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Mathematics and Mechanics of Solids
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General Solutions for the Statics of Anisotropic, Transversely Inhomogeneous Elastic Plates in Terms of Complex Functions

Kostas P. Soldatos

School of Mathematical Sciences, Theoretical Mechanics Section, University of Nottingham, Nottingham NG7 2RD, UK

This paper develops the general solution of high-order partial differential equations (PDEs) that govern the static behavior of transversely inhomogeneous, anisotropic, elastic plates, in terms of complex functions. The basic development deals with the derivation of such a form of general solution for the PDEs associated with the most general, two-dimensional ("equivalent single-layered"), elastic plate theory available in the literature. The theory takes into consideration the effects of bending–stretching coupling due to possible un-symmetric forms of through-thickness material inhomogeneity. Most importantly, it also takes into consideration the effects of both transverse shear and transverse normal deformation in a manner that allows for a posteriori, multiple choices of transverse strain distributions. As a result of this basic and most general development, some interesting specializations yield, as particular cases, relevant general solutions of high-order PDEs associated with all of the conventional, elastic plate theories available in the literature.

Key Words: elastic material • plates • C–analytic functions

This version was published on December 1, 2006

Mathematics and Mechanics of Solids, Vol. 11, No. 6, 596-628 (2006)
DOI: 10.1177/1081286505052340
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