Stress intensity factor by p-adaptive refinement based on ordinary Kriging interpolation

This paper aims at achieving two specific objectives. The first one is to examine the applicability of ordinary Kriging (OK) interpolation to the finite element method based on variogram modeling, and the second one is to present an adaptive procedure for hierarchical p-refinement in conjunction with a posteriori error estimator based on the modified superconvergent patch recovery (S.P.R.) method. For this purpose, the weighted least-square method is applied to predict the exact solution from derivative values computed at the Gauss points. The weight factor is determined by experimental and theoretical variogram-based interpolation of derivative data, in contrast to conventional interpolation methods based on an equal weight factors. In the p-refinement, the analytical domain is refined automatically to obtain an acceptable level of accuracy, by a selective increment of the p-level. To verify the performance of the modified S.P.R. method, a new error estimator based on the limit value is proposed. The validity of the proposed approach is tested by analyzing two-dimensional cracked plates under tension modeled with quadrilateral elements.