Fractal two-level finite element method for cracked Kirchoff’s plates using DKT elements

Abstract

A technique for calculating moment intensity factors (MIF) and stress intensity factors (SIF) for through-thickness cracks in thin plates subjected to out-of-plane bending by means of fractal two-level finite element method is proposed. It is based on the nodal displacements transformation near the crack tip in terms of some analytical functions. The similarity characteristic properties of the plate element stiffness are employed. Fractal transformation technique is developed to transform infinitely many nodal displacements around the crack tip to a small set of generalized displacements including the MIF and SIF as direct unknowns. Examples are given on the centre cracked plates in bending. The results are in good agreement with analytical results and with other researchers. Comparison of the results from Kirchhoff's theory and from Reissner's plate theory shows large differences up to ca 50%.