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TECHNICAL PAPERS

A Unified Formalism of Two-Dimensional Anisotropic Elasticity, Piezoelectricity and Unsymmetric Laminated Plates

[+] Author and Article Information
Wan-Lee Yin

School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0355e-mail: yinwl@aol.com

J. Appl. Mech 72(3), 422-431 (May 06, 2005) (10 pages) doi:10.1115/1.1828060 History: Received May 18, 2004; Revised July 18, 2004; Online May 06, 2005
Copyright © 2005 by ASME
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References

Lekhnitskii, S. G., 1963, Theory of Elasticity of an Anisotropic Body, Holden-Day, San Francisco.
Stroh,  A. N., 1958, “Dislocations and Cracks in Anisotropic Elasticity,” Philos. Mag., 3, pp. 625–646.
Ting, T. C. T., 1996, Anisotropic Elasticity: Theory and Application, Oxford University Press, New York.
Yin,  W.-L., 2000, “Deconstructing Plane Anisotropic Elasticity, Part I: The Latent Structure of Lekhnitskii’s Formalism,” Int. J. Solids Struct., 37, pp. 5257–5276.
Yin,  W.-L., 2000, “Deconstructing Plane Anisotropic Elasticity, Part II: Stroh’s Formalism Sans Frills,” Int. J. Solids Struct., 37, pp. 5277–5296.
Sosa,  H., 1991, “Plane Problems in Piezoelectric Media With Defects,” Int. J. Solids Struct., 28, pp. 491–505.
Yin,  W.-L., 2005, “Two-Dimensional Piezoelectricity, Part I: Eigensolutions of Nondegenerate and Degenerate Materials,” Int. J. Solids Struct., 42, pp. 2645–2668.
Yin,  W.-L., 2005, “Two-Dimensional Piezoelectricity, Part II: General Solution, Green’s Function and Interface Cracks,” Int. J. Solids Struct., 42, pp. 2669–2687.
Becker,  W., 1991, “A Complex Potential Method for Plate Problems With Bending Extension Coupling,” Arch. Appl. Mech., 61, pp. 318–326.
Lu,  P., and Mahrenholtz,  O., 1994, “Extension of the Stroh Formalism to the Analysis of Bending of Anisotropic Elastic Plates,” J. Mech. Phys. Solids, 42, pp. 1725–1741.
Cheng,  Z.-Q., and Reddy,  J. N., 2002, “Octet Formalism for Kirchhoff Anisotropic Plates,” Proc. R. Soc. London, Ser. A, 458, pp. 1499–1517.
Chen,  P., and Shen,  Z., 2001, “Extension of Lekhnitskii’s Complex Potential Approach to Unsymmetric Composite Laminates,” Mech. Res. Commun., 28, pp. 423–428.
Hwu,  C., 2003, “Stroh-Like Formalism for the Coupled Stretching-Bending Analysis of Composite Laminates,” Int. J. Solids Struct., 40, pp. 3681–3705.
Yin,  W.-L., 2003, “General Solutions of Laminated Anisotropic Plates,” ASME J. Appl. Mech., 70, pp. 496–504.
Yin,  W.-L., 2003, “Structure and Properties of the Solution Space of General Anisotropic Laminates,” Int. J. Solids Struct., 40, pp. 1825–1852.
Yin, W.-L., 2005, “Green’s Function of Anisotropic Plates With Unrestricted Coupling and Degeneracy, Part 1: The Infinite Plate,” Composite Struct., in press.
Yin, W.-L., 2005, “Green’s Function of Anisotropic Plates With Unrestricted Coupling and Degeneracy, Part 2: Other Domains and Special Laminates,” Composite Struct., in press.
Ting,  T. C. T., 1992, “Anatomy of Green’s Functions for Line Forces and Dislocations in Anisotropic Media and Degenerate Materials,” The Jens Lothe Symposium Volume, Phys. Scr., T, T44, pp. 137–144.
Yin,  W.-L., 2004, “Degeneracy, Derivative Rule, and Green’s Function of Anisotropic Elasticity,” ASME J. Appl. Mech., 71, pp. 273–282.
Yin,  W.-L., 2003, “Anisotropic Elasticity and Multi-Material Singularities,” J. Elast., 71, pp. 263–292.
Yin, W.-L., 2005, “Green’s Function of Bimaterials Comprising all Cases of Material Degeneracy,” Int. J. Solids Struct., 42 , pp. 1–19.
Muskhelishvili, N. I., 1953, Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoof, Leyden.

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