Buckling Optimization of Beams and Plates on Elastic Foundation
Publication: Journal of Engineering Mechanics
Volume 116, Issue 1
Abstract
The structural optimization problem of minimizing the weight of beams and orthotropic plates on elastic foundation for a given critical buckling load is formulated and solved. The cross‐sectional area and thickness variations are sought for the beam and plate problems, respectively. Optimality conditions are first derived via variational calculus, and the semianalytical truncated Fourier series approach is used to obtain optimal designs that indicate up to 50% increase in buckling load for the beam and about 112% increase in buckling load for the plate.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Athans, M., and Falb, P. L. (1966). Optimal control—An introduction to the theory and its application. McGraw‐Hill Book Company, New York, N.Y.
2.
Banichuk, N. V. (1983). Problems and methods of optimal structural design. Plenum Press, New York, N.Y.
3.
Beiner, L., and Librescu, L. (1986). “Least weight design of cylindrical shells with fixed fundamental frequency.” Israel J. Tech., 23, 64–68.
4.
Carmichael, D. G. (1981). Structural modelling and optimization: A general methodology for engineering and control. Ellis Horwood Limited, Chichester, West Sussex, England, 177–182.
5.
Haug, E. J. (1981). “A review of distributed parameter structural optimization literature.” Optimization of distributed parameter structures, E. J. Haug and J. Cea, eds., Sijthhoff & Noordhoff, Alpen aan den Rijn, Netherlands, 3–68.
6.
Keller, J. B. (1960). “The shape of the strongest column.” Arch. Rat. Mech. Analysis, 5, 275–285.
7.
Levy, R., and Spillers, W. R. (1989). “Optimal design for axisymmetric cylindrical shell buckling.” J. Engrg. Mech., ASCE, 115(8), 1683–1690.
8.
Plaut, R. H., Johnson, L. W., and Olhoff, N. (1986). “Bimodal optimization of compressed columns on elastic foundations.” J. Appl. Mech., ASME, 53, 130–134.
9.
Spillers, W. R., and Levy, R. (1987). “Optimal design for plate buckling.” J. Struct. Engrg., ASCE, (submitted for publication).
10.
Tadjbakhsh, I., and Keller, J. B. (1962). “Strongest columns and isoperimetric inequalities for eigenvalues.” J. Appl. Mech., ASME, 29, 159–164.
11.
Timoshenko, S. P. (1976). Strength of materials. Part II—Advanced theory and problems. 3d Ed., Robert E. Krieger Publishing Company, Huntington, N.Y.
12.
Timoshenko, S. P., and Gere, J. M. (1961). Theory of elastic stability. McGraw‐Hill Book Company, New York, N.Y.
13.
Timoshenko, S. P., and Krieger, S. W. (1959). Theory of plates and shells. 2d Ed., McGraw‐Hill Book Company, New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1990 ASCE.
History
Published online: Jan 1, 1990
Published in print: Jan 1990
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.