Fractal two-level finite element method for two-dimensional cracks

Abstract

Fractal two-level finite-element method has been extended to mode II crack problems. In order to encourage the use of this versatile tool on crack problems, some user guidelines for evaluating the stress intensity factor and for improving the convergence of stress intensity factors are suggested for structural engineers. The study is focused on (1) the effect of the numerical integration scheme on the convergency of stress intensity factors, (2) the configuration of fractal meshes, and (3) the influence of the aspect ratio of the fractal mesh on the accuracy of stress intensity factors. Both mode I and mode II two-dimensional crack problems are discussed. Examples for both the lagrangian and the serendipity types of elements are used to demonstrate the numerical efficiency and accuracy of the present method. In summary, it is not difficult to achieve accuracy within 3% error on stress intensity factors with a personal computer in a few seconds of execution time.