Exact Equations for the Inextensional Deformation of Cantilevered Plates

[+] Author and Article Information
J. G. Simmonds

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

A. Libai

Department of Aeronautical Engineering, Israel Institute of Technology, The Technion, Haifa, Israel

J. Appl. Mech 46(3), 631-636 (Sep 01, 1979) (6 pages) doi:10.1115/1.3424618 History: Received December 01, 1978; Revised March 01, 1979; Online July 12, 2010


A set of first-order ordinary differential equations with initial conditions is derived for the exact, nonlinear, inextensional deformation of a loaded plate bounded by two straight edges and two curved ones. The analysis extends earlier approximate work of Mansfield and Kleeman, Ashwell, and Lin, Lin, and Mazelsky. For a plate clamped along one straight edge and subject to a force and couple along the other, there are 13 differential equations, but an independent set of 9 may be split off. In a subsequent paper, we consider alternate forms of these 9 equations for plates that twist as they deform. Their structure and solutions are compared to Mansfield’s approximate equations and particular attention is given to tip-loaded triangular plates.

Copyright © 1979 by ASME
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