A full field solution for an anisotropic elastic plate with a hole perturbed from an ellipse

A full-field solution for an infinite anisotropic plate containing a hole perturbed from an ellipse subjected to uniform loading at infinity is derived with Stroh formalism. With perturbation technique, the solution is expanded into a series with reference to the solution of the elliptical hole problem. Through the traction-free condition on the hole boundary, the unknown coefficients of the series are solved using the method of analytical continuation. The explicit full-field solution up to the first order and its corresponding explicit expression of the hoop stress along the hole boundary is presented. Numerical examples with different hole shapes (triangle, quadrilateral, oval, and pentagon), material types (isotropic, orthotropic, and anisotmpic), and loading types (inplane stresses and anti-plane shear) are provided. The results along the hole boundary and in the full field are verified with existing solution and commercial finite element software ANSYS. Through this verification, we conclude that although the hoop stress along the hole boundary provided by the existing analytical solutions is correct, their associated full-field solutions are incorrect because of the non-conformal mapping functions. The solutions presented in this paper are the first verified correct full-field analytical solutions published in the literature.

Automated summary

In this study, a full-field solution for an infinite anisotropic plate containing a hole perturbed from an ellipse subjected to uniform loading at infinity is derived using Stroh formalism. Through perturbation technique and the method of analytical continuation, the unknown coefficients of the solution series are solved, resulting in an accurate explicit full-field solution up to the first order. Numerical examples are provided to verify the results against existing solutions and commercial finite element software ANSYS, concluding that the solutions presented in this paper are the first verified correct full-field analytical solutions published in the literature.