Laminated anisotropic thin plate with an elliptic inhomogeneity

This work is concerned with a through-thickness elliptic elastic inhomogeneity in a laminated anisotropic elastic thin plate within the context of the Kirchhoff theory. By means of the octet formalism recently established by the authors, an exact closed-form solution is obtained, for the first time, for coupled stretching and bending deformations of the plate subjected to remote uniform membrane stress resultants and bending moments. The stress resultants inside the elastic elliptic inhomogeneity are uniform, which is consistent with the uniformity property of the Eshelby inclusion solution in three-dimensional elasticity. In two special limit cases where the elliptic inhomogeneity becomes an elliptic rigid inclusion or hole, the corresponding solutions are also obtained. A relation between the rotational moment and the rotation is given for the elliptic rigid inclusion problem. The concentration factors of hoop membrane stress resultants and hoop bending moments are given for the elliptic hole problem. The intensity factors of membrane stress resultants and moments are obtained for a Griffith crack. Displacements, slopes, membrane stress resultants and bending moments along the elliptic boundary for the elliptic inhomogeneity, rigid inclusion and hole problems are all presented in a real form. 2003 Elsevier Ltd. All rights reserved.

Laminated anisotropic thin plate with an elliptic inhomogeneity Academic Article