides the 1.676 times higher convergence rate than the uniform grid refinement.