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TECHNICAL PAPERS

Elastic Analysis for Defects in an Orthotropic Kirchhoff Plate

[+] Author and Article Information
Kyeong-Jin Yang

Nuclear Hydrogen Project,  Korea Atomic Energy Research Institute, Yuseong, Daejeon 305-353, Republic of Koreakjyang@kaeri.re.kr

Ki-Young Lee, Jong-Hwa Chang

Nuclear Hydrogen Project,  Korea Atomic Energy Research Institute, Yuseong, Daejeon 305-353, Republic of Korea

J. Appl. Mech 74(3), 438-446 (Apr 17, 2006) (9 pages) doi:10.1115/1.2338051 History: Received June 27, 2005; Revised April 17, 2006

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.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Infinite plate containing an elliptic cylindrical inclusion with principal half axes a1 and a2, in which uniform eigenstrain is prescribed

Grahic Jump Location
Figure 2

Infinite plate containing an elliptic cylindrical inclusion with principal half axes a1 and a2, in which uniform mid-plane eigenstrain and eigencurvature are prescribed

Grahic Jump Location
Figure 3

Schematic illustration for equivalent inclusion method; (a) infinite plate containing an inhomogeneous inclusion with mid-plane eigenstrain and eigencurvature, (b) infinite plate containing an homogeneous inclusion with equivalent eigenstrain and eigencurvature, which are properly chosen to give the same resultant stress and bending moment inside the inclusion.

Grahic Jump Location
Figure 4

Schematic diagram for edge dislocation on the x2=0 plane (x1>0) with Burger’s vector b1.

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