An adaptive polytree approach to the scaled boundary boundary finite element method

Abstract

In this paper, a h-adaptive methodology based on the polytopal meshes is proposed for capturing high stress gradients at the materials corners and the stress singularities at the vicinity of a crack tip. The adaptive refinement is based on the error indicator directly computed from the displacement solutions of the scaled boundary finite element method. Based on the error indicator, a polygon of n-sides which has an error exceeding a specified tolerance is subdivided recursively into $$(n+1)$$ child polygons. The salient features of the proposed framework are: (a) circumvents a need for post-processing techniques for error estimation; (b) elements with hanging nodes are treated as polygons without a need for special treatment and (c) stress gradients and stress singularities are accurately captured due to the semi-analytical formulation. The robustness and the convergence properties of the proposed framework is demonstrated with three benchmark examples.