Numerical solutions of two-dimensional anisotropic crack problems

Abstract

A complete set of series form solutions of stress and displacement functions, including all higher order terms, around the crack tip for anisotropic crack problems have been newly derived by eigenfunction expansion approach. The analytical solutions of displacement functions were classified into four cases with respect to different types of complex parameters and different corresponding physical meanings. By employing these displacement functions as global interpolation functions, fractal two-level finite element method (F2LFEM) was applied to evaluate the stress intensity factors (SIFs) for various kinds of anisotropic crack problems. In the method of F2LFEM, the infinite number of nodal displacements was transformed to a small set of generalized coordinates by fractal transformation technique. New element matrices need not be generated and the singular numerical integration was avoided completely. Numerical examples of the four cases were studied and high accurate results of SIFs were obtained.