Numerical solution of cracked thin plates subjected to bending, twisting and shear loads

A semi-analytical method namely fractal finite element method is presented for the determination of mode I and mode II moment intensity factors for thin plate with crack using Kirchhoff's theory. Using the concept of fractal geometry, infinite many of finite elements is generated virtually around the crack border. Based on the analytical global displacement function, numerous degrees of freedom (DOF) are transformed to a small set of generalised coordinates in an expeditious way. The stress intensity factors can be obtained directly from the generalized coordinates. No post-processing and special finite elements are required to develop for extracting the stress intensity factors. Examples of cracked plate subjected to bending, twisting and shear loads are given to illustrate the accuracy and efficiency of the present method. The influence of finite boundaries on the calculation of the moment intensity factors is studied in details. Very accuracy results when compare with the theoretical and numerical counterparts are found.