STRESS INTENSITY FACTOR ANALYSIS OF AN EDGE CRACK PERPENDICULAR TO THE INTERFACE IN BI-MATERIALS

The purpose of this paper is to investigate the stress intensity factor in the problem of a crack perpendicular to the interface in bi-materials. Based on the theory of an edge crack perpendicular to the interface between two dissimilar isotropic half-planes, the stress intensity factor was yield out from the stress singularity eigen-equation. The stress intensity factor for a composite beam segment with an edge crack under bending and tension was computed by the ordinary finite element and the singular finite element, and it was found that the singular element method is more accurate and applicable than the ordinary element method. The influence of the distance from the crack tip to the interface and the material’s mechanical properties to the stress intensity factor were analyzed. The results show that the stress intensity factor increases first, and then decreases with decreasing of the distance from the crack tip to the interface, and the stress intensity factor increases with increasing of the elastic modulus of the cracked material.

Spectral Analysis, Properties and Nonsingular Preconditioners for Singular Saddle Point Problems

We first derive some explicit bounds on the spectra of generalized non-symmetric singular or nonsingular saddle point matrices. Then we propose two new nonsingular preconditioners for solving generalized singular saddle point problems, and show that GMRES determines a solution without breakdown when applied to the resulting preconditioned systems with any initial guess. Furthermore, the detailed spectral properties of the preconditioned systems are analyzed. The nonsingular preconditioners are also applied to solve the singular finite element saddle point systems arising from the discretization of the Stokes problems to test their performance.