Alternate Exact Equations for the Inextensional Deformation of Arbitrary, Quadrilateral, and Triangular 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, The Technion, Israel Institute of Technology, Haifa, Israel

J. Appl. Mech 46(4), 895-900 (Dec 01, 1979) (6 pages) doi:10.1115/1.3424674 History: Received January 01, 1979; Revised May 01, 1979; Online July 12, 2010


Previously, a set of 9 exact differential equations was derived for the inextensional deformation of a plate bounded by two straight edges and two arbitrary curves. One straight edge is built-in. The other moves rigidly and is subject to a force and couple. The curved edges are stress-free. If the plate twists as it deforms, then, as shown herein, the 9 equations may be replaced by 7. The equations are written in a dimensionless form allowing a ready comparison with Mansfield’s theory that assumes small but finite angles of rotation. If the end load is a couple only, then an independent set of 5 equations emerges. These reduce to 4 for a quadrilateral plate. A numerical example compares the prediction of the exact equations against those of Mansfield. For triangular plates under tip forces only, an alternate, better conditioned, set of 9 differential equations is derived, and the behavior of the solutions near the tip is analyzed.

Copyright © 1979 by ASME
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