Modified r-method for the finite element adaptive analysis of plane elastic problems

The nodal relocation method (r-method) is used to uniformly distribute element discretization errors over an analytic model and improve the solution quality. When this r-method is performed with Zienkiewicz-Zhu’s error estimator, its converged solution can not be easily obtained without many iterative calculations. Further, this method also may deteriorate solution quality because of serious element distortion. This paper suggests a new error estimator which can evaluate the size and the distortion error of an isoparametric element separately and proposes a modified r-method based on this error estimator. Various numerical experiments show that the proposed error estimator properly evaluates the element discretization errors and the modified r-method can be easily applied to the practical analysis owing to the comparatively fast convergent characteristics.