Abstract:

Due to the complex distribution of the displacements and stresses around the crack tip, it is not easy to obtain the Stress Intensity Factor (SIF) with a rapid convergence when using conventional interpolation approaches of numerical methods such as Finite Element Method (FEM). On the basis of Numerical Manifold Method (NMM), a novel method is presented to compute the SIFs via combining analytical solutions with numerical solutions. The Williams expansion is used as the analytical solution, which is formed by applying the constraints of nodal freedoms in the mesh containing the crack tip. High-order polynomial functions are used as the numerical solutions which are connected with the analytical solution via shape functions in the surrounding meshes. Meanwhile, the meshes in NMM need not conform to the physical boundaries including the crack edges, and discontinuous covers are used to allow the cracks arbitrarily align within the meshes, providing the convenience of mesh generation. Numerical example shows the validity of the method. Considering that the Williams expansion is the best approximation for the displacement field around the crack tip, the method has a more rapid convergence than other new methods such as extended Finite Element Method (XFEM).

Key words: stress intensity factor (SIF), numerical manifold method (NMM), Williams expansion for crack tip, combining analytical solutions with numerical solutions