A structured grid based B-Spline finite elements method combining local isogeometry analysis technique for crack problems

Abstract

In this paper, a structured mesh based B-Spline finite elements (BSFE) method combining the isogeometry analysis technique is developed for analyzing crack problems. The BSFE is used for the global approximation and the isogeometry analysis technique is performed on the local crack tip region which is covered by several elements around the crack tip. The geometry of the selected crack tip region is described by the B-Spline basis functions in parameter space. Meanwhile, a specific function with relevant parameters is introduced into geometry description for catching the characters of the solution around the crack tip. In addition, the B-Spline basis functions are also used as basis functions to approximate the displacement field in the local region under the parameter space. The relevant B spline basis functions used for approximation in local region are replaced by the corresponding BSFE basis functions used in the interface elements adjacent to the local region and the seamless connection between the global approximation and the local isogeometry analysis can be easily achieved. For crack problems, no enrichment functions and remeshing are needed in this new method. This newly developed method is applied to the stress analysis of 2D linear elasticity crack problems in order to investigate its performance and study parameters. Numerical results show that the present method is highly accurate and stable. The new method has a promising potential for practical applications.