Mode I crack problems by fractal two level finite element methods

Abstract

A semi-analytical method is suggested to determine the stress intensity factor (SIF) of two-dimensional (2D) crack problems. In it, the singularity is eliminated from the computational domain by the fractal two level finite element method (F2LFEM). In the present method, the fractal geometry concept and two level finite element method (2LFEM) are employed to automatically generate an infinitesimal mesh and transform these large number of degrees of freedom around the crack tip to a small set of generalized coordinates. By taking advantage of the same stiffness of 2D elements with similar shape, one transformation of the stiffness for the first layer of mesh is enough for all. This simple method is very economical in terms of computational time and computer memory. Highly accurate results of SIF and stresses are obtained.