Bending of Thin Plate with Three‐Point Support
Publication: Journal of Structural Engineering
Volume 118, Issue 5
Abstract
A series solution for stresses and displacements in a rectangular plate that is simply supported at three corners has been developed. Surprisingly simple and rigorous formulae for maximum displacement under arbitrary load are given. This is due to the fact that only one term in the series contributes to the displacement of the unsupported corner. This term is orthogonal in energy to all the other terms, and therefore can be immediately found without solving the system of equations. The system of equations to find the coefficients in the series is obtained by applying the conditions of minimum potential energy. A table with maximum displacements and maximum absolute values for principal moments for different ratios of sides has been given. Results are used for an aluminum auto part design optimization.
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References
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Nadai, A. (1922). “Über die Biegung durchlaufender Platten and der rechteckigen Platte mit freien Rändern,” Z. Angew Math. Mech., 2(1), 1–24.
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Marcus, H. (1932). Die Theorie Elastischer Gewebe and ihre Anwendung and die Berechnung biegsamer Platten. 2nd Ed., 173, Springer, Berlin, Germany.
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Manfield, E. H. (1989). The bending and stretching of plates. 2nd Ed., Cambridge University Press, Cambridge, Mass.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 118 • Issue 5 • May 1992
Pages: 1416 - 1419
Copyright
Copyright © 1992 ASCE.
History
Published online: May 1, 1992
Published in print: May 1992
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