This paper presents fundamental solutions of an anisotropic elastic thin plate within the context of the Kirchhoff theory. The plate material is inhomogeneous in the thickness direction. Two systems of problems with non-self-equilibrated loads are solved. The first is concerned with in-plane concentrated forces and moments and in-plane discontinuous displacements and slopes, and the second with transverse concentrated forces. Exact closed-form Green’s functions for infinite and semi-infinite plates are obtained using the recently established octet formalism by the authors for coupled stretching and bending deformations of a plate. The Green functions for an infinite plate and the surface Green functions for a semi-infinite plate are presented in a real form. The hoop stress resultants are also presented in a real form for a semi-infinite plate.
Green’s Functions for Infinite and Semi-infinite Anisotropic Thin Plates
Contributed by the Applied Mechanics Division of THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS for publication in the ASME JOURNAL OF APPLIED MECHANICS. Manuscript received by the Applied Mechanics Division, Jan. 29, 2002; final revision, July 23, 2002. Associate Editor: D. A. Kouris. Discussion on the paper should be addressed to the Editor, Prof. Robert M. McMeeking, Chair, Department of Mechanics and Environmental Engineering, University of California–Santa Barbara, Santa Barbara, CA 93106-5070, and will be accepted until four months after final publication in the paper itself in the ASME JOURNAL OF APPLIED MECHANICS.
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Cheng, Z., and Reddy, J. N. (March 27, 2003). "Green’s Functions for Infinite and Semi-infinite Anisotropic Thin Plates ." ASME. J. Appl. Mech. March 2003; 70(2): 260–267. https://doi.org/10.1115/1.1533806
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