A high-order finite element technique with automatic treatment of stress singularities by semi-analytical enrichment

This paper presents an approach to the automatic enrichment of finite elements in the vicinity of a stress singularity. The enrichment consists of semi-analytical singular modes constructed using the Scaled Boundary Finite Element Method (SBFEM). In contrast to analytical methods, the SBFEM provides modes for inhomogeneous and anisotropic materials without additional effort. The finite element basis can be of arbitrary order and remains unaltered by the enrichment. The approach requires enrichment in only one layer of elements around a node. Due to the compatibility of SBFEM with FEM, there is no need for transitional elements, and there are no parasitic terms. The approach is tested for several benchmark problems. The stress intensity factors are computed based on techniques inspired by the SBFEM. The proposed procedure is compared to a standard finite element implementation and shows a significant improvement in the error of the displacement field for problems involving singular stresses.