Interaction between a screw dislocation and an elliptical hole or rigid inclusion by using the angular basis function

Abstract

The complex-valued fundamental solution ln(z) can be decomposed into the radial basis function (RBF) and the angular basis function (ABF). In this paper, not only the RBF but also the ABF are employed to solve the problem of interaction between a screw dislocation and an elliptical hole or rigid inclusion. The problem is decomposed into a free field with a screw dislocation and a boundary value problem subject to a specific boundary condition. The boundary value problem is solved by using the RBF and the boundary integral equation. Since the geometric shape is an ellipse, the degenerate kernel is expanded to a series form under the elliptic coordinates, while the unknown boundary densities are expanded to Fourier series. By combining the degenerate kernel and the null-field integral equation, the boundary value problem can be easily solved. Finally, two examples are demonstrated to verify the validity of the present approach.