Determination of singularity exponents in 3D elasticity problems using enriched base functions in the Scaled Boundary Finite Element Method

Abstract

The SBFEM is employed for the extraction of 3D stress singularity exponents and their associated deformation modes. It makes use of a separation of variables approach, which is substituted into the virtual work equation so that only parts of the boundary need to be discretized while the 3D boundary value problem is considered analytically in a scaling variable. The enrichment of the standard separation of variables representation for the displacements with a decomposition of the analytical crack displacement field yields a substantial improvement of the method's accuracy and convergence properties.

Convergence behaviour of the enriched scaled boundary finite element method

“…However, while such graded meshes yield the desired convergence rates, they generally are not very efficient regarding the necessary degrees of freedom. A more efficient approach, concerning the degrees of freedom, has been proposed in the works of Hell and Becker where stress singularity exponents were determined using an enriched formulation of the SBFEM (enrSBFEM) and then compared, within the frame of a convergence study, to the results obtained from a standard formulation.…”