Optimal Design for Plate Buckling
Publication: Journal of Structural Engineering
Volume 116, Issue 3
Abstract
This paper extends Keller's classic solution for the optimal design of columns to the case of plates. After the introduction of nondimensional variables, a calculus of variations technique is used to derive an optimality condition, which states that “the strain‐energy density is proportional to the thickness of an optimal plate design.” The case of a simply supported plate is then discussed, using a truncated Fourier series solution. For a square, isotropic plate, the buckling load of the optimal design is larger than that of the uniform plate by a factor of (ν is Poisson's ratio). An appendix is included which discusses Keller's original solution and shows how it can be applied when a fourth‐order differential equation is used rather than the second‐order one used by Keller. This appendix also discusses the use of a truncated Fourier series and Rayleigh's method as an approximation of Keller's result, thus laying the groundwork for the use of Fourier series in the plate problem.
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References
1.
Balasubramanyam, K., and Spillers, W. R. (1986). “Examples of the use of Fourier series in structural optimization.” Q. Appl. Math., XLIV(3), 559–566.
2.
Brunelle, E. J., and Oyibo, G. A. (1983). “Generic buckling curves for specially orthotropic plates.” AIAA J., 21(8), 1150–1156.
3.
Keller, J. B. (1960). “The shape of the strongest column.” Arch. Ration. Mech. Anal., 5, 275–285.
4.
Tadjbakhsh, I., and Keller, J. B. (1962). “Strongest columns and Isoperimeteric inequalities for eigenvalues.” J. Appl. Math., 9, Mar., 159–164.
5.
Timoshenko, S. (1940). Theory of plates and shells. McGraw‐Hill, Inc., New York, N.Y., 329.
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Copyright © 1990 ASCE.
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Published online: Mar 1, 1990
Published in print: Mar 1990
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