Anisotropic Plates With Various Openings Under Uniform Loading or Pure Bending

Abstract

In the case when an anisotropic plate contains a triangular, oval, or square opening, the only solution available in the literature is an approximate solution for orthotropic plates with openings, which was obtained by Lekhnitskii using the complex variable formulation. Solutions for any kind of anisotropic plates with various openings are presented in this paper by applying the Stroh formalism and using the technique of conformal mapping. Unlike the former results, which have different orders of approximation for different openings, the solutions presented here have only one simple unified expression for various openings such as the ellipse, circle, crack, triangle, oval, and square. Two special loading conditions are considered: one is uniform loading, the other is pure bending. Through the use of identities developed in the literature, the hoop stress along the opening boundary is obtained in real form. The results show that the effect of anisotropy on the stress concentration is totally determined through the fundamental elasticity matrices N1 and N3 introduced by Stroh.