An analytical solution for the orthotropic semi-infinite plane with an arbitrary-shaped hole

Abstract

The application of analytical methods to solve the problem of an anisotropic semi-infinite plane with a hole has not been observed thus far. This paper presents an analytical solution for an orthotropic semi-infinite plane with an arbitrary-shaped hole, considering the condition of a uniform stress applied at the hole boundary. First, the shapes of holes on the $z_1$ - and $z_2$ -planes are determined based on the shape of the hole on the z-plane. Next, the regions outside the holes on these physical planes are mapped to the rings on the ${\zeta }_1$ - and ${\zeta }_2$ -planes, respectively. Therefore, the boundary conditions with ${\zeta }_1$ and ${\zeta }_2$ as independent variables are established. Then, the boundary collocation method is used to solve the stress boundary conditions along the upper boundary and the hole boundary, thereby obtaining two analytical functions for calculating the stress and displacement of the structure. Finally, the correctness of the proposed method is verified by conducting boundary condition checks and comparing the stress and displacement results obtained by the proposed method with those obtained from ANSYS, and further investigates the influence of anisotropic parameters on normal stress and displacement.