Elastic Harmonic Inhomogeneity Near a Concentrated Rotational Moment in Isotropic Laminated Plates

Abstract

This work studied the coupled stretching and bending deformations of a through-thickness nonelliptical elastic inhomogeneity embedded in an infinite matrix within the context of Kirchhoff isotropic and laminated plate theory. The matrix was subjected to uniform remote membrane stress resultants and bending moments, and was also subjected to a concentrated rotational moment at any position. Our analysis, based on complex variable methods, indicated that when the nonelliptical shape of the inhomogeneity is suitably designed and when three specific conditions on the remote loading are met for a given set of material and geometric parameters characterizing the composite: (1) the elastic inhomogneity is harmonic, (2) the internal stress resultants inside the inhomogeneity are uniform and hydrostatic, and (3) the hoop membrane stress resultant and hoop bending moment on the matrix side are uniform along the inhomogeneity–matrix interface. A couple-loaded rigid harmonic inhomogeneity in the absence of remote loading and in the presence of a concentrated rotational moment at any position in the matrix was also obtained using a similar procedure.