An Analytical Singular Element For Inclined Crack Terminating At Bimaterial Interface

In this study, an inclined crack terminating at the bi-material interface is investigated. Based on the symplectic system, the corresponding transcendental equation of symplectic eigenvalue and symplectic eigen vectors can be obtained under polar coordinate, and then an analytical singular element can be constructed. Combining the analytical singular element with the regular finite elements, the inclined crack problem can be solved numerically. As the analytical singular element fully contains the information of the analytical solution for the boundary value problem of elasticity, it possesses arbitrary order accuracy, and the stress and displacement fields around crack tip can be described accurately, that is to say fracture parameters such as stress intensity factor(SIF) with highly solving accuracy can be obtained efficiently. Finally, several numerical examples have been given, and numerical results illustrate that the proposed analytical singular element not only has highly solving accuracy but also has stable numerical solutions. The analytical singular element is found to be effective under a large range of element sizes, and there is no need to use dense meshes or transient elements. Furthermore, the proposed analytical singular element is found to possess satisfactory versatility and compatibility, and it makes the analytical singular element can be integrated into most existing finite element method(FEM) software systems. So there is no doubt that this kind of the analytical singular element will play an important role in the actual structure analysis.