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
* To whom correspondence should be addressed.
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Abstract |
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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.
