Two-level finite element method for plane cracks

Abstract

A new method to evaluate the stress intensity factors for plates of arbitary shape by conventional finite elements is introduced. The problems of the large number of unknowns and the round-off errors associated with fine meshes are eliminated by means of global interpolation functions. These global interpolation functions are actually the analytical solutions of the displacement patterns near the crack tips. While the analytical solutions do not satisfy the boundary conditions in general, the present method considers the boundary conditions by master nodes. Very few unknowns can predict accurate results and no unconventional finite elements are required. The stress intensity factors can be calculated from the nodal displacements of the super-element in one go. Plates with single and double notch edges and centre crack are taken as examples. The method can be generalized to other crack problems without difficulty.