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.
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September 1979
Research Papers
Exact Equations for the Inextensional Deformation of Cantilevered Plates
J. G. Simmonds,
J. G. Simmonds
Department of Applied Mathematics and Computer Science, University of Virginia, Charlottesville, Va. 22901
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A. Libai
A. Libai
Department of Aeronautical Engineering, Israel Institute of Technology, The Technion, Haifa, Israel
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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. Sep 1979, 46(3): 631-636 (6 pages)
Published Online: September 1, 1979
Article history
Received:
December 1, 1978
Revised:
March 1, 1979
Online:
July 12, 2010
Citation
Simmonds, J. G., and Libai, A. (September 1, 1979). "Exact Equations for the Inextensional Deformation of Cantilevered Plates." ASME. J. Appl. Mech. September 1979; 46(3): 631–636. https://doi.org/10.1115/1.3424618
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