An enhanced extended isogeometric analysis with strong imposition of essential boundary conditions for crack problems using B++ splines

Abstract

We present the extended isogeometric analysis (XIGA) based on B++ splines for linear elastic fracture problems. The proposed approach converts the control points associated with crack elements into collocation points on the crack surface. The opening of the crack surface is characterized by double-layer collocation points whereas the tip singularity is simulated by additional collocation points. In doing so, the additional control points associated with tip elements are replaced by the additional collocation points on the crack surface, which reduces the number of unknowns. The collocation points on the entire crack surface satisfy the Kronecker Delta property, which allows directly imposing Dirichlet boundary condition on the crack surface. A posteriori error estimation technique is also presented in this paper. The values of the normalised stress intensity factors (SIFs) are calculated by interaction integral technique. Finally, the suggested approach is verified by 2D benchmark problems.