Exact Equations for the Large Inextensional Motion of Elastic Plates

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

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

J. Appl. Mech 48(1), 109-112 (Mar 01, 1981) (4 pages) doi:10.1115/1.3157551 History: Received April 01, 1980; Online July 21, 2009


The governing equations for plates that twist as they deform are reduced to 14 differential equations, first-order in a single space variable and second-order in time. Many of the equations are the same as for statics. Nevertheless, the extension to dynamics is nontrivial because the natural coordinates to use to describe the deformed, developable midsurface are not Lagrangian. The plate is assumed to have two curved, stress-free edges, one built-in straight edge, and one free straight edge acted upon by a force and a couple. There are 7 boundary conditions at the built-in end and 7 at the free end.

Copyright © 1981 by ASME
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