Description:
In this paper, a technique to model strong and weak discontinuities with the scaled boundary finite element method through enrichment is proposed. The main advantage of the method is that the enriched elements, in the spirit of the extended finite element method (XFEM), do not need to physically conform to the geometry of features, e.g. internal interfaces and cracks, and remeshing is unnecessary as the interfaces evolve. All the advantages of the SBFEM and the XFEM are retained. The stress singularity at the crack tip can be captured accurately and the stress intensity factors (SIFs) can be directly computed based on the singular displacement or stress at the crack tip within the framework of the SBFEM. The numerical properties and performance for the proposed method are assessed using several numerical examples. In particular, problems with discontinuities, e.g. voids, inclusions, and cracks are analysed. The results show that the accuracy and convergence rate of the new approach for solving void or inclusion problems are identical to those of the XFEM, but requires less number of degrees-of-freedom than the XFEM. For crack problems, compared with the XFEM with topological enrichment, the developed method is superior.
Description:
The stress intensity factors and the electrical displacement intensity factor for functionally graded piezoelectric materials (FGPMs) are influenced by: (a) the spatial variation of the mechanical property and (b) the electrical and mechanical boundary conditions. In this work, a semi-analytical technique is proposed to study the fracture parameters of FGPMs subjected to far field traction and electrical boundary conditions. A scaled boundary finite element formulation for the analysis of functionally graded piezoelectric materials is developed. The formulation is linearly complete for uncracked polygons and can capture crack tip singularity for cracked polygons. These salient features enable the computation of the fracture parameters directly from their definition. Numerical examples involving cracks in FGPMs show the accuracy and efficiency of the proposed technique.