On a One-Dimensional Theory of Finite Torsion and Flexure of Anisotropic Elastic Plates

[+] Author and Article Information
E. Reissner

Department of Applied Mechanics and Engineering Sciences, University of California, San Diego, La Jolla, Calif. 92093

J. Appl. Mech 48(3), 601-605 (Sep 01, 1981) (5 pages) doi:10.1115/1.3157681 History: Received May 01, 1980; Revised December 01, 1980; Online July 21, 2009


Equations for small finite displacements of shear-deformable plates are used to derive a one-dimensional theory of finite deformations of straight slender beams with one cross-sectional axis of symmetry. The equations of this beam theory are compared with the corresponding case of Kirchhoff’s equations, and with a generalization of Kirchhoff’s equations which accounts for the deformational effects of cross-sectional forces. Results of principal interest are: 1. The equilibrium equations are seven rather than six, in such a way as to account for cross-sectional warping. 2. In addition to the usual six force and moment components of beam theory, there are two further stress measures, (i) a differential plate bending moment, as in the corresponding linear theory, and (ii) a differential sheet bending moment which does not occur in linear theory. The general results are illustrated by the two specific problems of finite torsion of orthotropic beams, and of the buckling of an axially loaded cantilever, as a problem of bending-twisting instability caused by material anisotropy.

Copyright © 1981 by ASME
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