Theories for Elastic Plates Via Orthogonal Polynomials

[+] Author and Article Information
S. Krenk

Department of Applied Mathematics and Computer Science, University of Virginia, Charlottesville, Va. 22901

J. Appl. Mech 48(4), 900-904 (Dec 01, 1981) (5 pages) doi:10.1115/1.3157753 History: Received April 01, 1981; Online July 21, 2009


A complementary energy functional is used to derive an infinite system of two-dimensional differential equations and appropriate boundary conditions for stresses and displacements in homogeneous anisotropic elastic plates. Stress boundary conditions are imposed on the faces a priori, and this introduces a weight function in the variations of the transverse normal and shear stresses. As a result the coupling between the two-dimensional differential equations is described in terms of a single difference operator. Special attention is given to a truncated system of equations for bending of transversely isotropic plates. This theory has three boundary conditions, like Reissner’s, but includes the effect of transverse normal strain, essentially through a reinterpretation of the transverse displacement function. Full agreement with general integrals to the homogeneous three-dimensional equations is established to within polynomial approximation.

Copyright © 1981 by ASME
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