A generalized enriched finite element method for blunt cracks

This paper develops a generalized enriched finite element method to analyze the displacement and stress fields near a blunt crack tip by including the near-field analytic solutions to the shape functions of a conventional isoparametric element using the partition of unity finite element method. In addition, a transitional element is developed by introducing a weighting function to the added near-field solutions to ensure the displacement compatibility between the enriched and conventional elements. The weighting function is constructed by polynomials of the same order as the shape functions of corresponding conventional element. Thus, the enriched, transitional and conventional elements can be expressed in a unified formulation for easy computer implementation. The accuracy of this formulation is demonstrated by numerical examples. The results are in good agreement with theory and conventional finite elements with excessive fine mesh. The examples also show that the newly proposed enriched scheme is more accurate and computational efficient than the conventional isoparametric element with coarse mesh.