\(p\)-adaptive refinement based on stress recovery technique considering ordinary Kriging interpolation in L-shaped domain
Summary: The primary objectives of this study are twofold. Firstly, the original SPR method of stress recovery has been modified by incorporating the kriging interpolation technique to fit a polynomial to the derivatives recovered at the Gauss points. For this purpose, the \(p\)-version of finite element analysis is performed to produce the stresses at the fixed \(10 \times 10\) Gauss points where the integrals of Legendre polynomials are used as a basis function. In contrast to the conventional least square method for stress recovery, the weight factor is determined by experimental and theoretical variograms for interpolation of stress data, unlike the conventional interpolation methods that use an equal weight factor. Secondly, an adaptive procedure for hierarchical \(p\)-refinement in conjunction with a posteriori error based on the modified SPR (superconvergent patch recovery) method is proposed. Thirdly, a new error estimator based on the limit value approach is proposed by predicting the exact strain energy to verify the kriging-based SPR method. The validity of the proposed approach has been tested by analyzing two-dimensional plates with a rectangular cutout in the presence of stress singularity.
scientific article; zbMATH DE number 6971795
scientific article