Isogeometric analysis enhanced by the scaled boundary finite element method

Abstract

By leveraging the information of a typical CAD model in the analysis, the intensive process of discretization can be circumvented. This unification has led to the ‘Isogeometric Analysis’ (IGA) (Hughes et al., 2005). However, as the CAD model provides information only of the boundary, a 2D/3D stress analysis is still one major step away. In this work, the concepts of isogeometric analysis and the scaled boundary finite element method (SBFEM) are combined. The SBFEM requires only the boundary information and hence provides a seamless integration with the CAD modeling. Within the proposed framework, the NURBS basis functions are used to discretize the unknown fields in the circumferential direction, whilst analytical solution is sought in the radial direction. We further extend the framework to problems with singularities and to dynamic analysis. The accuracy and the convergence properties of the proposed method are demonstrated with benchmark problems in the context of linear elasticity and linear elastic fracture mechanics.