An extended wavelet Galerkin method with a high-order B-spline for 2D crack problems

Two-dimensional (2D) crack problems are solved employing a novel technique based on a combination of wavelet Galerkin method and X-FEM with a high-order interpolant. Multiresolution analysis of the wavelet basis functions (scaling/wavelet functions) plays an important role in the numerical simulation. High-order B-spline scaling/wavelet functions are chosen as the basis functions. Severe stress concentration near a crack tip is represented by superposing the multiresolution wavelet functions. In addition, the crack modeling is easy to treat by introducing enrichment functions of the X-FEM. In the proposed approach, the governing equation is discretized based on fixed grid, and fracture mechanics problems with complicated shaped geometries can be analyzed effectively, reducing the model generation tasks. 2D linear fracture mechanics problems are solved, and the accuracy is studied for numerical examples.