Elastic Analysis for Defects in an Orthotropic Kirchhoff Plate

Abstract

Defects such as inhomogeneities, inclusions with eigenstrains, and dislocations in an infinite orthotropic Kirchhoff plate are analyzed. These results could be applied to thin plate problems regardless of whether the plate is homogeneous or inhomogeneous in the direction of a thickness. An orthotropic laminated plate with a symmetric plane normal to the direction of the thickness is included as a special case. The eigenstrain is assumed to vary throughout the direction of the thickness. Thus, a bending of the plate due to the eigenstrain is considered. Employing Green’s functions, which are expressed in explicit compact forms in a Cartesian coordinates system and were recently obtained by using a Stroh-type formalism, the elastic fields for defects are obtained by way of Eshelby’s inclusion method. The general solutions for the extension and bending deformations due to the mid-plane eigenstrain and eigencurvature are expressed in quasi-Newtonian potentials and their derivatives, which appear in a closed form for the elliptic inclusion. For the bending problem of an inclusion with uniform eigencurvature, the curvature inside the inclusion becomes uniform, corresponding to that from Eshelby’s analysis of an isotropic solid. Edge dislocation and elliptic inclusions with polynomial eigenstrains are also discussed in this work.