Anisotropic elastic plates with holes/cracks/inclusions subjected to out-of-plane bending moments

Abstract

The problems of anisotropic plates containing holes, cracks and/or inclusions have been studied extensively for two-dimensional deformations. Although the correspondence between the two-dimensional problems and the plate bending problems has been observed long time ago, without clarifying the involved mathematical details one still cannot get the solutions of the plate bending problems directly from the solutions of the corresponding two-dimensional problems. Based upon the correspondence relation, recently we developed a Stroh-like formalism for the bending theory of anisotropic plates. By this newly developed formalism, most of the relations for bending problems can be organized into the forms for two-dimensional problems. Thus, by using the Stroh-like formalism, the analytical solutions for problems of anisotropic plates with holes/cracks/inclusions subjected to out-of-plane bending moments can be obtained directly from the solutions of the corresponding two-dimensional problems. The stresses (or resultant bending moments) around the hole/crack/inclusion boundaries are also given explicitly in this paper. Since the explicit closed-form solutions for the present cases have not been found in the literature, comparison is made with some special cases of which the analytical solutions exist, which shows that our solutions are exact, simple and general.